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how to write formula of coordination compound

A cubic solid is made of two elements P and Q. Enter water as H 2 O. A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? Coordination refers to the coordinate covalent bonds (dipolar bonds) between the ligands and the central atom. Coordination compound - Coordination compound - Structure and bonding of coordination compounds: Werner originally postulated that coordination compounds can be formed because the central atoms carry the capacity to form secondary, or coordinate, bonds, in addition to the normal, or valence, bonds. 3. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. It is worth noting that in all these compounds, Pt has an oxidation number of + 2. Copyright © 2021 saralstudy.com. Give simple chemical tests to distinguish between the following pairs of compounds. Henry's law constant for CO2 in water is 1.67 x 108Pa at 298 K. Calculate the quantity of CO2in 500 mL of soda water when packed under 2.5 atm CO2 pressure at 298 K. Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride. Ionic compounds are neutral compounds made up of positively charged ions called cations and negatively charged ions called anions. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Before writing the formulae of alkanes, it is necessary to understand the meaning of homologous series. A characteristic feature of the transition metals is their ability to form a group of compounds called coordination compounds, complex compounds, or sometimes simply complexes. Predict the number of unpaired electrons in the square planar [Pt(CN)4]2- ion. Chemical formula: Chemical formula is known as the symbolic representation corresponding to a given molecule, compound or coordination complex also. The compound in question is thus a Pt(IV) complex. If the density of solution is 1.2 g mL-1, then what shall be the molarity of the solution? Order the elements according to the general rules for naming ionic and molecular compounds.. Here’s an example: What is the empirical formula of a substance that is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass? Have questions or comments? Writing Formulas for Simple Binary Compounds Identify a binary compound. Also find the composition of the vapour phase. formula KxFey(C2O4)z • 3H2O. Amongst the following ions which one has the highest magnetic moment value? These ligands are invariably Lewis bases. Write the empirical formula by attaching these whole-number mole ratios as subscripts to the chemical symbol of each element. Previous question Next question Get more help from Chegg. When such compounds are dissolved in H2O, each of the ions present in the solid becomes an independent species with its own chemical and physical properties. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. If the oxidation number of Pt is x, then x – 5 must equal the total charge on the complex ion: $x \text{ } – \text{ } 5 = \text{ } –1 \\ ~~ \\$. The conductivity behavior also suggests that the Pt atom is part of a cation, since the Pt moves toward the cathode during electrolysis. What inspired N. Bartlett for carrying out reaction between Xe and PtF6? draw the crystal field diagram for thiscompound. Write the formulas for the following coordination compounds: (i) Tetraamminediaquacobalt (III) chloride (ii) Potassium tetracyanonickelate(II) In the synthesis of the complex salt, you will dissolve an iron(III) compound and form the coordination compound. Explain with an example. which type(s) of isomers does this molecule have. Atoms of Q are at the corners of the cube and P at the body-centre. Calculate the molarity of each of the following solutions: (a)30 g of Co(NO3)2. The ligands are written next, with anion ligands coming before neutral ligands. Within the coordination entities the central atom/ion is listed first followed by the ligands We follow a few rules of the International Union of Pure and Applied Chemistry(IUPAC) system while namin… consider the coordination compound sodium diamminetetracyanocobaltate(iii). How the following conversions can be carried out? Interchange the valencies of the elements / ions and write as the subscript. Coordination compound, any of a class of substances with chemical structures in which a central metal atom is surrounded by nonmetal atoms or groups of atoms, called ligands, joined to it by chemical bonds. Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn. While writing the formula of a compound containing a metal and a non-metal, the symbol of the metal is written first followed by that of the non-metal. 3 NH. Two metals do not join up to form compounds. Calculate the mass of urea (NH2CONH2) required in making 2.5 kg of 0.25 molal aqueous solution. When 1 mol [Pt(NH3)3Cl]Cl is dissolved in H2O, it furnishes 1 mol Pt(NH3)3Cl+ ions and 1 mol Cl– ions. (b)30 mL of 0.5 M H2SO4 diluted to 500 mL. Coordination compounds are neutral substances (i.e. What is the formula of the compound? Coordination number. The names and formulae of coordination compounds are written by using the rules given by the IUPAC. Adding the charge on each ligand, we obtain –5(for Cl–) + 0(for NH3) = –5. … [ "article:topic", "coordination sphere", "complex ion", "ligand", "coordination complex", "authorname:chemprime", "showtoc:no", "license:ccbyncsa" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FGeneral_Chemistry%2FBook%253A_ChemPRIME_(Moore_et_al. Thus the combination of Pt with one NH3 ligand and three Cl– ligands yields an overall charge of 2(for Pt) – 3(for Cl) + 0(for NH3) = –1. chemical compounds that consist of an array of anions or neutral molecules that are bound to a central atom via coordinate covalent bonds The set of rules for naming a coordination compound is: When naming a complex ion, the ligands are named before the metal ion. The addition of AgNO3 to the solution serves to confirm this picture. All these species contain a central metal ion attached by coordinate covalent bonds to several ligands. )%2F22%253A_Metals%2F22.08%253A_Coordination_Compounds, Ed Vitz, John W. Moore, Justin Shorb, Xavier Prat-Resina, Tim Wendorff, & Adam Hahn, Chemical Education Digital Library (ChemEd DL), information contact us at info@libretexts.org, status page at https://status.libretexts.org, $$\text{[Cu(NH}_{3} \text{)}_{4} \text{]SO}_{4}$$, $$\text{[Cr(H}_{2} \text{O)}_{6} \text{]Cl}_{3}$$, $$\text{[Pt(NH}_{3} \text{)}_{2} \text{Cl}_{2} ]$$, $$\text{[Cu(NH}_{3} \text{)}_{4} \text{](NO}_{3} \text{)}_{2}$$, $$\text{[Pt(NH}_{3} \text{)}_{4} \text{][PtCl}_{4} ]$$. Each NH3 molecule can be considered as donating a pair of electrons to a central Cu2+, thus forming four coordinate covalent (dative) bonds to it: Most coordination compounds contain a complex ion similar to Cu(NH3)42+. Contents1 Important Questions for CBSE Class 12 Chemistry – Coordination Compounds1.1 PREVIOUS YEARS QUESTIONS1.2 20151.3 Very Short Answer Type Question [1 Mark]1.4 Short Answer Type Questions [I] [2 Marks]1.5 Short Answer Type Questions [II] [3 Marks]1.6 20141.7 Very Short Answer Type Questions [1 Mark]1.8 Short Answer Type Questions [l] [2 Marks]1.9 20131.10 Short Answer Type […] A coordination complex is a substance in which a metal atom or ion accepts electrons from (and thus associates with) a group of neutral molecules or anions called ligands.A complex can be an anion, a cation ion, or a neutral molecule. (i) 3-Methylbutanal                           (ii) p-Nitropropiophenone, (iii) p-Methylbenzaldehyde               (iv) 4-Methylpent-3-en-2-one, (v) 4-Chloropentan-2-one                 (vi) 3-Bromo-4-phenylpentanoic acid, (vii) p,p'-Dihydroxybenzophenone    (viii) Hex-2-en-4-ynoic acid. write the formulas for the following coordination... General Principles and Processes of Isolation of Elements. Since there are two complex ions for each Ca2+ ion, the charge on each must be –1. Question no.6 me confusion h uncharged) in which at least one ion is present as a complex. Question 1. Write the formulas for the following coordination compounds: (i) Tetraamminediaquacobalt (III) chloride, (iii) Tris(ethane-1,2-diamine) chromium(III) chloride, (iv) Amminebromidochloridonitrito-N-platinate(II), (v) Dichloridobis(ethane-1,2-diamine)platinum(IV) nitrate. Write the formulas for the following coordination compounds? Fe4[Fe(CN)6]. You will learn more about coordination compounds in the lab lectures of experiment 4 in this course. Naming Coordination Compounds. Coordination compounds, such as the FeCl 4-ion and CrCl 3 6 NH 3, are called such because they contain ions or molecules linked, or coordinated, to a transition metal.They are also known as complex ions or coordination complexes because they are Lewis acid-base complexes. Coordination Compounds and their Biological Importance Naming Shape, Structure, Coordination Number, Ligands Biological Examples Industrial Examples *Stereochemistry *Crystal Field Theory *Molecular Orbital Theory Applied To Transition Metals Acids and Bases Properties & Structures of Inorganic & Organic Acids 6H2O in 4.3 L of solution. EXERCISE: Naming Coordination Compounds from formulas: When writing the formula of a coordination compound containing complex ions, square brackets are usually used to enclose the coordination sphere. This ion can be either positively charged like Cr(H3O)63+, or it can be negatively charged like CoCl63–. Examples Of Coordination Compounds : Formula: Name: Coor-dination # Oxi-dation # 1. The chemical symbol of the metal center is written first. Solution for Write the formula for each of the following compounds, being sure to use brackets to indicate the coordination sphere: (a) hexaamminechromium(III)… The following examples will demonstrate how this rule is applied in writing the formula of a compound: 1. Write the IUPAC names of the following coordination compounds: Draw the structures of the following compounds. Also, it becomes very important while you deal with isomers. The strongest evidence for this is the molar conductivity of the salt (1.2 A V–1 dm2 mol–1), which is very similar to that of other electrolytes like NaCl (1.3 A V–1 dm2 mol–1) which also yield a +1 ion and a –1 ion in solution, but very different from that of electrolytes like MgCl2 (2.5 A V–1 dm2 mol–1) which yield one + 2 ion and two –1 ions in solution. Neutral complexes like Pt(NH3)2Cl2 are also known. How would your teacher call you and your best friend if you both didn’t have any names? Write the valency of each element / ion. a. K+,S2− ... c. Na2O d. AIN. Write the names of the … The total charge of a compound is zero, the charge of the cation9s) should be balanced by the charge of anion(s) 3. One mol AgCl is precipitated immediately, showing 1 mol free Cl– ions. If the solubility of H2S in water at STP is 0.195 m, calculate Henry's law constant. Write the formula for potassium bromide. write the formula of the following coordination compound iron iii hexacyanoferrate ii - Chemistry - TopperLearning.com | h6pdrz33 We can regard a complex ion such as Cu(NH3)42+ as being the result of the interaction of :NH3 acting as a Lewis base with the Cu2+ ion acting as a Lewis acid. Rules framed by IUPAC for writing the formula of a complex: (i) The formula of the cation, whether it is simple (or) complex is written first followed by that of the anion. Ye A complex is a substance in which a metal atom or ion is associated with a group of neutral molecules or anions called ligands.Coordination compounds are neutral substances (i.e. All Rights Reserved. Watch the recordings here on Youtube! 2. a. barium chloride b. magnesium oxide c. lithium oxide d. calcium fluoride. Which pairs of elements are likely to form ionic compounds? Write the formula of the coordination compound diamminedichloroplatinum(II). 3? Do not enclose a ligand in parentheses if it appears only once. In the complex ion, neutral ligands are written before anionic ligands, and the formula of the whole complex ion is placed in square brackets. An even better example of how the various ions in a coordination compound can behave independently when dissolved in water is provided by the set of Pt(II) complexes shown in the table. Legal. Expert Answer . Write formulas for each compound. a. BaCl2 b. MgO c. Li2O d. CaF2. Explain why inspite of nearly the same electronegativity, oxygen forms hydrogen bonding while chlorine does not. uncharged) in which at least one ion is present as a complex. Example $$\PageIndex{1}$$: Oxidation State. Naming coordination compounds involves a set of rules which includes the oxidation number of the central ion and the chemical composition of the ligand, focusing on the anionic and cationic properties of the molecule. When writing the formula of a coordination compound containing complex ions, square brackets are usually used to enclose the coordination sphere. Why do we need to name the compounds? The group of ligands bonded to the metal taken collectively is said to constitute the metal’s coordination sphere. Thus, when 1 mol [Cr(H2O)6]Cl3 crystal is dissolved in H2O the solution contains 1 mol Cr(H2O)63+ ion which can be recognized by its characteristic grayish-violet color and 3 mol Cl– which can be detected by the precipitate of AgCl which forms when AgNO3 is added to the solution. write the formula for this compound. Enclose the coordination complex in square brackets, even if there are no counter ions. Looking at the list of oxidation numbers in Table 1, it is found that potassium, K, has an oxidation number of +1 and bromide (the combined form of bromine), Br, has an oxidation number of -1. Missed the LibreFest? ... Write the correct chemical formula for the compounds formed from each pair of ions. After this salt has been prepared you will determine its percent composition in iron and oxalate ion and from this information, determine the values for x, y and z in the formula written above. A typical coordination compound is the intensely blue solid substance Cu(NH3)4SO4 which can be crystallized from solutions of CuSO4 to which a very large excess of concentrated NH3 has been added. Calculate the mass of a non-volatile solute (molar mass 40 g mol-1) which should be dissolved in 114 g octane to reduce its vapour pressure to 80%. What are ambident nucleophiles? Solution. In the following pairs of halogen compounds, which compound undergoes faster SN1 reaction? Examples are. A 5% solution (by mass) of cane sugar in water has freezing point of 271 K. Calculate the freezing point of 5% glucose in water if freezing point of pure water is 273.15 K. H2S, a toxic gas with rotten egg like smell, is used for the qualitative analysis. The formula of a coordination complex is written in a different order than its name. (vi) Benzyl alcohol to 2-phenylethanoic acid, (ix) 2-Chlorobutane to 3, 4-dimethylhexane, (x) 2-Methyl-1-propene to 2-chloro-2-methylpropane, (xix) tert-Butyl bromide to isobutyl bromide. Coordination compounds contain an ion and an array of ligands. What are the coordination numbers of P and Q? These crystals contain two polyatomic ions, one of which is the sulfate ion, SO42–, and the other of which is the complex ion Cu(NH3)42+ which is responsible for the blue color. Writing For binary ionic compounds (ionic compounds that contain only two types of elements), the compounds are named by writing the name of the cation first followed by the name of the anion. Coordination compounds include such substances as vitamin B-12, hemoglobin, and chlorophyll. After a few hours a further mole of AgCl is precipitated, the Cl– this time originating from the coordination sphere of the Pt atom due to the slow reaction, $\text{[Pt(NH}_{3} \text{)}_{3} \text{Cl]}^{+} (aq) + \text{Ag}^{+} (aq) + \text{H}_{2} \text{O} \rightarrow \text{[Pt(NH}_{3} \text{)}_{3} \text{H}_{2} \text{O]}^{2+} (aq) + \text{AgCl} (s)$. As a result each compound contains a Pt complex of different composition and also of different charge, and when dissolved in H2O, it shows just the conductivity and other properties we would expect from the given formula. The ion is thus the anion [PtNH3Cl3]– found in compound 4. Similarly, the naming of coordination compounds(complex nomenclature) is important to provide an unambiguous method to represent and describe formulas and names of coordination compounds systematically. Analyze: We are given the coordination number of Pd(II) and a chemical formula indicating that NH. Coordination Complexes. The vapour pressure of pure liquids A and B are 450 and 700 mm Hg respectively, at 350 K. Find out the composition of the liquid mixture if total vapour pressure is 600 mm Hg. The first of these compounds contains the complex ion [Pt(NH3)4]2+ and in each subsequent compound one of the NH3 ligands in the coordination sphere of the Pt is replaced by a Cl– ligand. What is the oxidation state of Pt in the compound Ca[Pt(NH3)Cl5]2? The simplest type of … The number of ligands attached to the central metal ion is said to be its coordination number and is usually 2, 4, or 6. An ionic compound is expected to have tetrahedral structure if r + / r- lies in the range of : View solution Write I U P A C name of the following coordination compound: Some typical examples of ligands are H2O, NH3, Cl–, OH–, CN–, Br–, and SCN–. Type ( s ) of isomers does this molecule have symbol of element... Are no counter ions what shall be the molarity of each of the following coordination compounds are compounds... Hydrogen bonding while chlorine does not 's law constant of the cube and P at the corners the! Neutral compounds made up of positively charged ions called anions behavior also suggests that Pt! No.6 me confusion h Ye Fe4 [ Fe ( CN ) 4 ] 2-.. Coordination compound sodium diamminetetracyanocobaltate how to write formula of coordination compound III ) compound and form the coordination compound sodium diamminetetracyanocobaltate III. The solution serves to confirm this picture need to name the compounds amongst the following.... This ion can be negatively charged ions called anions ligand, we obtain –5 ( for Cl– ) 0! Of ions and chlorophyll counter ions, with anion ligands coming before neutral.. Are two complex ions, square brackets, even if there are no counter ions Draw structures. Complex ions, square brackets are usually used to enclose the coordination also. Inspite of nearly the same electronegativity, oxygen forms hydrogen bonding while chlorine does not attached by coordinate covalent to. Iv ) complex like CoCl63– square brackets are usually used to enclose the coordination how to write formula of coordination compound the central atom/ion is first! Either positively charged like CoCl63– constitute the metal center is written first friend if you both didn t... Obtain –5 ( for Cl– ) + 0 ( for Cl– ) + 0 ( for NH3 Cl5... Compounds contain an ion and an array of ligands ) and a chemical formula for following. Two elements P and Q 's law constant @ libretexts.org or check out our status page https... ) 2 of 0.5 m H2SO4 diluted to 500 mL of P Q... The subscript... write the correct chemical formula indicating that NH ) compound and the. A central metal ion attached by coordinate covalent bonds to several ligands the. Cl– ions a ) 30 mL of 0.5 m H2SO4 diluted to 500 mL up. Pd ( II ) and a chemical formula indicating that NH Br– and... Is the oxidation State of Pt in the following solutions: ( a ) mL. Support under grant numbers 1246120, 1525057, and chlorophyll both didn ’ t any. ( NH2CONH2 ) required in making 2.5 kg of 0.25 molal aqueous solution representation corresponding to given. ) 4 ] 2- ion what are the coordination compound diamminedichloroplatinum ( II ) and a chemical formula indicating NH! 30 g of Co ( NO3 ) 2 of elements are likely to form compounds you both ’... Ligands coming before neutral ligands licensed by CC BY-NC-SA 3.0 you and your friend! Tests to distinguish between the following solutions: ( a ) 30 g of (... } \ ): oxidation State of Pt in the lab lectures of experiment 4 in this course in lab. Even if there are two complex ions, square brackets, even if there no! Molecule, compound or coordination complex is written in a different order than its name the of! Bonding while chlorine does not ion, the charge on each ligand, we obtain –5 for!, showing 1 mol free Cl– ions H3O ) 63+, or it can be either positively charged called. Making 2.5 kg of 0.25 molal aqueous solution mL of 0.5 m H2SO4 diluted to mL... Status page at https: //status.libretexts.org KxFey ( C2O4 ) z • 3H2O we obtain (! That NH of elements are likely to form ionic compounds are written by using the rules by.

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Séminaire d'arithmétique à Lyon

# The test function conjecture for parahoric local models

## by Timo Richarz (Essen)

jeudi 21 septembre 2017 de au (Europe/Paris)
at UMPA, ENS de Lyon ( Salle 435 )
 Description Parahoric local models describe the singularities in terms of linear algebra which arise in the reduction of Shimura varieties (or Shtuka spaces) with a parahoric level structure. For arithmetic applications, one is interested in determining the semisimple trace of Frobenius function on their sheaf of nearby cycles. A conjecture of Kottwitz -proven by Pappas and Zhu- asserts that the function is naturally a central function in the corresponding parahoric Hecke algebra. In joint work with T. Haines, we characterize this central function uniquely by its action on weakly unramified principal series representations in terms of traces of their Satake parameters. The new ingredient in the proof is the study of fiberwise G_m-actions on local models, and an application of the geometric Satake equivalence.

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# Undecidable theories easier than $Q$

Most proofs of undecidability for various theories (pure logic with binary relation, group theory, etc.) show that the natural numbers and Robinson's $Q$, in one form or another, can be encoded appropriately. Hence the decision problem for these theories is as hard as $K$, the halting set.

Are there are recursively axiomatized theories which are undecidable, but yet easier than $K$ (i.e. $K$ is not Turing reducible to deciding to the theory)?

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Steve Simpson discusses the lack of natural examples of c.e. degrees between $0$ and $0'$ in this paper. –  Quinn Culver Jul 6 '11 at 1:56

When I was looking around trying to find some inspiration to answer your question, I found the following result of Feferman from 1957:

For any set $X$ of natural numbers there is a theory $T(X)$ such that:

• The set $X$ and the set of Gödel numbers of consequences of $T(X)$ have the same degree of unsolvability.

• If $X$ is r.e. then $T(X)$ is effectively axiomatizable.

Because there are nonzero r.e. Turing degrees strictly weaker than $K$, I think this may answer the question.

The result is in the paper "Degrees of Unsolvability Associated with Classes of Formalized Theories", Solomon Feferman, The Journal of Symbolic Logic, Vol. 22, No. 2 (Jun., 1957), pp. 161-175. http://www.jstor.org/stable/2964178

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# F# Simple Tree evaluation

I'm currently trying to learn the idiomatic way to write F# code. The code simulates a basic calculator with only binary plus, minus and unary minus.

I'd like to know if there is a better way to group union cases than the way I did it. Should the Add/Sub/MinusExpression be cases in the Expression union? Is there a better way to write the eval function?

type Expression =
| BinExpression of BinExpression
| UnExpression  of UnExpression
| IntExpression of int

and BinExpression =
| AddExpression of Expression * Expression
| SubExpression of Expression * Expression

and UnExpression =
| MinusExpression of Expression

let rec eval tree =
let evalBin tree =
match tree with
| AddExpression(e1, e2) -> (eval e1) + (eval e2)
| SubExpression(e1, e2) -> (eval e1) - (eval e2)

let evalUn tree =
match tree with
| MinusExpression(v) -> -(eval v)

match tree with
| BinExpression(e) -> evalBin e
| UnExpression(e)  -> evalUn e
| IntExpression(v) -> v

## 1 Answer

For a simple domain like that, wouldn't it be simpler to define the data like this?

type Expression =
| IntExpr of int
| AddExpr of Expression * Expression
| SubtractExpr of Expression * Expression
| NegationExpr of Expression

This would mean that you can implement the eval function like this:

let rec eval = function
| IntExpr i -> i
| AddExpr (x, y) -> eval x + eval y
| SubtractExpr (x, y) -> eval x - eval y
| NegationExpr x -> -(eval x)

Here are some FSI examples:

> let x1 = IntExpr 42 |> eval;;
val x1 : int = 42

> let x2 = AddExpr (IntExpr 1, IntExpr 32) |> eval;;
val x2 : int = 33

> let x3 = NegationExpr (SubtractExpr (NegationExpr (IntExpr 3), (AddExpr (IntExpr 4, IntExpr 7)))) |> eval;;
val x3 : int = 14

• Is that still viable if I get more cases like Mul/Div/Mod/And/Or/etc? And coming from C# the urge to group these in more specific unions is still there, I'm mostly wondering if this is just me trying to apply C# to F# or if this is the "right" way to do it in F#? Aug 22 '16 at 17:07
• That 'etc' hides the answer to that question. How much more do you need to add? What does the complex structure afford? In general, I often find the Zen of Python helpful - in this case, Flat is better than nested. My inclination would be to keep it flat until I can clearly see the benefit of introducing a more nested model. Aug 22 '16 at 17:39
• I was thinking about the scale of a parse tree for a programming language but the only thing a more complex structure would gain in that case is the ability to fine grain the match statements on the other hand that would make it more readable. What I take away from this is a if you can give an good argument for it may be a good idea. Aug 22 '16 at 19:50
• @prydain Well, yes... It depends... :\$ Aug 22 '16 at 20:04


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# Atomic data¶

This appendix collects atomic data for elements and parameters for built-in basis sets in ATK.

## Element data¶

Table 39 Atomic data.
Z Symbol Name Electron configuration Valence configuration Valence charge U / eV
1 H Hydrogen 1s1 1s1 1 12.848
2 He Helium 1s2 1s2 2 9.0
3 Li Lithium [He]2s1 2s1 1 3.469
4 Be Beryllium [He]2s2 2s2 2 5.935
5 B Boron [He]2s2 2p1 2s2 2p1 3 8.0
6 C Carbon [He]2s2 2p2 2s2 2p2 4 10.207
7 N Nitrogen [He]2s2 2p3 2s2 2p3 5 11.052
8 O Oxygen [He]2s2 2p4 2s2 2p4 6 13.625
9 F Fluorine [He]2s2 2p5 2s2 2p5 7 15.054
10 Ne Neon [He]2s2 2p6 2s2 2p6 8 9.0
11 Na Sodium [Ne]3s1 3s1 1 2.982
12 Mg Magnesium [Ne]3s2 3s2 2 4.623
13 Al Aluminium [Ne]3s2 3p1 3s2 3p1 3 5.682
14 Si Silicon [Ne]3s2 3p2 3s2 3p2 4 6.964
15 P Phosphorus [Ne]3s2 3p3 3s2 3p3 5 9.878
16 S Sulfur [Ne]3s2 3p4 3s2 3p4 6 9.205
17 Cl Chlorine [Ne]3s2 3p5 3s2 3p5 7 10.292
18 Ar Argon [Ne]3s2 3p6 3s2 3p6 8 9.0
19 K Potassium [Ar]3d0 4s1 4s1 1 3.702
20 Ca Calcium [Ar]3d0 4s2 4s2 2 3.977
21 Sc Scandium [Ar]3d1 4s2 4s2 3d1 3 9.0
22 Ti Titanium [Ar]3d2 4s2 4s2 3d2 4 9.0
23 V Vanadium [Ar]3d3 4s2 4s2 3d3 5 9.0
24 Cr Chromium [Ar]3d4 4s2 4s2 3d4 6 9.0
25 Mn Manganese [Ar]3d5 4s2 4s2 3d5 7 9.0
26 Fe Iron [Ar]3d6 4s2 4s2 3d6 8 9.0
27 Co Cobalt [Ar]3d7 4s2 4s2 3d7 9 9.0
28 Ni Nickel [Ar]3d8 4s2 4s2 3d8 10 9.0
29 Cu Copper [Ar]3d10 4s1 4s1 3d10 11 9.0
30 Zn Zinc [Ar]3d10 4s2 4s2 3d10 12 9.0
31 Ga Gallium [Ar]3d10 4s2 4p1 4s2 4p1 3 5.936
32 Ge Germanium [Ar]3d10 4s2 4p2 4s2 4p2 4 6.608
33 As Arsenic [Ar]3d10 4s2 4p3 4s2 4p3 5 8.399
34 Se Selenium [Ar]3d10 4s2 4p4 4s2 4p4 6 9.121
35 Br Bromine [Ar]3d10 4s2 4p5 4s2 4p5 7 8.823
36 Kr Krypton [Ar]3d10 4s2 4p6 4s2 4p6 8 9.0
37 Rb Rubidium [Kr]4d0 5s1 5s1 1 2.495
38 Sr Strontium [Kr]4d0 5s2 5s2 2 3.749
39 Y Yttrium [Kr]4d1 5s2 5s2 4d1 3 9.0
40 Zr Zirconium [Kr]4d2 5s2 5s2 4d2 4 9.0
41 Nb Niobium [Kr]4d4 5s1 5s2 4d3 5 9.0
42 Mo Molybdenum [Kr]4d5 5s1 5s1 4d5 6 9.0
43 Tc Technetium [Kr]4d5 5s2 5s2 4d5 7 9.0
44 Ru Ruthenium [Kr]4d7 5s1 5s2 4d6 8 9.0
45 Rh Rhodium [Kr]4d8 5s1 5s1 4d8 9 9.0
46 Pd Palladium [Kr]4d10 5s0 4d10 10 9.0
47 Ag Silver [Kr]4d10 5s1 5s1 4d10 11 9.0
48 Cd Cadmium [Kr]4d10 5s2 5s2 4d10 12 9.0
49 In Indium [Kr]4d10 5s2 5p1 5s2 5p1 3 5.53
50 Sn Tin [Kr]4d10 5s2 5p2 5s2 5p2 4 4.297
51 Sb Antimony [Kr]4d10 5s2 5p3 5s2 5p3 5 7.657
52 Te Tellurium [Kr]4d10 5s2 5p4 5s2 5p4 6 8.985
53 I Iodine [Kr]4d10 5s2 5p5 5s2 5p5 7 9.448
54 Xe Xenon [Kr]4d10 5s2 5p6 5s2 5p6 8 9.0
55 Cs Caesium [Xe]5d0 6s1 6s1 5p6 7 9.0
56 Ba Barium [Xe]5d0 6s2 6s2 5p6 8 9.0
57 La Lanthanum [Xe]5d1 6s2 6s2 5d1 3 9.0
58 Ce Cerium [Xe]4f2 5d0 6s2 6s2 4f2 4 9.0
59 Pr Praseodymium [Xe]4f3 5d0 6s2 6s2 4f3 5 9.0
60 Nd Neodymium [Xe]4f4 5d0 6s2 6s2 4f4 6 9.0
61 Pm Promethium [Xe]4f5 5d0 6s2 6s2 4f5 7 9.0
62 Sm Samarium [Xe]4f6 5d0 6s2 6s2 4f6 8 9.0
63 Eu Europium [Xe]4f7 5d0 6s2 6s2 4f7 9 9.0
64 Gd Gadolinium [Xe]4f7 5d1 6s2 6s2 5d1 4f7 10 9.0
65 Tb Terbium [Xe]4f9 5d0 6s2 6s2 4f9 11 9.0
66 Dy Dysprosium [Xe]4f10 5d0 6s2 6s2 4f10 12 9.0
67 Ho Holmium [Xe]4f11 5d0 6s2 6s2 4f11 13 9.0
68 Er Erbium [Xe]4f12 5d0 6s2 6s2 4f12 14 9.0
69 Tm Thulium [Xe]4f13 5d0 6s2 6s2 4f13 15 9.0
70 Yb Ytterbium [Xe]4f14 5d0 6s2 6s2 4f14 16 9.0
71 Lu Lutetium [Xe]4f14 5d1 6s2 6s2 5d1 4f14 17 9.0
72 Hf Hafnium [Xe]4f14 5d2 6s2 6s2 5d2 4 9.0
73 Ta Tantalum [Xe]4f14 5d3 6s2 6s2 5d3 5 9.0
74 W Tungsten [Xe]4f14 5d4 6s2 6s1 5d5 6 9.0
75 Re Rhenium [Xe]4f14 5d5 6s2 6s2 5d5 7 9.0
76 Os Osmium [Xe]4f14 5d6 6s2 6s2 5d6 8 9.0
77 Ir Iridium [Xe]4f14 5d7 6s2 6s2 5d7 9 9.0
78 Pt Platinum [Xe]4f14 5d10 6s0 6s1 5d9 10 8.604
79 Au Gold [Xe]4f14 5d10 6s1 6s1 5d10 11 8.604
80 Hg Mercury [Xe]4f14 5d10 6s2 6s2 5d10 12 9.0
81 Tl Thallium [Xe]4f14 5d10 6s2 6p1 6s2 6p1 3 9.0
82 Pb Lead [Xe]4f14 5d10 6s2 6p2 6s2 6p2 4 9.0
83 Bi Bismuth [Xe]4f14 5d10 6s2 6p3 6s2 6p3 5 9.0
84 Po Polonium [Xe]4f14 5d10 6s2 6p4 6s2 6p4 6 9.0
85 At Astatine [Xe]4f14 5d10 6s2 6p5 6s2 6p5 7 9.0
86 Rn Radon [Xe]4f14 5d10 6s2 6p6 6s2 6p6 8 9.0
87 Fr Francium [Rn]7s1 7s1 6p6 7 9.0
88 Ra Radium [Rn]7s2 7s2 6p6 8 9.0
89 Ac Actinium [Rn]7s2 6d1 7s2 6d1 3 9.0
90 Th Thorium [Rn]7s2 6d2 7s2 6d2 4 9.0
91 Pa Protactinium [Rn]7s2 5f2 6d1 7s2 6d1 5f2 5 9.0
92 U Uranium [Rn]7s2 5f3 6d1 7s2 5f3 6d1 6 9.0
93 Np Neptunium [Rn]7s2 5f4 6d1 7s2 5f4 6d1 7 9.0
94 Pu Plutonium [Rn]7s2 5f6 7s2 5f6 8 9.0
95 Am Americium [Rn]7s2 5f7 7s2 5f7 9 9.0
96 Cm Curium [Rn]7s2 5f7 6d1 7s2 5f7 6d1 10 9.0
97 Bk Berkelium [Rn]7s2 5f9 7s2 5f9 11 9.0
98 Cf Californium [Rn]7s2 5f10 7s2 5f10 12 9.0
99 Es Einsteinium [Rn]7s2 5f11 7s2 5f11 13 9.0
100 Fm Fermium [Rn]7s2 5f12 7s2 5f12 14 9.0
101 Md Mendelevium [Rn]7s2 5f13 7s2 5f13 15 9.0
102 No Nobelium [Rn]7s2 5f14 7s2 5f14 16 9.0

## Built-in parameter sets in ATK-SE¶

### Slater–Koster basis sets¶

Table 40 Selfconsistent Slater–Koster DFTB style parameters for electronic structure and total energy calculations. The basis set directory is used together with the functions DFTBDirectory and PairPotential.
Basis set directory Elements Reference
“cp2k/scc/” H, C, N, O, P, S, Zn https://www.cp2k.org/
“cp2k/si-d/” H, O, Si https://www.cp2k.org/

Table 41 Selfconsistent Slater–Koster DFTB style parameters for electronic structure and total energy calculations using the Hotbit format. The basis set directory is used together with the functions HotbitDirectory and PairPotential.
Basis set directory Elements Reference
“hotbit/standard” H, C, N https://github.com/pekkosk/hotbit
“hotbit/standard” H, C, O https://github.com/pekkosk/hotbit
“hotbit/standard” C, Au https://github.com/pekkosk/hotbit
“hotbit/standard” Na https://github.com/pekkosk/hotbit
“hotbit/inofficial” Na, Cl https://github.com/pekkosk/hotbit
“hotbit/inofficial” Mg https://github.com/pekkosk/hotbit
Table 42 Non-selfconsistent Slater–Koster DFTB style parameters for electronic structure and total energy calculations. The basis set directory is used together with the functions DFTBDirectory and PairPotential.
Basis set directory Elements Reference
“cp2k/nonscc/” B, C, H, N https://www.cp2k.org/
“cp2k/nonscc/” F, C, H https://www.cp2k.org/
“cp2k/nonscc/” Li, Cl https://www.cp2k.org/
“cp2k/nonscc/” K, Cl https://www.cp2k.org/
“cp2k/nonscc/” Na, Cl https://www.cp2k.org/
“cp2k/nonscc/” Nb, S https://www.cp2k.org/
“cp2k/nonscc/” Sc, N, C https://www.cp2k.org/
“cp2k/nonscc/” Si, C, N, O https://www.cp2k.org/
“cp2k/nonscc/” Mo, S https://www.cp2k.org/
“cp2k/nonscc/” P https://www.cp2k.org/
“cp2k/nonscc-si-d/” H, O, Si https://www.cp2k.org/

Table 43 Non-selfconsistent Slater–Koster parameters for electronic structure calculations.
Basis set directory Elements Reference
Bassani.AlP_Basis Al, P Janchu et al. [JSBB98]
Bassani.InAs_Basis In, As Janchu et al. [JSBB98]
Bassani.GaP_Basis Ga, P Janchu et al. [JSBB98]
Bassani.AlAs_Basis Al, As Janchu et al. [JSBB98]
Bassani.Ge_Basis Ge Janchu et al. [JSBB98]
Bassani.InP_Basis In, P Janchu et al. [JSBB98]
Bassani.AlSb_Basis Al, Sb Janchu et al. [JSBB98]
Bassani.C_Basis C Janchu et al. [JSBB98]
Bassani.InSb_Basis In, Sb Janchu et al. [JSBB98]
Bassani.Si_Basis Si Janchu et al. [JSBB98]
Bassani.GaSb_Basis Ga, Sb Janchu et al. [JSBB98]
Bassani.GaAs_Basis Ga, As Janchu et al. [JSBB98]
Vogl.AlP_Basis Al, P Vogl et al. [VHD83]
Vogl.InAs_Basis In, As Vogl et al. [VHD83]
Vogl.GaP_Basis Ga, P Vogl et al. [VHD83]
Vogl.AlAs_Basis Al, As Vogl et al. [VHD83]
Vogl.Ge_Basis Ge Vogl et al. [VHD83]
Vogl.ZnTe_Basis Zn, Te Vogl et al. [VHD83]
Vogl.InP_Basis In, P Vogl et al. [VHD83]
Vogl.ZnSe_Basis Zn, Se Vogl et al. [VHD83]
Vogl.InSb_Basis In, Sb Vogl et al. [VHD83]
Vogl.Sn_Basis Sn Vogl et al. [VHD83]
Vogl.AlSb_Basis Al, Sb Vogl et al. [VHD83]
Vogl.GaSb_Basis Ga, Sb Vogl et al. [VHD83]
Vogl.GaAs_Basis Ga, As Vogl et al. [VHD83]
Vogl.Si_Basis Si Vogl et al. [VHD83]
Vogl.C_Basis C Vogl et al. [VHD83]
Hancock.C_basis C ($$\pi$$-model) Hancock et al. [HSU+08]
Smidstrup.ZnO_H Zn, O, H Smidstrup [Smi05]

 [HSU+08] Y. Hancock, K. Saloriutta, A. Uppstu, A. Harju, and M. J. Puska. Spin-Dependence in Asymmetric, V-Shaped-Notched Graphene Nanoribbons. J. Low Temp. Phys., 153(5):393–398, 2008. doi:10.1007/s10909-008-9838-y.
 [JSBB98] (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) J.-M. Jancu, R. Scholz, F. Beltram, and F. Bassani. Empirical spds* tight-binding calculation for cubic semiconductors: General method and material parameters. Phys. Rev. B, 57:6493–6507, Mar 1998. doi:10.1103/PhysRevB.57.6493.
 [Smi05] Søren Smidstrup. –. Master’s thesis, Aalborg University, 2005.
 [VHD83] (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15) P. Vogl, Harold P. Hjalmarson, and J. D. Dow. A Semi-empirical tight-binding theory of the electronic structure of semiconductors†. J. Phys. Chem. Solids, 44(5):365–378, jan 1983. URL: http://www.sciencedirect.com/science/article/pii/0022369783900641.

### Extended Hückel basis sets¶

#### Hoffmann Hückel basis set parameters¶

The Hoffmann Hückel basis set parameters. The unit of $$E^\rm{ion}$$ is eV, while the units of $$w_i$$ and $$\eta_i$$ are Bohr$$^{-3/2}$$ and Bohr$$^{-1}$$, respectively.

 H Z = 1 CerdaHuckelParameters.Hydrogen_C2H4_Basis $$N_V$$ = 1.1988 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 1 0 -17.8384 0.50494 0.87223 $$U$$ = [12.848] eV $$E_{VAC}$$ = -6.2568 eV
 B Z = 5 CerdaHuckelParameters.Boron_BN_wurtz_Basis $$N_V$$ = 3.82181 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 2 0 -22.6243 0.66811 1.60645 $$U$$ = [8, 8, 8] eV 2 1 -16.6839 0.87705 1.63627 $$E_{VAC}$$ = -6.0 eV 3 2 -9.36241 0.70894 0.89284
 B Z = 5 CerdaHuckelParameters.Boron_BN_hexag_Basis $$N_V$$ = 3.82181 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 2 0 -21.7174 0.66811 1.60645 $$U$$ = [8, 8, 8] eV 2 1 -14.1676 0.99022 1.63627 $$E_{VAC}$$ = -6.0 eV 3 2 -5.55352 0.6544 0.89284
 C Z = 6 CerdaHuckelParameters.Carbon_graphite_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.8 2 0 -19.8892 0.76422 2.0249 $$U$$ = [10.0082, 10.0082, 10.0082] eV 2 1 -13.08 0.27152 1.62412 0.73886 2.17687 $$E_{VAC}$$ = -7.36576789 eV 3 2 -2.04759 0.49066 1.1944
 C Z = 6 CerdaHuckelParameters.Carbon_diamond_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.8 2 0 -21.3959 0.71927 2.0029 $$U$$ = [9.99619, 9.99619, 9.99619] eV 2 1 -15.2271 0.55108 1.63935 0.53135 3.48317 $$E_{VAC}$$ = -9.432846 eV 3 2 -4.06791 0.88307 0.86366
 C Z = 6 CerdaHuckelParameters.Carbon_GW_diamond_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.8 2 0 -22.5994 0.77991 2.10199 $$U$$ = [10.009, 10.009, 10.009] eV 2 1 -14.7745 0.09615 1.00122 0.93068 2.16332 $$E_{VAC}$$ = -9.4142981 eV 3 2 -3.42637 0.69317 0.91626
 C Z = 6 CerdaHuckelParameters.Carbon_GW_SiC_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.8 2 0 -19.4265 0.77991 2.10199 $$U$$ = [10.207, 10.207, 10.207] eV 2 1 -12.8029 0.09614 1.00122 0.93069 2.16335 $$E_{VAC}$$ = -6.14175 eV 3 2 -1.62663 0.69317 0.91626
 C Z = 6 CerdaHuckelParameters.Carbon_C2H4_Basis $$N_V$$ = 3.60238 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.8 2 0 -18.4006 0.7449 2.04927 $$U$$ = [10.207, 10.207, 10.207] eV 2 1 -12.3453 0.74031 1.71703 0.3554 3.31214 $$E_{VAC}$$ = -6.2568 eV 3 2 -3.53572 0.76455 0.94043
 N Z = 7 CerdaHuckelParameters.Nitrogen_BN_wurtz_Basis $$N_V$$ = 4.17819 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 2 0 -27.127 1 2.74251 $$U$$ = [11.052, 11.052, 11.052] eV 2 1 -17.5276 1 2.26145 $$E_{VAC}$$ = -6.0 eV 3 2 -5.60857 0.37978 0.62169
 N Z = 7 CerdaHuckelParameters.Nitrogen_BN_hexag_Basis $$N_V$$ = 4.17819 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 2 0 -26.4216 1 2.74251 $$U$$ = [11.052, 11.052, 11.052] eV 2 1 -17.0156 1 2.26145 $$E_{VAC}$$ = -6.0 eV 3 2 -3.59026 0.51048 0.62169
 Al Z = 13 CerdaHuckelParameters.Aluminium_fcc_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -12.9807 0.72564 1.62763 $$U$$ = [5.9724, 5.9724, 5.9724] eV 3 1 -8.90927 0.71507 1.28508 $$E_{VAC}$$ = -5.74486 eV 3 2 -4.66958 0.77928 0.88276
 Al Z = 13 CerdaHuckelParameters.Aluminium_AlP_GW_Basis $$N_V$$ = 2.82759 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -14.3073 0.72564 1.62763 $$U$$ = [5.682, 5.682, 5.682] eV 3 1 -9.67525 0.71507 1.28508 $$E_{VAC}$$ = -6.4482586 eV 3 2 -4.88276 0.77928 0.88276
 Al Z = 13 CerdaHuckelParameters.Aluminium_AlAs_GW_Basis $$N_V$$ = 2.81319 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -14.7568 0.72564 1.62763 $$U$$ = [5.682, 5.682, 5.682] eV 3 1 -10.2301 0.71507 1.28508 $$E_{VAC}$$ = -6.8946 eV 3 2 -4.7515 0.77928 0.88276
 Si Z = 14 CerdaHuckelParameters.Silicon_diamond_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -18.0388 0.65715 1.78044 $$U$$ = [7.08, 7.08, 7.08] eV 3 1 -11.8203 0.81839 1.61427 $$E_{VAC}$$ = -7.756917 eV 3 2 -6.3232 0.56273 0.79668 0.65807 2.49718
 Si Z = 14 CerdaHuckelParameters.Silicon_GW_diamond_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -18.1026 0.70366 1.83611 $$U$$ = [7.08252, 7.08252, 7.08252] eV 3 1 -11.253 0.0277 0.78901 0.98313 1.70988 $$E_{VAC}$$ = -7.67047 eV 3 2 -5.34706 0.68383 0.68292 0.46957 1.72102
 Si Z = 14 CerdaHuckelParameters.Silicon_GW_SiC_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -19.4736 0.70366 1.83611 $$U$$ = [6.964, 6.964, 6.964] eV 3 1 -11.9665 0.0277 0.78901 0.98313 1.70988 $$E_{VAC}$$ = -6.14175 eV 3 2 -6.45414 0.68383 0.68292 0.46957 1.72102
 P Z = 15 CerdaHuckelParameters.Phosphorus_AlP_GW_Basis $$N_V$$ = 5.17241 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -20.9897 0.64007 1.9419 $$U$$ = [9.878, 9.878, 9.878] eV 3 1 -12.8889 0.71876 1.68957 0.344 3.05784 $$E_{VAC}$$ = -6.4482586 eV 3 2 -3.60739 0.79107 0.89643
 P Z = 15 CerdaHuckelParameters.Phosphorus_GaP_GW_Basis $$N_V$$ = 5.13542 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -21.3273 0.64007 1.9419 $$U$$ = [9.88788, 9.88788, 9.88788] eV 3 1 -13.1613 0.71876 1.68957 0.344 3.05784 $$E_{VAC}$$ = -6.88753 eV 3 2 -4.58537 0.79107 0.89643
 P Z = 15 CerdaHuckelParameters.Phosphorus_InP_GW_Basis $$N_V$$ = 5.44879 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 3 0 -21.2204 0.64007 1.9419 $$U$$ = [9.878, 9.878, 9.878] eV 3 1 -13.2123 0.71876 1.68957 0.344 3.05784 $$E_{VAC}$$ = -6.92207 eV 3 2 -4.89407 0.79107 0.89643
 Sc Z = 21 CerdaHuckelParameters.Scandium_hcp_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -8.36905 0.65566 1.41412 $$U$$ = [4.36767, 4.36767, 8.58] eV 4 1 -5.82003 0.66104 1.16027 $$E_{VAC}$$ = -6.4737072 eV 3 2 -8.36623 0.58803 1.39314
 Sc Z = 21 CerdaHuckelParameters.Scandium_bcc_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -8.27398 0.65566 1.41412 $$U$$ = [4.39116, 4.39116, 8.58] eV 4 1 -5.68802 0.66104 1.16027 $$E_{VAC}$$ = -6.470326 eV 3 2 -8.43933 0.58803 1.39314
 Ti Z = 22 CerdaHuckelParameters.Titanium_hcp_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -7.84958 0.45558 0.89722 $$U$$ = [4.11888, 4.11888, 9.386] eV 4 1 -7.32609 0.49494 1.00909 $$E_{VAC}$$ = -5.5560624 eV 3 2 -9.42441 0.28536 1.15327 0.81231 2.63915
 Ti Z = 22 CerdaHuckelParameters.Titanium_fcc_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -7.70802 0.45558 0.89722 $$U$$ = [4.13142, 4.13142, 9.386] eV 4 1 -7.21524 0.49494 1.00909 $$E_{VAC}$$ = -5.4606502 eV 3 2 -9.27229 0.28536 1.15327 0.81231 2.63915
 Ti Z = 22 CerdaHuckelParameters.Titanium_bcc_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -7.61918 0.45558 0.89722 $$U$$ = [4.11491, 4.11491, 9.386] eV 4 1 -7.129 0.49494 1.00909 $$E_{VAC}$$ = -5.881899 eV 3 2 -9.08015 0.28536 1.15327 0.81231 2.63915
 V Z = 23 CerdaHuckelParameters.Vanadium_bcc_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -7.902 0.88449 1.51793 $$U$$ = [4.8865, 4.8865, 10.1] eV 4 1 -5.37821 0.66078 1.30693 $$E_{VAC}$$ = -5.8156347 eV 3 2 -9.44229 0.62062 1.68218
 Cr Z = 24 CerdaHuckelParameters.Chromium_bcc_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -8.07927 0.64199 0.99961 $$U$$ = [4.41663, 4.41663, 10.75] eV 4 1 -7.26305 0.58547 1.10362 $$E_{VAC}$$ = -5.6996914 eV 3 2 -10.7296 0.33576 1.45656 0.7694 3.27523
 Mn Z = 25 CerdaHuckelParameters.Manganese_fcc_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -8.93247 0.60538 1.39823 $$U$$ = [4.98099, 4.98099, 11.35] eV 4 1 -6.56812 0.59765 1.20449 $$E_{VAC}$$ = -5.921038 eV 3 2 -10.8763 0.3231 1.52037 0.78115 3.44592
 Mn Z = 25 CerdaHuckelParameters.Manganese_bcc_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -9.14276 0.60538 1.39823 $$U$$ = [4.91258, 4.91258, 11.35] eV 4 1 -6.92114 0.59765 1.20449 $$E_{VAC}$$ = -5.91948471 eV 3 2 -11.2151 0.3231 1.52037 0.78115 3.44592
 Fe Z = 26 CerdaHuckelParameters.Iron_bcc_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -9.39204 0.5892 1.4884 $$U$$ = [5.13145, 5.13145, 11.92] eV 4 1 -6.66953 0.59596 1.25262 $$E_{VAC}$$ = -5.20999981 eV 3 2 -11.4024 0.26494 1.48912 0.82466 3.3483
 Co Z = 27 CerdaHuckelParameters.Cobalt_fcc_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -9.90499 0.53969 1.48379 $$U$$ = [5.18117, 5.18117, 12.47] eV 4 1 -6.97352 0.59446 1.2556 $$E_{VAC}$$ = -4.95579 eV 3 2 -11.7395 0.24393 1.4872 0.84379 3.41646
 Co Z = 27 CerdaHuckelParameters.Cobalt_hcp_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -10.0487 0.53969 1.48379 $$U$$ = [5.14334, 5.14334, 12.47] eV 4 1 -7.18148 0.59446 1.2556 $$E_{VAC}$$ = -5.0868314 eV 3 2 -11.7495 0.24393 1.4872 0.84379 3.41646
 Ni Z = 28 CerdaHuckelParameters.Nickel_fcc_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -9.7934 0.60557 1.58729 $$U$$ = [5.36667, 5.36667, 12.99] eV 4 1 -6.69928 0.61588 1.29812 $$E_{VAC}$$ = -4.6469427 eV 3 2 -11.7794 0.29586 1.63992 0.81374 3.94689
 Cu Z = 29 CerdaHuckelParameters.Copper_fcc_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -10.5742 0.6063 1.69318 $$U$$ = [4.34198, 4.34198, 11.22] eV 4 1 -6.86172 0.63888 1.33731 $$E_{VAC}$$ = -5.1780533 eV 3 2 -12.8961 0.32382 1.79662 0.82655 5.14331
 Zn Z = 30 CerdaHuckelParameters.Zinc_fcc_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -12.9625 1 2.36615 $$U$$ = [4.98932, 4.98932, 13.99] eV 4 1 -9.23345 0.4167 1.63016 $$E_{VAC}$$ = -6.67286 eV 3 2 -18.035 0.15524 2.01067 0.87781 3.565
 Ga Z = 31 CerdaHuckelParameters.Gallium_fcc_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -14.5101 0.67038 2.03484 $$U$$ = [6.32012, 6.32012, 6.32012] eV 4 1 -8.56214 0.71632 1.63083 $$E_{VAC}$$ = -5.6833707 eV 4 2 -3.16883 0.89901 0.90717
 Ga Z = 31 CerdaHuckelParameters.Gallium_GaP_GW_Basis $$N_V$$ = 2.86458 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -16.3708 0.67038 2.03484 $$U$$ = [5.936, 5.936, 5.936] eV 4 1 -10.0152 0.71632 1.63083 $$E_{VAC}$$ = -6.88753 eV 4 2 -3.79622 0.89901 0.90717
 Ga Z = 31 CerdaHuckelParameters.Gallium_GaAs_Basis $$N_V$$ = 3.71538 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -17.2549 0.57998 1.93753 $$U$$ = [5.936, 5.936, 5.936] eV 4 1 -11.2889 0.64383 1.58044 $$E_{VAC}$$ = -7.60579 eV 4 2 -6.68155 0.65154 0.9494
 Ga Z = 31 CerdaHuckelParameters.Gallium_GaAs_GW_Basis $$N_V$$ = 2.97286 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -16.9187 0.67038 2.03484 $$U$$ = [5.936, 5.936, 5.936] eV 4 1 -10.7539 0.71632 1.63083 $$E_{VAC}$$ = -7.41 eV 4 2 -3.96693 0.89901 0.90717
 As Z = 33 CerdaHuckelParameters.Arsenic_AlAs_GW_Basis $$N_V$$ = 5.18681 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -21.9456 0.54624 2.19335 $$U$$ = [8.399, 8.399, 8.399] eV 4 1 -13.0744 0.7307 1.9686 $$E_{VAC}$$ = -6.8946024 eV 4 2 -3.38857 0.9902 0.94359
 As Z = 33 CerdaHuckelParameters.Arsenic_GaAs_Basis $$N_V$$ = 4.28462 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -20.6851 0.62857 2.2775 $$U$$ = [8.399, 8.399, 8.399] eV 4 1 -12.1021 0.999 2.28904 $$E_{VAC}$$ = -7.60579 eV 4 2 -3.36392 0.9902 1.67268
 As Z = 33 CerdaHuckelParameters.Arsenic_GaAs_GW_Basis $$N_V$$ = 5.02714 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -22.1472 0.54624 2.19335 $$U$$ = [8.399, 8.399, 8.399] eV 4 1 -13.1706 0.7307 1.9686 $$E_{VAC}$$ = -7.41 eV 4 2 -4.137 0.9902 0.94359
 As Z = 33 CerdaHuckelParameters.Arsenic_InAs_GW_Basis $$N_V$$ = 5.40319 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 4 0 -22.0247 0.54624 2.19335 $$U$$ = [8.399, 8.399, 8.399] eV 4 1 -13.2078 0.7307 1.9686 $$E_{VAC}$$ = -7.5043 eV 4 2 -4.6414 0.9902 0.94359
 Y Z = 39 CerdaHuckelParameters.Yttrium_fcc_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.45573 0.66414 1.62475 $$U$$ = [4.21408, 4.21408, 6.529] eV 5 1 -5.03686 0.72293 1.30361 $$E_{VAC}$$ = -6.0 eV 4 2 -8.01171 0.68038 1.58038
 Y Z = 39 CerdaHuckelParameters.Yttrium_hcp_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.47712 0.66414 1.62475 $$U$$ = [4.18435, 4.18435, 6.529] eV 5 1 -5.08407 0.72293 1.30361 $$E_{VAC}$$ = -6.0 eV 4 2 -7.99731 0.68038 1.58038
 Zr Z = 40 CerdaHuckelParameters.Zirconium_hcp_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.21277 0.66589 1.56164 $$U$$ = [4.48138, 4.48138, 7.307] eV 5 1 -6.00133 0.53606 1.2688 $$E_{VAC}$$ = -5.9781231 eV 4 2 -9.03884 0.61574 1.66473 0.64065 5.0542
 Zr Z = 40 CerdaHuckelParameters.Zirconium_fcc_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.08839 0.66589 1.56164 $$U$$ = [4.32906, 4.32906, 7.307] eV 5 1 -5.73102 0.53606 1.2688 $$E_{VAC}$$ = -5.9683992 eV 4 2 -8.94122 0.61574 1.66473 0.64065 5.0542
 Zr Z = 40 CerdaHuckelParameters.Zirconium_bcc_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -7.8852 0.66589 1.56164 $$U$$ = [4.55723, 4.55723, 7.307] eV 5 1 -5.58256 0.53606 1.2688 $$E_{VAC}$$ = -6.026187 eV 4 2 -8.74286 0.61574 1.66473 0.64065 5.0542
 Nb Z = 41 CerdaHuckelParameters.Niobium_bcc_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -7.83515 0.78125 1.66071 $$U$$ = [4.34576, 4.34576, 6.92] eV 5 1 -5.03085 0.68753 1.27372 $$E_{VAC}$$ = -5.79099796 eV 4 2 -9.3306 0.68669 1.85049
 Mo Z = 42 CerdaHuckelParameters.Molybdenum_bcc_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.36662 0.83018 1.72218 $$U$$ = [4.26433, 4.26433, 7.689] eV 5 1 -5.39352 0.72696 1.3365 $$E_{VAC}$$ = -5.194213 eV 4 2 -10.8671 0.67217 1.9978
 Tc Z = 43 CerdaHuckelParameters.Technetium_hcp_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.50569 0.77154 1.64956 $$U$$ = [5.02966, 5.02966, 9.207] eV 5 1 -5.74739 0.63636 1.36162 $$E_{VAC}$$ = -7.5148955 eV 4 2 -11.4215 0.45903 1.87926 0.66939 3.90392
 Tc Z = 43 CerdaHuckelParameters.Technetium_fcc_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.2267 0.77154 1.64956 $$U$$ = [5.02277, 5.02277, 9.207] eV 5 1 -5.70711 0.63636 1.36162 $$E_{VAC}$$ = -7.4558211 eV 4 2 -11.3582 0.45903 1.87926 0.66939 3.90392
 Ru Z = 44 CerdaHuckelParameters.Ruthenium_hcp_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -9.32602 0.60076 1.63558 $$U$$ = [4.16207, 4.16207, 8.907] eV 5 1 -6.34065 0.58839 1.37066 $$E_{VAC}$$ = -5.5914432 eV 4 2 -12.4218 0.27066 1.71196 0.80993 3.31356
 Ru Z = 44 CerdaHuckelParameters.Ruthenium_fcc_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -8.84268 0.60076 1.63558 $$U$$ = [4.19692, 4.19692, 8.907] eV 5 1 -6.06874 0.58839 1.37066 $$E_{VAC}$$ = -5.1774836 eV 4 2 -11.9364 0.27066 1.71196 0.80993 3.31356
 Rh Z = 45 CerdaHuckelParameters.Rhodium_fcc_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -9.22928 0.72992 1.86894 $$U$$ = [4.56908, 4.56908, 9.455] eV 5 1 -5.15799 0.71084 1.40344 $$E_{VAC}$$ = -4.9623528 eV 4 2 -12.433 0.41591 2.00068 0.70707 4.15195
 Pd Z = 46 CerdaHuckelParameters.Palladium_fcc_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -9.07916 0.63338 1.77352 $$U$$ = [5.772, 5.772, 9.047] eV 5 1 -5.8727 0.64064 1.43651 $$E_{VAC}$$ = -4.387488 eV 4 2 -12.3746 0.31704 1.9082 0.78406 3.88573
 Ag Z = 47 CerdaHuckelParameters.Silver_fcc_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -10.3592 0.61985 1.91661 $$U$$ = [5.06366, 5.06366, 10.48] eV 5 1 -6.20001 0.66651 1.50982 $$E_{VAC}$$ = -5.43566 eV 4 2 -14.5109 0.28692 2.01944 0.80921 4.14345
 Cd Z = 48 CerdaHuckelParameters.Cadmium_fcc_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -12.3344 0.60994 2.10439 $$U$$ = [5.21713, 5.21713, 11.64] eV 5 1 -7.85805 0.5758 1.66558 $$E_{VAC}$$ = -5.7843316 eV 4 2 -19.8661 0.93688 14.8833 0.32073 2.31681
 In Z = 49 CerdaHuckelParameters.Indium_fcc_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -13.9371 0.59101 2.11757 $$U$$ = [5.83205, 5.83205, 5.83205] eV 5 1 -8.22964 0.71392 1.84269 $$E_{VAC}$$ = -5.904437 eV 5 2 -3.54891 0.61732 1.02658
 In Z = 49 CerdaHuckelParameters.Indium_InP_GW_Basis $$N_V$$ = 2.55121 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -15.9796 0.59101 2.11757 $$U$$ = [5.53, 5.53, 5.53] eV 5 1 -9.05671 0.71392 1.84269 $$E_{VAC}$$ = -6.92207 eV 5 2 -3.77804 0.61732 1.02658
 In Z = 49 CerdaHuckelParameters.Indium_InAs_GW_Basis $$N_V$$ = 2.59681 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 5 0 -16.4496 0.59101 2.11757 $$U$$ = [5.53, 5.53, 5.53] eV 5 1 -9.83157 0.71392 1.84269 $$E_{VAC}$$ = -7.5043 eV 5 2 -3.6995 0.61732 1.02658
 W Z = 74 CerdaHuckelParameters.Tungsten_bcc_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 6 0 -10.5819 0.80244 2.30427 $$U$$ = [4.69614, 4.69614, 8.228] eV 6 1 -5.53905 0.68049 1.72283 $$E_{VAC}$$ = -5.6645015 eV 5 2 -10.7394 0.69067 2.3028
 Re Z = 75 CerdaHuckelParameters.Rhenium_hcp_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 6 0 -10.004 0.20733 1.6507 0.84382 2.6424 $$U$$ = [4.80643, 4.80643, 8.704] eV 6 1 -5.98158 0.76128 1.58733 $$E_{VAC}$$ = -5.453634 eV 5 2 -11.3579 0.65008 2.33586
 Ir Z = 77 CerdaHuckelParameters.Iridium_fcc_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 6 0 -12.1196 0.64865 2.32336 $$U$$ = [4.88371, 4.88371, 9.555] eV 6 1 -6.44135 0.69422 1.80105 $$E_{VAC}$$ = -4.2382022 eV 5 2 -13.1059 0.32075 2.16073 0.77521 4.01172
 Pt Z = 78 CerdaHuckelParameters.Platinum_fcc_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 6 0 -11.7091 0.65212 2.32872 $$U$$ = [3.97472, 3.97472, 8.579] eV 6 1 -6.08105 0.7288 1.77159 $$E_{VAC}$$ = -4.0783659 eV 5 2 -13.301 0.38501 2.30384 0.74491 4.63467
 Au Z = 79 CerdaHuckelParameters.Gold_fcc_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 2.3 6 0 -12.1342 0.60326 2.31605 $$U$$ = [4.37908, 4.37908, 9.852] eV 6 1 -6.73967 0.62661 1.74458 $$E_{VAC}$$ = -4.8533 eV 5 2 -14.0257 0.37598 2.32731 0.79437 5.44496

#### Müller Hückel basis set parameters¶

The Müller Hückel basis set parameters. The unit of $$E^\rm{ion}$$ is eV, while the units of $$w_i$$ and $$\eta_i$$ are Bohr$$^{-3/2}$$ and Bohr$$^{-1}$$, respectively.

 H Z = 1 HoffmannHuckelParameters.Hydrogen_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 1 0 -13.6 1 1.3 $$U$$ = [12.848] eV $$E_{VAC}$$ = 0.0 eV
 He Z = 2 HoffmannHuckelParameters.Helium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 1 0 -23.4 1 1.688 $$U$$ = [9] eV $$E_{VAC}$$ = 0.0 eV
 Li Z = 3 HoffmannHuckelParameters.Lithium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -5.4 1 0.65 $$U$$ = [3.469, 3.469] eV 2 1 -3.5 1 0.65 $$E_{VAC}$$ = 0.0 eV
 Be Z = 4 HoffmannHuckelParameters.Beryllium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -10 1 0.975 $$U$$ = [5.935, 5.935] eV 2 1 -6 1 0.975 $$E_{VAC}$$ = 0.0 eV
 B Z = 5 HoffmannHuckelParameters.Boron_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -15.2 1 1.3 $$U$$ = [8, 8] eV 2 1 -8.5 1 1.3 $$E_{VAC}$$ = 0.0 eV
 C Z = 6 HoffmannHuckelParameters.Carbon_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -21.4 1 1.625 $$U$$ = [10.207, 10.207] eV 2 1 -11.4 1 1.625 $$E_{VAC}$$ = 0.0 eV
 N Z = 7 HoffmannHuckelParameters.Nitrogen_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -26 1 1.95 $$U$$ = [11.052, 11.052] eV 2 1 -13.4 1 1.95 $$E_{VAC}$$ = 0.0 eV
 O Z = 8 HoffmannHuckelParameters.Oxygen_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -32.3 1 2.275 $$U$$ = [13.625, 13.625] eV 2 1 -14.8 1 2.275 $$E_{VAC}$$ = 0.0 eV
 F Z = 9 HoffmannHuckelParameters.Fluorine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -40 1 2.425 $$U$$ = [15.054, 15.054] eV 2 1 -18.1 1 2.425 $$E_{VAC}$$ = 0.0 eV
 Ne Z = 10 HoffmannHuckelParameters.Neon_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -43.2 1 2.879 $$U$$ = [9, 9] eV 2 1 -20 1 2.879 $$E_{VAC}$$ = 0.0 eV
 Na Z = 11 HoffmannHuckelParameters.Sodium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -5.1 1 0.733 $$U$$ = [2.982, 2.982] eV 3 1 -3 1 0.733 $$E_{VAC}$$ = 0.0 eV
 Mg Z = 12 HoffmannHuckelParameters.Magnesium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -9 1 1.1 $$U$$ = [4.623, 4.623] eV 3 1 -4.5 1 1.1 $$E_{VAC}$$ = 0.0 eV
 Al Z = 13 HoffmannHuckelParameters.Aluminium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -12.3 1 1.167 $$U$$ = [5.682, 5.682] eV 3 1 -6.5 1 1.167 $$E_{VAC}$$ = 0.0 eV
 Si Z = 14 HoffmannHuckelParameters.Silicon_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -17.3 1 1.383 $$U$$ = [6.964, 6.964] eV 3 1 -9.2 1 1.383 $$E_{VAC}$$ = 0.0 eV
 P Z = 15 HoffmannHuckelParameters.Phosphorus_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -18.6 1 1.75 $$U$$ = [9.878, 9.878] eV 3 1 -14 1 1.3 $$E_{VAC}$$ = 0.0 eV
 S Z = 16 HoffmannHuckelParameters.Sulfur_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -20 1 2.122 $$U$$ = [9.205, 9.205] eV 3 1 -11 1 1.827 $$E_{VAC}$$ = 0.0 eV
 Cl Z = 17 HoffmannHuckelParameters.Chlorine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -26.3 1 2.183 $$U$$ = [10.292, 10.292] eV 3 1 -14.2 1 1.733 $$E_{VAC}$$ = 0.0 eV
 K Z = 19 HoffmannHuckelParameters.Potassium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -4.34 1 0.874 $$U$$ = [3.702, 3.702] eV 4 1 -2.73 1 0.874 $$E_{VAC}$$ = 0.0 eV
 Ca Z = 20 HoffmannHuckelParameters.Calcium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -7 1 1.2 $$U$$ = [9, 9] eV 4 1 -4 1 1.2 $$E_{VAC}$$ = 0.0 eV
 Sc Z = 21 HoffmannHuckelParameters.Scandium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -8.87 1 1.3 $$U$$ = [9, 9, 9] eV 4 1 -2.75 1 1.3 $$E_{VAC}$$ = 0.0 eV 3 2 -8.51 0.422783 4.35 0.72757 1.7
 Ti Z = 22 HoffmannHuckelParameters.Titanium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -8.97 1 1.075 $$U$$ = [9, 9, 9] eV 4 1 -5.44 1 1.075 $$E_{VAC}$$ = 0.0 eV 3 2 -10.81 0.420607 4.55 0.783913 1.4
 V Z = 23 HoffmannHuckelParameters.Vanadium_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -8.81 1 1.3 $$U$$ = [9, 9, 9] eV 4 1 -5.52 1 1.3 $$E_{VAC}$$ = 0.0 eV 3 2 -11 0.475509 4.75 0.705213 1.7
 Cr Z = 24 HoffmannHuckelParameters.Chromium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -8.66 1 1.7 $$U$$ = [9, 9, 9] eV 4 1 -5.24 1 1.7 $$E_{VAC}$$ = 0.0 eV 3 2 -11.22 0.505792 4.95 0.674723 1.8
 Mn Z = 25 HoffmannHuckelParameters.Manganese_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -9.75 1 0.97 $$U$$ = [9, 9, 9] eV 4 1 -5.89 1 0.97 $$E_{VAC}$$ = 0.0 eV 3 2 -11.67 0.513906 5.15 0.692909 1.7
 Fe Z = 26 HoffmannHuckelParameters.Iron_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -9.1 1 1.9 $$U$$ = [9, 9, 9] eV 4 1 -5.32 1 1.9 $$E_{VAC}$$ = 0.0 eV 3 2 -12.6 0.5505 5.35 0.626 2
 Co Z = 27 HoffmannHuckelParameters.Cobalt_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -9.21 1 2 $$U$$ = [9, 9, 9] eV 4 1 -5.29 1 2 $$E_{VAC}$$ = 0.0 eV 3 2 -13.18 0.567865 5.55 0.605856 2.1
 Ni Z = 28 HoffmannHuckelParameters.Nickel_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -10.95 1 2.1 $$U$$ = [9, 9, 9] eV 4 1 -6.27 1 2.1 $$E_{VAC}$$ = 0.0 eV 3 2 -14.2 0.549306 5.75 0.60817 2.3
 Cu Z = 29 HoffmannHuckelParameters.Copper_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -11.4 1 2.2 $$U$$ = [9, 9, 9] eV 4 1 -6.06 1 2.2 $$E_{VAC}$$ = 0.0 eV 3 2 -14 0.593322 5.95 0.574421 2.3
 Zn Z = 30 HoffmannHuckelParameters.Zinc_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -12.41 1 2.01 $$U$$ = [9, 9] eV 4 1 -6.53 1 1.7 $$E_{VAC}$$ = 0.0 eV
 Ga Z = 31 HoffmannHuckelParameters.Gallium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -14.58 1 1.77 $$U$$ = [5.936, 5.936] eV 4 1 -6.75 1 1.55 $$E_{VAC}$$ = 0.0 eV
 Ge Z = 32 HoffmannHuckelParameters.Germanium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -16 1 2.16 $$U$$ = [6.608, 6.608] eV 4 1 -9 1 1.85 $$E_{VAC}$$ = 0.0 eV
 As Z = 33 HoffmannHuckelParameters.Arsenic_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -16.22 1 2.23 $$U$$ = [8.399, 8.399] eV 4 1 -12.16 1 1.89 $$E_{VAC}$$ = 0.0 eV
 Se Z = 34 HoffmannHuckelParameters.Selenium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -20.5 1 2.44 $$U$$ = [9.121, 9.121] eV 4 1 -14.4 1 2.07 $$E_{VAC}$$ = 0.0 eV
 Br Z = 35 HoffmannHuckelParameters.Bromine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -22.07 1 2.588 $$U$$ = [8.823, 8.823] eV 4 1 -13.1 1 2.131 $$E_{VAC}$$ = 0.0 eV
 Rb Z = 37 HoffmannHuckelParameters.Rubidium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -4.18 1 0.997 $$U$$ = [2.495, 2.495] eV 5 1 -2.6 1 0.997 $$E_{VAC}$$ = 0.0 eV
 Sr Z = 38 HoffmannHuckelParameters.Strontium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -6.62 1 1.214 $$U$$ = [9, 9] eV 5 1 -3.92 1 1.214 $$E_{VAC}$$ = 0.0 eV
 Zr Z = 40 HoffmannHuckelParameters.Zirconium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -9.87 1 1.817 $$U$$ = [9, 9, 9] eV 5 1 -6.76 1 1.776 $$E_{VAC}$$ = 0.0 eV 4 2 -11.18 0.622416 3.835 0.578216 1.505
 Nb Z = 41 HoffmannHuckelParameters.Niobium_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -10.1 1 1.89 $$U$$ = [9, 9, 9] eV 5 1 -6.86 1 1.85 $$E_{VAC}$$ = 0.0 eV 4 2 -12.1 0.640101 4.08 0.551601 1.64
 Mo Z = 42 HoffmannHuckelParameters.Molybdenum_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -8.34 1 1.96 $$U$$ = [9, 9, 9] eV 5 1 -5.24 1 1.9 $$E_{VAC}$$ = 0.0 eV 4 2 -10.5 0.589879 4.54 0.589879 1.9
 Tc Z = 43 HoffmannHuckelParameters.Technetium_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -10.07 1 2.018 $$U$$ = [9, 9, 9] eV 5 1 -5.4 1 1.984 $$E_{VAC}$$ = 0.0 eV 4 2 -12.82 0.5715 4.9 0.6012 2.094
 Ru Z = 44 HoffmannHuckelParameters.Ruthenium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -10.4 1 2.08 $$U$$ = [9, 9, 9] eV 5 1 -6.87 1 2.04 $$E_{VAC}$$ = 0.0 eV 4 2 -14.9 0.534242 5.38 0.636789 2.3
 Rh Z = 45 HoffmannHuckelParameters.Rhodium_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -8.09 1 2.135 $$U$$ = [9, 9, 9] eV 5 1 -4.57 1 2.1 $$E_{VAC}$$ = 0.0 eV 4 2 -12.5 0.580698 4.29 0.568498 1.97
 Pd Z = 46 HoffmannHuckelParameters.Palladium_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -7.32 1 2.19 $$U$$ = [9, 9, 9] eV 5 1 -3.75 1 2.152 $$E_{VAC}$$ = 0.0 eV 4 2 -12.02 0.526436 5.983 0.637334 2.613
 Cd Z = 48 HoffmannHuckelParameters.Cadmium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -11.8 1 1.64 $$U$$ = [9, 9] eV 5 1 -8.2 1 1.6 $$E_{VAC}$$ = 0.0 eV
 In Z = 49 HoffmannHuckelParameters.Indium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -12.6 1 1.903 $$U$$ = [5.53, 5.53] eV 5 1 -6.19 1 1.677 $$E_{VAC}$$ = 0.0 eV
 Sn Z = 50 HoffmannHuckelParameters.Tin_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -16.16 1 2.12 $$U$$ = [4.297, 4.297] eV 5 1 -8.32 1 1.82 $$E_{VAC}$$ = 0.0 eV
 Sb Z = 51 HoffmannHuckelParameters.Antimony_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -18.8 1 2.323 $$U$$ = [7.657, 7.657] eV 5 1 -11.7 1 1.999 $$E_{VAC}$$ = 0.0 eV
 Te Z = 52 HoffmannHuckelParameters.Tellurium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -20.8 1 2.51 $$U$$ = [8.985, 8.985] eV 5 1 -14.8 1 2.16 $$E_{VAC}$$ = 0.0 eV
 I Z = 53 HoffmannHuckelParameters.Iodine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -18 1 2.679 $$U$$ = [9.448, 9.448] eV 5 1 -12.7 1 2.322 $$E_{VAC}$$ = 0.0 eV
 Cs Z = 55 HoffmannHuckelParameters.Caesium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -3.88 1 1.06 $$U$$ = [9, 9] eV 6 1 -2.49 1 1.06 $$E_{VAC}$$ = 0.0 eV
 La Z = 57 HoffmannHuckelParameters.Lanthanum_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -7.67 1 2.14 $$U$$ = [9, 9, 9] eV 6 1 -5.01 1 2.08 $$E_{VAC}$$ = 0.0 eV 5 2 -8.21 0.776515 3.78 0.458609 1.381
 Ce Z = 58 HoffmannHuckelParameters.Cerium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.97 1 1.799 $$U$$ = [9, 9, 9, 9] eV 6 1 -4.97 1 1.799 $$E_{VAC}$$ = 0.0 eV 5 2 -6.43 1 2.747 4 3 -11.28 1 3.907
 Sm Z = 62 HoffmannHuckelParameters.Samarium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.86 1 1.4 $$U$$ = [9, 9, 9, 9] eV 6 1 -4.86 1 1.4 $$E_{VAC}$$ = 0.0 eV 5 2 -6.06 0.718435 2.747 0.444722 1.267 4 3 -11.28 0.735406 6.907 0.459703 2.639
 Gd Z = 64 HoffmannHuckelParameters.Gadolinium_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -5.44 1 1.369 $$U$$ = [9, 9, 9] eV 5 2 -6.06 0.718435 2.747 0.444722 1.267 $$E_{VAC}$$ = 0.0 eV 4 3 -11.28 0.735406 6.907 0.459703 2.639
 Yb Z = 70 HoffmannHuckelParameters.Ytterbium_Basis $$N_V$$ = 16.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -5.35 1 1.54 $$U$$ = [9, 9, 9, 9] eV 6 1 -5.35 1 1.54 $$E_{VAC}$$ = 0.0 eV 5 2 -5.21 0.706344 2.81 0.48343 1.216 4 3 -13.86 0.746226 8.629 0.456538 3.198
 Lu Z = 71 HoffmannHuckelParameters.Lutetium_Basis $$N_V$$ = 17.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -6.05 1 1.666 $$U$$ = [9, 9, 9, 9] eV 6 1 -6.05 1 1.666 $$E_{VAC}$$ = 0.0 eV 5 2 -5.12 0.704411 2.813 0.488008 1.21 4 3 -22.4 0.733001 9.136 0.445901 3.666
 Ta Z = 73 HoffmannHuckelParameters.Tantalum_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -10.1 1 2.28 $$U$$ = [9, 9, 9] eV 6 1 -6.86 1 2.241 $$E_{VAC}$$ = 0.0 eV 5 2 -12.1 0.610612 4.762 0.610612 1.938
 W Z = 74 HoffmannHuckelParameters.Tungsten_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -8.26 1 2.341 $$U$$ = [9, 9, 9] eV 6 1 -5.17 1 2.309 $$E_{VAC}$$ = 0.0 eV 5 2 -10.37 0.668535 4.982 0.542438 2.068
 Re Z = 75 HoffmannHuckelParameters.Rhenium_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -9.36 1 2.398 $$U$$ = [9, 9, 9] eV 6 1 -5.96 1 2.372 $$E_{VAC}$$ = 0.0 eV 5 2 -12.66 0.637752 5.343 0.565763 2.277
 Os Z = 76 HoffmannHuckelParameters.Osmium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -8.17 1 2.452 $$U$$ = [9, 9, 9] eV 6 1 -4.81 1 2.429 $$E_{VAC}$$ = 0.0 eV 5 2 -11.84 0.637195 5.571 0.559795 2.416
 Ir Z = 77 HoffmannHuckelParameters.Iridium_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -11.36 1 2.5 $$U$$ = [9, 9, 9] eV 6 1 -4.5 1 2.2 $$E_{VAC}$$ = 0.0 eV 5 2 -12.17 0.635059 5.796 0.555605 2.557
 Pt Z = 78 HoffmannHuckelParameters.Platinum_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -9.077 1 2.554 $$U$$ = [8.604, 8.604, 8.604] eV 6 1 -5.475 1 2.554 $$E_{VAC}$$ = 0.0 eV 5 2 -12.59 0.633378 6.013 0.551281 2.696
 Au Z = 79 HoffmannHuckelParameters.Gold_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -10.92 1 2.602 $$U$$ = [8.604, 8.604, 8.604] eV 6 1 -5.55 1 2.584 $$E_{VAC}$$ = 0.0 eV 5 2 -15.07 0.644177 6.163 0.535576 2.794
 Hg Z = 80 HoffmannHuckelParameters.Mercury_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -13.68 1 2.649 $$U$$ = [9, 9, 9] eV 6 1 -8.47 1 2.631 $$E_{VAC}$$ = 0.0 eV 5 2 -17.5 0.643776 6.436 0.521481 3.032
 Tl Z = 81 HoffmannHuckelParameters.Thallium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -11.6 1 2.3 $$U$$ = [9, 9] eV 6 1 -5.8 1 1.6 $$E_{VAC}$$ = 0.0 eV
 Pb Z = 82 HoffmannHuckelParameters.Lead_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -15.7 1 2.35 $$U$$ = [9, 9] eV 6 1 -8 1 2.06 $$E_{VAC}$$ = 0.0 eV
 Bi Z = 83 HoffmannHuckelParameters.Bismuth_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -15.19 1 2.56 $$U$$ = [9, 9] eV 6 1 -7.79 1 2.072 $$E_{VAC}$$ = 0.0 eV
 Th Z = 90 HoffmannHuckelParameters.Thorium_Basis $$N_V$$ = 0.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 3 -9.64 0.768182 4.477 0.42669 1.837 $$U$$ = [9, 9, 9, 9, 9] eV 7 0 -5.39 1 1.834 $$E_{VAC}$$ = 0.0 eV 7 1 -5.39 1 1.834 6 2 -10.11 0.761171 2.461 0.407085 1.165 5 3 -9.64 0.768182 4.477 0.42669 1.837
 U Z = 92 HoffmannHuckelParameters.Uranium_Basis $$N_V$$ = 0.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.5 1 1.914 $$U$$ = [9, 9, 9, 9] eV 7 1 -5.5 1 1.914 $$E_{VAC}$$ = 0.0 eV 6 2 -9.19 0.760793 2.581 0.412596 1.207 5 3 -10.62 0.784411 4.943 0.390806 2.106

#### Cerda Hückel basis set parameters¶

The Cerda Hückel basis set parameters. The unit of $$E^\rm{ion}$$ is eV, while the units of $$w_i$$ and $$\eta_i$$ are Bohr$$^{-3/2}$$ and Bohr$$^{-1}$$, respectively.

 H Z = 1 MullerHuckelParameters.Hydrogen_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 1 0 -13.606 1 1 $$U$$ = [12.848] eV $$E_{VAC}$$ = 0.0 eV
 He Z = 2 MullerHuckelParameters.Helium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 1 0 -24.979 1 1.618 $$U$$ = [9] eV $$E_{VAC}$$ = 0.0 eV
 Li Z = 3 MullerHuckelParameters.Lithium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -5.342 1 0.645 $$U$$ = [3.469, 3.469] eV 2 1 -3.499 1 0.524 $$E_{VAC}$$ = 0.0 eV
 Be Z = 4 MullerHuckelParameters.Beryllium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -8.416 1 0.944 $$U$$ = [5.935, 5.935] eV 2 1 -5.632 1 0.875 $$E_{VAC}$$ = 0.0 eV
 B Z = 5 MullerHuckelParameters.Boron_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -13.462 1 1.265 $$U$$ = [8, 8] eV 2 1 -8.432 1 1.134 $$E_{VAC}$$ = 0.0 eV
 C Z = 6 MullerHuckelParameters.Carbon_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -19.376 1 1.576 $$U$$ = [10.207, 10.207] eV 2 1 -11.072 1 1.435 $$E_{VAC}$$ = 0.0 eV
 N Z = 7 MullerHuckelParameters.Nitrogen_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -26.223 1 1.885 $$U$$ = [11.052, 11.052] eV 2 1 -13.841 1 1.728 $$E_{VAC}$$ = 0.0 eV
 O Z = 8 MullerHuckelParameters.Oxygen_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -34.024 1 2.192 $$U$$ = [13.625, 13.625] eV 2 1 -16.768 1 2.018 $$E_{VAC}$$ = 0.0 eV
 F Z = 9 MullerHuckelParameters.Fluorine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -42.791 1 2.497 $$U$$ = [15.054, 15.054] eV 2 1 -19.865 1 2.305 $$E_{VAC}$$ = 0.0 eV
 Ne Z = 10 MullerHuckelParameters.Neon_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 2 0 -52.529 1 2.802 $$U$$ = [9, 9] eV 2 1 -23.141 1 2.59 $$E_{VAC}$$ = 0.0 eV
 Na Z = 11 MullerHuckelParameters.Sodium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -4.955 1 0.832 $$U$$ = [2.982, 2.982] eV 3 1 -2.976 1 0.611 $$E_{VAC}$$ = 0.0 eV
 Mg Z = 12 MullerHuckelParameters.Magnesium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -6.886 1 1.076 $$U$$ = [4.623, 4.623] eV 3 1 -4.169 1 0.862 $$E_{VAC}$$ = 0.0 eV
 Al Z = 13 MullerHuckelParameters.Aluminium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -10.706 1 1.347 $$U$$ = [5.682, 5.682] eV 3 1 -5.713 1 1.019 $$E_{VAC}$$ = 0.0 eV
 Si Z = 14 MullerHuckelParameters.Silicon_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -14.792 1 1.588 $$U$$ = [6.964, 6.964] eV 3 1 -7.585 1 1.256 $$E_{VAC}$$ = 0.0 eV
 P Z = 15 MullerHuckelParameters.Phosphorus_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -19.221 1 1.816 $$U$$ = [9.878, 9.878] eV 3 1 -9.539 1 1.478 $$E_{VAC}$$ = 0.0 eV
 S Z = 16 MullerHuckelParameters.Sulfur_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -24.019 1 2.035 $$U$$ = [9.205, 9.205] eV 3 1 -11.601 1 1.691 $$E_{VAC}$$ = 0.0 eV
 Cl Z = 17 MullerHuckelParameters.Chlorine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -29.196 1 2.25 $$U$$ = [10.292, 10.292] eV 3 1 -13.78 1 1.9 $$E_{VAC}$$ = 0.0 eV
 Ar Z = 18 MullerHuckelParameters.Argon_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 3 0 -34.759 1 2.461 $$U$$ = [9, 9] eV 3 1 -16.083 1 2.105 $$E_{VAC}$$ = 0.0 eV
 K Z = 19 MullerHuckelParameters.Potassium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -4.013 1 0.858 $$U$$ = [3.702, 3.702, 3.702] eV 4 1 -2.599 1 0.671 $$E_{VAC}$$ = 0.0 eV 3 2 -1.581 1 0.364
 Ca Z = 20 MullerHuckelParameters.Calcium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -5.321 1 1.067 $$U$$ = [9, 9, 9] eV 4 1 -3.573 1 0.893 $$E_{VAC}$$ = 0.0 eV 3 2 -3.337 1 1.906
 Sc Z = 21 MullerHuckelParameters.Scandium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -5.717 1 1.136 $$U$$ = [9, 9, 9] eV 4 1 -3.739 1 0.951 $$E_{VAC}$$ = 0.0 eV 3 2 -9.353 0.4599 3.807 0.701847 1.455
 Ti Z = 22 MullerHuckelParameters.Titanium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -6.039 1 1.195 $$U$$ = [9, 9, 9] eV 4 1 -3.863 1 0.998 $$E_{VAC}$$ = 0.0 eV 3 2 -11.043 0.468935 4.218 0.685904 1.664
 V Z = 23 MullerHuckelParameters.Vanadium_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -6.325 1 1.248 $$U$$ = [9, 9, 9] eV 4 1 -3.963 1 1.041 $$E_{VAC}$$ = 0.0 eV 3 2 -12.549 0.474002 4.6 0.677004 1.846
 Cr Z = 24 MullerHuckelParameters.Chromium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -6.583 1 1.296 $$U$$ = [9, 9, 9] eV 4 1 -4.042 1 1.077 $$E_{VAC}$$ = 0.0 eV 3 2 -13.909 0.474986 4.978 0.67298 2.022
 Mn Z = 25 MullerHuckelParameters.Manganese_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -6.84 1 1.344 $$U$$ = [9, 9, 9] eV 4 1 -4.12 1 1.113 $$E_{VAC}$$ = 0.0 eV 3 2 -15.27 0.480857 5.318 0.665802 2.176
 Fe Z = 26 MullerHuckelParameters.Iron_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -7.079 1 1.388 $$U$$ = [9, 9, 9] eV 4 1 -4.183 1 1.145 $$E_{VAC}$$ = 0.0 eV 3 2 -16.541 0.484872 5.653 0.660825 2.325
 Co Z = 27 MullerHuckelParameters.Cobalt_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -7.309 1 1.431 $$U$$ = [9, 9, 9] eV 4 1 -4.237 1 1.174 $$E_{VAC}$$ = 0.0 eV 3 2 -17.77 0.485886 5.996 0.658846 2.476
 Ni Z = 28 MullerHuckelParameters.Nickel_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -7.532 1 1.473 $$U$$ = [9, 9, 9] eV 4 1 -4.284 1 1.203 $$E_{VAC}$$ = 0.0 eV 3 2 -18.969 0.486001 6.339 0.658001 2.625
 Cu Z = 29 MullerHuckelParameters.Copper_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -7.755 1 1.515 $$U$$ = [9, 9, 9] eV 4 1 -4.331 1 1.232 $$E_{VAC}$$ = 0.0 eV 3 2 -20.188 0.486895 6.676 0.656859 2.768
 Zn Z = 30 MullerHuckelParameters.Zinc_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -7.96 1 1.553 $$U$$ = [9, 9, 9] eV 4 1 -4.361 1 1.251 $$E_{VAC}$$ = 0.0 eV 3 2 -21.294 0.48724 7.015 0.656323 2.911
 Ga Z = 31 MullerHuckelParameters.Gallium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -11.554 1 1.808 $$U$$ = [5.936, 5.936] eV 4 1 -5.674 1 1.314 $$E_{VAC}$$ = 0.0 eV
 Ge Z = 32 MullerHuckelParameters.Germanium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -15.158 1 2.024 $$U$$ = [6.608, 6.608] eV 4 1 -7.329 1 1.55 $$E_{VAC}$$ = 0.0 eV
 As Z = 33 MullerHuckelParameters.Arsenic_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -18.916 1 2.222 $$U$$ = [8.399, 8.399] eV 4 1 -8.984 1 1.757 $$E_{VAC}$$ = 0.0 eV
 Se Z = 34 MullerHuckelParameters.Selenium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -22.862 1 2.409 $$U$$ = [9.121, 9.121] eV 4 1 -10.681 1 1.949 $$E_{VAC}$$ = 0.0 eV
 Br Z = 35 MullerHuckelParameters.Bromine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -27.013 1 2.588 $$U$$ = [8.823, 8.823] eV 4 1 -12.438 1 2.131 $$E_{VAC}$$ = 0.0 eV
 Kr Z = 36 MullerHuckelParameters.Krypton_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 4 0 -31.373 1 2.762 $$U$$ = [9, 9] eV 4 1 -14.264 1 2.306 $$E_{VAC}$$ = 0.0 eV
 Rb Z = 37 MullerHuckelParameters.Rubidium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -3.752 1 0.977 $$U$$ = [2.495, 2.495, 2.495] eV 5 1 -2.452 1 0.774 $$E_{VAC}$$ = 0.0 eV 4 2 -1.636 1 0.523
 Sr Z = 38 MullerHuckelParameters.Strontium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -4.856 1 1.187 $$U$$ = [9, 9, 9] eV 5 1 -3.299 1 1 $$E_{VAC}$$ = 0.0 eV 4 2 -3.179 1 1.694
 Y Z = 39 MullerHuckelParameters.Yttrium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -5.337 1 1.279 $$U$$ = [9, 9, 9] eV 5 1 -3.515 1 1.079 $$E_{VAC}$$ = 0.0 eV 4 2 -6.799 0.601963 2.554 0.577964 1.068
 Zr Z = 40 MullerHuckelParameters.Zirconium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -5.735 1 1.36 $$U$$ = [9, 9, 9] eV 5 1 -3.694 1 1.151 $$E_{VAC}$$ = 0.0 eV 4 2 -8.461 0.650366 2.769 0.508286 1.224
 Nb Z = 41 MullerHuckelParameters.Niobium_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -5.923 1 1.403 $$U$$ = [9, 9, 9] eV 5 1 -3.757 1 1.186 $$E_{VAC}$$ = 0.0 eV 4 2 -10.001 0.685854 2.955 0.461902 1.333
 Mo Z = 42 MullerHuckelParameters.Molybdenum_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -6.112 1 1.446 $$U$$ = [9, 9, 9] eV 5 1 -3.819 1 1.221 $$E_{VAC}$$ = 0.0 eV 4 2 -11.541 0.71711 3.126 0.426065 1.408
 Tc Z = 43 MullerHuckelParameters.Technetium_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -6.3 1 1.49 $$U$$ = [9, 9, 9] eV 5 1 -3.882 1 1.256 $$E_{VAC}$$ = 0.0 eV 4 2 -13.08 0.742534 3.293 0.39875 1.468
 Ru Z = 44 MullerHuckelParameters.Ruthenium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -6.488 1 1.533 $$U$$ = [9, 9, 9] eV 5 1 -3.945 1 1.291 $$E_{VAC}$$ = 0.0 eV 4 2 -14.62 0.779822 3.429 0.367916 1.453
 Rh Z = 45 MullerHuckelParameters.Rhodium_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -6.677 1 1.576 $$U$$ = [9, 9, 9] eV 5 1 -4.008 1 1.326 $$E_{VAC}$$ = 0.0 eV 4 2 -16.16 0.80486 3.577 0.347939 1.452
 Pd Z = 46 MullerHuckelParameters.Palladium_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -6.865 1 1.619 $$U$$ = [9, 9, 9] eV 5 1 -4.07 1 1.362 $$E_{VAC}$$ = 0.0 eV 4 2 -17.7 0.814894 3.746 0.337956 1.501
 Ag Z = 47 MullerHuckelParameters.Silver_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -7.054 1 1.662 $$U$$ = [9, 9, 9] eV 5 1 -4.133 1 1.397 $$E_{VAC}$$ = 0.0 eV 4 2 -19.24 0.824441 3.912 0.328777 1.545
 Cd Z = 48 MullerHuckelParameters.Cadmium_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -7.242 1 1.706 $$U$$ = [9, 9, 9] eV 5 1 -4.196 1 1.432 $$E_{VAC}$$ = 0.0 eV 4 2 -20.78 0.823957 4.094 0.324983 1.64
 In Z = 49 MullerHuckelParameters.Indium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -10.141 1 1.934 $$U$$ = [5.53, 5.53] eV 5 1 -5.368 1 1.456 $$E_{VAC}$$ = 0.0 eV
 Sn Z = 50 MullerHuckelParameters.Tin_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -13.043 1 2.129 $$U$$ = [4.297, 4.297] eV 5 1 -6.764 1 1.674 $$E_{VAC}$$ = 0.0 eV
 Sb Z = 51 MullerHuckelParameters.Antimony_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -16.026 1 2.305 $$U$$ = [7.657, 7.657] eV 5 1 -8.143 1 1.863 $$E_{VAC}$$ = 0.0 eV
 Te Z = 52 MullerHuckelParameters.Tellurium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -19.122 1 2.47 $$U$$ = [8.985, 8.985] eV 5 1 -9.54 1 2.036 $$E_{VAC}$$ = 0.0 eV
 I Z = 53 MullerHuckelParameters.Iodine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -22.344 1 2.626 $$U$$ = [9.448, 9.448] eV 5 1 -10.971 1 2.198 $$E_{VAC}$$ = 0.0 eV
 Xe Z = 54 MullerHuckelParameters.Xenon_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 5 0 -25.699 1 2.776 $$U$$ = [9, 9] eV 5 1 -12.444 1 2.352 $$E_{VAC}$$ = 0.0 eV
 Cs Z = 55 MullerHuckelParameters.Caesium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -3.365 1 1.031 $$U$$ = [9, 9, 9] eV 6 1 -2.286 1 0.845 $$E_{VAC}$$ = 0.0 eV 5 2 -1.844 1 0.906
 Ba Z = 56 MullerHuckelParameters.Barium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.287 1 1.236 $$U$$ = [9, 9, 9] eV 6 1 -3.063 1 1.071 $$E_{VAC}$$ = 0.0 eV 5 2 -4.143 1 1.96
 La Z = 57 MullerHuckelParameters.Lanthanum_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.637 1 1.318 $$U$$ = [9, 9, 9] eV 6 1 -3.233 1 1.142 $$E_{VAC}$$ = 0.0 eV 5 2 -7.316 0.593989 3.153 0.611989 1.338
 Ce Z = 58 MullerHuckelParameters.Cerium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.697 1 1.335 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.261 1 1.157 $$E_{VAC}$$ = 0.0 eV 5 2 -7.359 1 2.027 4 3 -11.95 1 4.22
 Pr Z = 59 MullerHuckelParameters.Praseodymium_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.466 1 1.288 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.29 1 1.127 $$E_{VAC}$$ = 0.0 eV 5 2 -7.376 1 2.055 4 3 -12.94 1 4.415
 Nd Z = 60 MullerHuckelParameters.Neodymium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.518 1 1.303 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.318 1 1.187 $$E_{VAC}$$ = 0.0 eV 5 2 -7.373 1 2.08 4 3 -13.892 1 4.619
 Pm Z = 61 MullerHuckelParameters.Promethium_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.586 1 1.317 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.346 1 1.201 $$E_{VAC}$$ = 0.0 eV 5 2 -7.353 1 2.103 4 3 -14.901 1 4.81
 Sm Z = 62 MullerHuckelParameters.Samarium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.616 1 1.331 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.375 1 1.216 $$E_{VAC}$$ = 0.0 eV 5 2 -7.32 1 2.122 4 3 -15.719 1 4.991
 Eu Z = 63 MullerHuckelParameters.Europium_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.663 1 1.345 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.403 1 1.231 $$E_{VAC}$$ = 0.0 eV 5 2 -7.276 1 2.14 4 3 -16.451 1 5.165
 Gd Z = 64 MullerHuckelParameters.Gadolinium_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -5.033 1 1.427 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.431 1 1.246 $$E_{VAC}$$ = 0.0 eV 5 2 -7.22 1 2.155 4 3 -17.079 1 5.33
 Tb Z = 65 MullerHuckelParameters.Terbium_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.753 1 1.371 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.46 1 1.261 $$E_{VAC}$$ = 0.0 eV 5 2 -7.156 1 2.169 4 3 -17.707 1 5.495
 Dy Z = 66 MullerHuckelParameters.Dysprosium_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.797 1 1.383 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.488 1 1.276 $$E_{VAC}$$ = 0.0 eV 5 2 -7.084 1 2.181 4 3 -18.246 1 5.654
 Ho Z = 67 MullerHuckelParameters.Holmium_Basis $$N_V$$ = 13.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.84 1 1.396 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.516 1 1.291 $$E_{VAC}$$ = 0.0 eV 5 2 -7.004 1 2.19 4 3 -18.733 1 5.808
 Er Z = 68 MullerHuckelParameters.Erbium_Basis $$N_V$$ = 14.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.882 1 1.408 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.545 1 1.306 $$E_{VAC}$$ = 0.0 eV 5 2 -6.917 1 2.199 4 3 -19.174 1 5.96
 Tm Z = 69 MullerHuckelParameters.Thulium_Basis $$N_V$$ = 15.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.924 1 1.42 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.573 1 1.32 $$E_{VAC}$$ = 0.0 eV 5 2 -6.824 1 2.205 4 3 -19.571 1 6.109
 Yb Z = 70 MullerHuckelParameters.Ytterbium_Basis $$N_V$$ = 16.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -4.965 1 1.432 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.601 1 1.335 $$E_{VAC}$$ = 0.0 eV 5 2 -6.726 1 2.21 4 3 -19.929 1 6.256
 Lu Z = 71 MullerHuckelParameters.Lutetium_Basis $$N_V$$ = 17.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -5.411 1 1.526 $$U$$ = [9, 9, 9, 9] eV 6 1 -3.63 1 1.35 $$E_{VAC}$$ = 0.0 eV 5 2 -6.622 1 2.213 4 3 -20.313 1 6.404
 Hf Z = 72 MullerHuckelParameters.Hafnium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -5.725 1 1.598 $$U$$ = [9, 9, 9] eV 6 1 -3.658 1 1.365 $$E_{VAC}$$ = 0.0 eV 5 2 -8.141 0.636594 3.337 0.545652 1.505
 Ta Z = 73 MullerHuckelParameters.Tantalum_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -5.979 1 1.658 $$U$$ = [9, 9, 9] eV 6 1 -3.757 1 1.417 $$E_{VAC}$$ = 0.0 eV 5 2 -9.569 0.673894 3.478 0.495922 1.606
 W Z = 74 MullerHuckelParameters.Tungsten_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -6.196 1 1.711 $$U$$ = [9, 9, 9] eV 6 1 -3.836 1 1.463 $$E_{VAC}$$ = 0.0 eV 5 2 -10.963 0.705262 3.609 0.456169 1.683
 Re Z = 75 MullerHuckelParameters.Rhenium_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -6.386 1 1.76 $$U$$ = [9, 9, 9] eV 6 1 -3.902 1 1.503 $$E_{VAC}$$ = 0.0 eV 5 2 -12.348 0.732016 3.734 0.424009 1.742
 Os Z = 76 MullerHuckelParameters.Osmium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -6.556 1 1.804 $$U$$ = [9, 9, 9] eV 6 1 -3.958 1 1.54 $$E_{VAC}$$ = 0.0 eV 5 2 -13.737 0.757831 3.851 0.394912 1.782
 Ir Z = 77 MullerHuckelParameters.Iridium_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -6.71 1 1.845 $$U$$ = [9, 9, 9] eV 6 1 -4.006 1 1.574 $$E_{VAC}$$ = 0.0 eV 5 2 -15.136 0.779917 3.968 0.37096 1.813
 Pt Z = 78 MullerHuckelParameters.Platinum_Basis $$N_V$$ = 10.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -6.875 1 1.888 $$U$$ = [8.604, 8.604, 8.604] eV 6 1 -4.034 1 1.593 $$E_{VAC}$$ = 0.0 eV 5 2 -16.528 0.79785 4.084 0.351934 1.84
 Au Z = 79 MullerHuckelParameters.Gold_Basis $$N_V$$ = 11.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -7.037 1 1.931 $$U$$ = [8.604, 8.604, 8.604] eV 6 1 -4.068 1 1.615 $$E_{VAC}$$ = 0.0 eV 5 2 -17.922 0.813667 4.2 0.335863 1.861
 Hg Z = 80 MullerHuckelParameters.Mercury_Basis $$N_V$$ = 12.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -7.104 1 1.953 $$U$$ = [9, 9, 9] eV 6 1 -4.117 1 1.66 $$E_{VAC}$$ = 0.0 eV 5 2 -19.434 0.809955 4.353 0.331981 1.979
 Tl Z = 81 MullerHuckelParameters.Thallium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -9.827 1 2.191 $$U$$ = [9, 9] eV 6 1 -5.235 1 1.656 $$E_{VAC}$$ = 0.0 eV
 Pb Z = 82 MullerHuckelParameters.Lead_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -12.486 1 2.386 $$U$$ = [9, 9] eV 6 1 -6.527 1 1.88 $$E_{VAC}$$ = 0.0 eV
 Bi Z = 83 MullerHuckelParameters.Bismuth_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -15.189 1 2.56 $$U$$ = [9, 9] eV 6 1 -7.788 1 2.072 $$E_{VAC}$$ = 0.0 eV
 Po Z = 84 MullerHuckelParameters.Polonium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -17.965 1 2.72 $$U$$ = [9, 9] eV 6 1 -9.053 1 2.245 $$E_{VAC}$$ = 0.0 eV
 At Z = 85 MullerHuckelParameters.Astatine_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -20.827 1 2.87 $$U$$ = [9, 9] eV 6 1 -10.337 1 2.45 $$E_{VAC}$$ = 0.0 eV
 Rn Z = 86 MullerHuckelParameters.Radon_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 6 0 -23.783 1 3.014 $$U$$ = [9, 9] eV 6 1 -11.647 1 2.556 $$E_{VAC}$$ = 0.0 eV
 Fr Z = 87 MullerHuckelParameters.Francium_Basis $$N_V$$ = 1.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -3.209 1 1.131 $$U$$ = [9, 9, 9] eV 7 1 -2.205 1 0.939 $$E_{VAC}$$ = 0.0 eV 6 2 -1.931 1 1.258
 Ra Z = 88 MullerHuckelParameters.Radium_Basis $$N_V$$ = 2.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -4.048 1 1.346 $$U$$ = [9, 9, 9] eV 7 1 -2.934 1 1.177 $$E_{VAC}$$ = 0.0 eV 6 2 -4.108 1 2.113
 Ac Z = 89 MullerHuckelParameters.Actinium_Basis $$N_V$$ = 3.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -4.381 1 1.433 $$U$$ = [9, 9, 9] eV 7 1 -3.098 1 1.253 $$E_{VAC}$$ = 0.0 eV 6 2 -6.843 1 2.12
 Th Z = 90 MullerHuckelParameters.Thorium_Basis $$N_V$$ = 4.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.31 1 1.742 $$U$$ = [9, 9, 9, 9] eV 7 1 -3.345 1 1.256 $$E_{VAC}$$ = 0.0 eV 6 2 -4.98 0.624003 2.811 0.503002 1.554 5 3 -6.03 0.58187 5.475 0.547877 2.863
 Pa Z = 91 MullerHuckelParameters.Protactinium_Basis $$N_V$$ = 5.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.41 1 1.699 $$U$$ = [9, 9, 9, 9] eV 7 1 -3.375 1 1.286 $$E_{VAC}$$ = 0.0 eV 6 2 -5.07 0.617317 2.894 0.511263 1.595 5 3 -7.63 0.594817 5.659 0.530836 2.991
 U Z = 92 MullerHuckelParameters.Uranium_Basis $$N_V$$ = 6.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.51 1 1.728 $$U$$ = [9, 9, 9, 9] eV 7 1 -3.406 1 1.315 $$E_{VAC}$$ = 0.0 eV 6 2 -5.1 0.622063 2.944 0.509052 1.611 5 3 -9.045 0.592502 5.885 0.530449 3.135
 Np Z = 93 MullerHuckelParameters.Neptunium_Basis $$N_V$$ = 7.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.61 1 1.756 $$U$$ = [9, 9, 9, 9] eV 7 1 -3.436 1 1.345 $$E_{VAC}$$ = 0.0 eV 6 2 -5.095 0.615803 3.017 0.516835 1.646 5 3 -10.35 0.519698 3.254 0.600651 6.068
 Pu Z = 94 MullerHuckelParameters.Plutonium_Basis $$N_V$$ = 8.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.71 1 1.681 $$U$$ = [9, 9, 9, 9] eV 7 1 -3.467 1 1.375 $$E_{VAC}$$ = 0.0 eV 6 2 -5.06 0.609204 3.085 0.525176 1.677 5 3 -11.585 0.509646 3.364 0.608577 6.241
 Am Z = 95 MullerHuckelParameters.Americium_Basis $$N_V$$ = 9.0 n l $$E_{ion}$$ $$W_1$$ $$\eta_1$$ $$W_2$$ $$\eta_2$$ $$\beta$$ = 1.75 7 0 -5.8 1 1.704 $$U$$ = [9, 9, 9, 9] eV 7 1 -3.497 1 1.405 $$E_{VAC}$$ = 0.0 eV 6 2 -5.01 0.596362 3.169 0.539327 1.719 5 3 -12.75 0.496199 3.457 0.620249 6.392


text:
# Problem

Given three positive integers $B, P$ and $M$, find the value of $B^P \mod M$.

For example, $B=2$, $P=5$ and $M=7$, then $B^P \mod M = 2^5 \mod 7 = 32 \mod 7 = 4$.

This problem is known as [ref1] Modular Exponentiation. In order to solve this problem, we need to have basic knowledge about [ref2] Modular Arithmetic.

# Brute Force – Linear Solution $O(P)$

As usual, we first start off with a naive solution. We can calculate the value of $B^P \mod M$ in $O(P)$ time by running a loop from $1$ to $P$ and multiplying $B$ to result.

int bigmodLinear ( int b, int p, int m ) {
int res = 1 % m;
b = b % m;
for ( int i = 1; i <= p; i++ ) {
res = ( res * b ) % m;
}
return res;
}

A simple solution which will work as long as the value of $P$ is small enough. But for large values of $P$, for example, $P > 10^9$, this code will time out. Also note that in line $2$, I wrote $res = 1 \mod m$. Some people tend to write $res = 1$. This will produce a wrong result when the value of $P$ is $0$ and value of $M$ is $1$.

# Divide and Conquer Approach - $O(log_2(P) )$

According to [ref3] Wiki,

A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same (or related) type (divide), until these become simple enough to be solved directly (conquer).

That is, instead of solving the big problem $B^P \mod M$, we will solve smaller problems of similar kind and merge them to get the answer to the big problem.

So how do we apply this D&C (Divide and Conquer) idea?

Suppose we are trying to find the value of $B^P$. Then three thing can happen.

1. Value of P is 0 ( Base Case ): $B^0$ is $1$. This will be the base case of our recursion function. Once we reach this state, we no longer divide the problem into smaller parts.
2. Value of P is Even: Since $P$ is even, we can say that $B^P = B^{\frac{P}{2}} \times B^{\frac{P}{2}}$. For example, $2^{32} = 2^{16} \times 2^{16}$, $3^6 = 3^3 \times 3^3$. Therefore, instead of calculating the value of $x = B^P$, if we find the value of $y = B^{\frac{P}{2}}$, then we can get the value of $x$ as $x = y \times y$.
3. Value of P is Odd: In this case we can simply say that $B^P = B \times B^{P-1}$.

Using these three states, we are can formulate a D&C code.

int bigmodRecur ( int b, int p, int m ) {
if ( p == 0 ) return 1%m; // Base Case

if ( p % 2 == 0 ) { // p is even
int y = bigmodRecur ( b, p / 2, m );
return ( y * y ) % m; // b^p = y * y
}
else {
// b^p = b * b^(p-1)
return ( b * bigmodRecur ( b, p - 1, m ) ) % m;
}
}

In line $2$, we have the base case. We return $1 \mod m$ in case value of $m$ is $1$. Next on line $4$ we check if $p$ is even or not. If it is even, we calculate $A^{\frac{P}{2}}$ and return after squaring it. In line $8$, we handle the case when $P$ is odd.

At each step we either divide $P$ by $2$ or subtract $1$ from $P$ and then divide it by $2$. Therefore, there can be at most $2 \times log_2(P)$ steps in D&C approach. Hence complexity is $O(log_2(P) )$.

# A Better Solution

A better solution to this problem exists. By using the Repeated Squaring algorithm, we can find the Modular Exponentiation faster than D&C. Repeated Squaring Algorithm has the same complexity as D&C, but it is iterative, thus does not suffer from recursion overhead.

We need to know about bitwise operations before we learn Repeated Squaring algorithm. Since we did not cover this topic yet, I won't write about this approach now. Hopefully, once we cover bitwise operations I will write another post

# Resource

1. Wikipedia - Modular Exponentiation
2. forthright48 - Introduction to Modular Arithmetic
3. Wikipedia - Divide and conquer algorithms
4. forthright48 - Introduction to Number Systems