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the knowledge of the formation energy of solid surfaces is of obvious importance for surface physics and technology . given the difficulties of a direct measurement of the surface energy , accurate calculations @xcite of this quantity play a relevant role in surface science .
the standard method for calculating the surface energy @xmath0 is to evaluate the total energy of a slab of the material of interest ( generally with a thickness between 5 to 15 layers ) and to subtract from that the bulk energy obtained from a separate calculation .
this procedure singles out the total energy contribution due to the presence of the surface .
it is based on the general and intuitively appealing expression @xmath1 with @xmath2 the total energy of a @xmath3-layer slab and @xmath4 the bulk total energy ; the limit is approximated in practice by the @xmath3th term .
the factor of 1/2 accounts for the two surfaces of the slab .
a central but often underestimated problem with this approach is what value should be chosen for the bulk energy . while at first sight this point might be dismissed as irrelevant , in a recent paper@xcite boettger pointed out that any difference between @xmath4 and the change in @xmath5 with slab thickness will cause the calculated surface energy to diverge linearly with @xmath3 .
thus , increasing the slab thickness _ must _ sooner or later lead to unacceptable results , because the bulk energy from a separate calculation will never exactly equal the slope of the slab energy vs @xmath3 .    in ref .
, severe errors incurred by this standard approach were reported .
their unusual magnitude was presumably due to a technical matter , namely the use of two completely different methods for calculating the bulk and surface properties .
thus , the practical importance of the divergent behavior of the surface energy remains unassessed for state - of - the - art methods , which carefully treat bulk and slab systems in the same way .
the aim of this paper is to supply such an assessment .
in particular , the natural objection to boettger s argument would be that , when using the same calculational method in a technically consistent way to obtain both bulk and slab quantities , this problem would simply not show up .
we show in this paper that this is not the case : the proper choice of the bulk energy according to boettger s principle is an important issue in surface energy calculations even when the bulk and slab systems are handled consistently within accurate methods such as fp - lmto , pseudopotentials - plane waves , or such .
further , we compare different approaches to remedy the problem , presenting what seems to be the best solution . as modern calculations advance to study more subtle surface effects and employ thicker slabs , these results will become increasingly relevant .
in this section we present _ ab initio _ surface calculations demonstrating that the surface energy is not only formally , but also practically divergent for accurate calculations . to this end , we compare results obtained by the standard approach with those calculated using an alternative procedure suggested by boettger @xcite and with a modified approach to be described below .
it will become clear that the latter method is the most reliable by a wide margin and should be prefered for high - accuracy applications .      for the standard methods , we first of all use eq .
( 1 ) whereby the bulk energy was obtained from a well - converged bulk calculation ( see below ) .
we also considered the slightly modified version @xcite @xmath6 whereby the total energies needed are that of a slab containing @xmath3 layers ( @xmath2 ) and that of a @xmath7-atom bulk supercell consisting of the slab plus the vacuum space between the slabs filled with atoms ( @xmath8 ) .
in other words , the weighted energy of the filled slab is taken as bulk energy . using eq .
( [ tre ] ) , many sources of difference between the slab and bulk energies can be eliminated since the same supercell is used for the bulk and slab systems , albeit at the cost of an increase in computational effort . for this approach
, we used @xmath9 with n up to 11 .
boettger@xcite suggested the following method to avoid the divergence problem . for each slab thickness @xmath3 , pick as bulk energy @xmath4 the differential increase in the slab total energy upon addition of one layer of material : @xmath10 where @xmath11 .
this formula has the obvious merit of using only slab - related quantities , making no reference to separately - calculated bulk energies .
consequently , the calculated surface energy should not suffer from the divergence problem of eq .
( [ uno ] ) .
the price to pay is that of repeatedly calculating total energies for slabs of increasing thickness . at slight variance with ref .
, we use @xmath12 in order to maintain inversion symmetry in our slabs .    as a fourth alternative
, we note that as @xmath3 becomes large and convergence is approached , the definition of the surface energy in eq .
( [ uno ] ) implies that @xmath13 this straight - line behaviour is already dominant for very thin slabs .
this can be understood on the basis that the energy of a given atom is determined to a large extent by its nearest - neighbor environment @xcite .
the most straightforward way to extract the quantity @xmath4 is to fit a straight line to all the slab total - energy data vs.  @xmath3 ( except for the thinnest slabs ) and to take its slope .
this value is then used in eq .
( [ uno ] ) .
this procedure uses the same data needed in boettger s suggested approach .
it is free of the divergence problem because no separately - calculated bulk energy enters .
the only uncertainty in the procedure is the assumed onset of the straight - line behaviour ; indeed , apart from the very thinnest slabs , the error bar in @xmath4 when starting the fit at different @xmath3 s in the range from 3 to 13 is @xmath140.01 mry ( see also table i below ) .    as a test case , we report results for the surface energy of pt ( 001 ) , evaluated by the four schemes just described .
total energies were calculated within the local density approximation to density functional theory @xcite , using the all - electron full - potential lmto method @xcite .
slab thicknesses of up to 15 layers , and a vacuum spacing equivalent to seven bulk layers were used .
the slabs were left unrelaxed in the ideal fcc geometry .
the technical ingredients ( basis set , k - point summation , etc . ) are given in ref . .
figure [ f - uno ] shows the calculated surface energies as function of slab thickness when the four described methods are used .
the two approaches using a separately - calculated bulk energy [ eqs .
( [ uno ] ) and ( [ tre ] ) ] are shown by open circles and triangles , respectively .
both evidently suffer from the divergence problem , shown by the linear decrease as the slabs are made thicker .
boettger s approach ( taking the bulk energy as differential increase of the slab energy , filled diamonds ) does indeed give a surface energy which does not have this systematic linear behaviour .
unfortunately , it shows large oscillations which decrease only very slowly as the slab is made thicker .
if only these three techniques were available , the best legitimate conclusion would be that the surface energy lies somewhere between 1.21 and 1.26 ev / atom .
this is an uncertainty of 5% even though slabs as thick as 15 layers were considered .
the fourth technique ( fitting a straight line to the @xmath2 data to obtain @xmath4 ) is shown by filled squares . in comparison to the other approaches , very fast convergence to a stable value
is achieved .
we can now accurately determine the calculated surface energy to be 1.246 ev , a value which is numerically stable to within 0.5 mev .
this reduces the uncertainty to below 0.1% . in order to suppress the weak residual oscillation , we averaged over the last three points in the curve : however , the deviations from the average are below 0.5 mev .
( for completeness , in table i we list the raw data for the slab total energies , where a constant offset of 36800 ry / atom was subtracted for convenience , and the bulk energies obtained by linear fittings to @xmath2 vs. @xmath3 starting at different values of the slab thickness @xmath3 . )
our main point here is that one should be wary of the standard technique ( which uses a separately calculated bulk energy ) even for calculations of high accuracy .
we can compare the bulk energy as deduced from the slope of the @xmath2 data ( @xmath15  ry ) with that from the well - converged bulk crystal calculation ( @xmath16  ry ) , finding a difference of only 0.6  mry  @xmath17  ev . despite this very small discrepancy
, the undesired linear behaviour in the calculated surface energy is already prominent for thicknesses of eight or more layers .
the accumulated bulk error for the ( typically used ) slab thickness of around seven is already uncomfortably large , namely 4.2  mry @xmath18  ev . optimistically going to thicker slabs
would soon lead to unacceptable values of the surface energy .
although previously calculated surface energies using the standard technique with slab thicknesses of below ten layers can be considered reasonably reliable , it is clearly important to keep the problem addressed here in mind when doing surface calculations .
to some extent , the severity of the problem will depend on the calculational method used . in terms of k - points and selfconsistency iterations ,
our bulk crystal energy was converged to within 0.01 mry .
thus , the discrepancy in @xmath4 presumably comes from the k - point mesh for the slab , which consisted of 15 irreducible special points in the @xmath19 plane .
it is highly desirable to be able to use a mesh of this typical size , independent of the exact _ ab - initio _
scheme used . in this context
, our conclusions apply in exactly the same way to other methods .
although our suggested scheme at first sight looks like a mere numerical procedure , there is a clear theoretical background to it . the squares in fig .
1 show small but definite oscillations of the surface energy as function of the slab thickness with a period of about six to eight layers .
these quantum size effects are due to the finite thickness of the slab .
the problem of boettger s scheme is that it artificially magnifies these oscillations by a large factor because the bulk energy is calculated from two slabs of similar thickness .
a technique which exploits the overall linear behaviour of the @xmath2 data , such as ours , eliminates this problem .    finally , we point out that our tests up to now , while informative , used all the @xmath2 data up to @xmath3=15 to obtain the converged surface energy . in practice ,
the aim is to use the data from slabs up to a thickness of typically 7 to 9 layers . using the same procedure as before ,
this gives surface energies of 1.2456 and 1.2457 ev / atom , respectively .
these values are much closer to the converged value than those of the three competing approaches . for completeness
, we mention that analogous results have been obtained for al ( 001)@xcite , and rh and ir low - index faces @xcite , as will be presented elsewhere .
in summary , it has been previously pointed out@xcite that the calculated surface energy will diverge with slab thickness if a bulk energy is used which is not exactly equal to the slope of the slab energy vs. slab thickness . here
, we have investigated this phenomenon in the context of accurate state - of - the art computational methods which are careful to treat bulk and slab systems in the same way .
the results show that the effect must be taken seriously for this type of calculation also .
the problem can be easily solved by obtaining the bulk crystal energy directly as the slope of the @xmath2 data , but care should be taken to eliminate quantum size effects .
this can be done by making an overall linear fit to the slab total energy as function of the thickness .
m. methfessel , d. hennig , and m. scheffler , phys .
rev . * b 46 * , 4816 ( 1992 ) ; v. fiorentini , m. methfessel , and m. scheffler , phys .
lett . * 71 * , 1050 ( 1993 ) , j. c. boettger , phys .
b * 49 * , 16798 ( 1994 ) . see _ e.g. _ r. j. needs , phys .
lett . * 58 * , 53 ( 1987 ) .
robertson , v. heine , and m.c .
payne , phys .
lett . * 70 * , 1944 ( 1993 ) .
r. dreizler and e. k. u. gross , _ density functional theory _ , ( springer , berlin , 1990 ) .
we use the exchange - correlation energy by d. m. ceperley and b. j. alder , phys .
* 45 * , 566 ( 1980 ) , parametrized by s. vosko , l. wilk , and m. nusair , can .
* 58 * , 1200 ( 1980 ) .
m. methfessel , phys .
b * 38 * , 1537 ( 1988 ) ; m. methfessel , c. o. rodriguez , and o. k. andersen , phys . rev .
b * 40 * , 2009 ( 1989 ) .
d. fois , s. oppo , and v. fiorentini , rivista italiana del vuoto , in print ( 1996 ) ; to be published .
a. filippetti , v. fiorentini , k. stokbro , r. valente , and s. baroni , in _ materials theory , simulations , and parallel algorithms _ , edited by e. kaxiras and j. d. johannopoulos , mrs proceedings * 408 * , in print ( material research society , pittsburgh , 1996 ) ; a. filippetti , v. fiorentini , r. valente , and s. baroni , to be published .    . in columns from left to right : total energies per atom in pt ( 100 ) slabs of thickness @xmath3 after subtraction of @xmath2036800 ry ( center ) ; bulk energy as the slope extracted from linear fitting of slab total energies vs. @xmath3 , starting the fit at different values of @xmath3 .
[ cols="^ , > , > " , ]
the formation energy of a solid surface can be extracted from slab calculations if the bulk energy per atom is known . 
 it has been pointed out previously that the resulting surface energy will diverge with slab thickness if the bulk energy is in error , in the context of calculations which used different methods to study the bulk and slab systems . 
 we show here that this result is equally relevant for state - of - the - art computational methods which carefully treat bulk and slab systems in the same way . 
 here we compare different approaches , and present a solution to the problem that eliminates the divergence and leads to rapidly convergent and accurate surface energies .    
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