text:
\section{Introduction}

Across a wide range of electronic structure theory methods, such as constrained density functional theory (cDFT)~\cite{WVV,KadukB_KT_VT},
density functional theory plus Hubbard $U$ (DFT+$U$)~\cite{PhysRevB.44.943,QUA:QUA24521}, DFT combined with dynamical
mean field theory (DMFT)~\cite{0953-8984-9-35-010,RevModPhys.78.865}, wave function-embedding~\cite{SimonB_MS_TM_FManby,SherwoodP_HV_A_JCS_PGS_ABN_AVM_HHI},
and some perturbative approaches in quantum chemistry~\cite{JCC:JCC23150},
the population of a particular subspace is physically relevant and the total energy depends explicitly upon it. Thus, the ability to define
appropriate subspaces for population analysis is of considerable importance. This is exemplified by the sustained efforts in recent years
in the development of physically-motivated orbitals such as maximally localized Wannier functions (MLWF)~\cite{PhysRevB.56.12847},
nonorthogonal localized molecular orbitals (NOLMO)~\cite{C3CP52989D}, muffin-tin orbitals (MTO)~\cite{2000LNP...535....3A}, and
natural bond orbitals (NBO)~\cite{B1RP90011K} for use in system-dependent, adaptive population analysis. Population analysis by
means of projection onto orbitally-defined subspaces has undergone detailed analysis in recent years~\cite{PhysRevB.90.075128,0953-8984-27-24-245606} and, in particular, the effects of projector orbital ambiguity in DFT+$U$~\cite{PhysRevB.82.081102,YueChaoWang_ZHC_HJ} and DFT+DMFT~\cite{PhysRevB.81.195107} have been investigated in detail.

In calculations in which the total energy depends explicitly upon localized  orbitals that are centred on atoms, Pulay
terms~\cite{doi:10.1021/ja00504a009,PhysRevB.48.4937} arise in the Hellmann-Feynman forces due to spatial translations of
the orbitals. It is, however, less known, although previously identified~\cite{WuVoorhisForce,DNDmMKVIA}, that additional Pulay
terms emerge when the total energy also depends on the overlap matrix of such orbitals. This is  necessary
 for correct
population analysis using nonorthogonal orbitals. In fact, these forces are present for any multi-centre atomic projection of the
density or the Kohn-Sham density matrix. They exist  when using orthonormal orbitals such as MLWFs, for example, since any ionic
movement typically breaks the orthornormality. Thus, unless the forces take into account that the orbitals are regenerated or
orthonormalized following a translation, a condition which is difficult to encode, then unconventional \emph{nonorthogonality
Pulay forces} arise even for  orbitals that are defined as orthonormal.

Approaches for calculating the necessary corrections, based on a L\"{o}wdin orthonormalized representation of the subspace
projection, invariably encounter a cumbersome, difficult to solve, Sylvester equation~\cite{Bartels:1972:SME:361573.361582} of the form
\begin{align}
\frac{ d \mathbf{O}
}{ d R_i }
&{}=
\mathbf{O}^{1/2} \frac{ d \mathbf{O}^{1/2}
}{ d R_i } +
\frac{ d \mathbf{O}^{1/2}
}{ d R_i }  \mathbf{O}^{1/2} \nonumber \quad
\mbox{or} \\
-   \frac{ d \mathbf{O}
}{ d R_i }
&{}=
\mathbf{O}^{1/2} \frac{ d \mathbf{O}^{-1/2}
}{ d R_i } +
\frac{ d \mathbf{O}^{-1/2}
}{ d R_i }  \mathbf{O}^{1/2}   , \end{align}
where $\mathbf{O}$ is the projector orbital overlap matrix and $R_i$ is a Cartesian component of the ionic position. Here
the solution for $\mathbf{O}^{1/2}$ is required. An approximate method for working around this problem, based on neglecting
off-diagonal matrix elements in $\mathbf{O}^{-1/2}$, has been recently proposed in reference~[\onlinecite{DNDmMKVIA}].
Reference~[\onlinecite{WuVoorhisForce}] instead provides a formula for the full matrix $d \mathbf{O}^{1/2} / d R_i$, which
makes use of the basis of the shared eigenvectors of $\mathbf{O}$ and $\mathbf{O}^{1/2}$. This necessitates matrix
diagonalization. The applicability and practicality of these two approaches depend on the  details of the force
calculations to be undertaken.

\rededit{In this work we use nonorthogonal basis functions and their appropriate tensor notation following a long standing tradition in electronic structure theory~\cite{doi:10.1063/1.1740588, doi:10.1063/1.437441, doi:10.1063/1.475423, PhysRevA.43.5770, PhysRevB.66.035119, PhysRevB.95.115155}. We furthermore use the modern tensorially invariant population analysis~\cite{ORPM}, which has appeared in various contexts~\cite{PhysRevB.90.075128, 0953-8984-27-24-245606} including that of cDFT~\cite{PhysRevB.93.165102, Lukman}. We extend this to calculate an exact, simple and intuitive expression for the nonorthogonality Pulay  forces,
which circumvents orbital orthonormalization and overlap matrix diagonalization entirely.}  This expression is applicable to real and complex valued orbitals alike, and whether or not they are orthonormal at the point of
force evaluation. Avoiding matrix diagonalization ensures its applicability to large systems using
linear-scaling DFT. Our scheme is put here to the test by calculating the reorganization energy of a pentacene molecule
physisorbed on a graphene sheet.

The paper is organized as follows. In the next section we will define the physical problem addressed by our work, namely the
calculation of the energies needed for extracting the reorganization energy of a molecular absorbate on a metallic substrate.
Then we will move on describing our computational methods,  focussing on the derivation of the forces in orbital-based
cDFT, the performance of orbital-based population analysis, and a number of practical considerations addressed using the
{\sc onetep} code. Our results for pentacene on graphene will be presented next, followed by our conclusions.

\section{Physical problem: reorganization of a charged molecule physisorbed on a metallic surface}
The reorganization energy holds paramount importance in charge transport calculations. Semi-classical Marcus theory~\cite{JofEC}
at high temperature, $T$, computes the probability per unit time of an electron hopping, $k_\textrm{ET}$, from the Fermi's
Golden Rule as~\cite{doi:10.1021/jp9605663,doi:10.1021/ct200388s}
\begin{equation}\label{FGR}
\begin{split}
k_\textrm{ET}=\frac{\lvert \bra{i}\hat{H}\ket{f} \rvert^2}{\hbar}\sqrt{\frac{\pi}{\lambda k_B T}}\exp\left[-\frac{(\lambda+\Delta G^0)^2}{4\lambda k_\textrm{B} T}\right]\:,
\end{split}
\end{equation}
where $\hat{H}$ is the Hamiltonian, $\ket{i}$ and $\ket{f}$ are the initial and final electronic states, respectively, and $\Delta G^0$
is the change in Gibbs' free energy associated to the charge transfer process. The reorganization energy, which enters the exponential
term defining $k_\textrm{ET}$, is thus an important ingredient~\cite{C4CP06078D,doi:10.1021/jp9535250, doi:10.1021/jp4046935} for the calculation of the charge hopping. In this work we compute the
reorganization energy of a pentacene molecule. In its crystalline solid state form, due to its high HOMO level, pentacene is a $p$-type
semiconductor~\cite{YoshiroYamashita} with a high hole mobility~\cite{THJT}. Thus, ionization reorganization effects in pentacene-based
systems are of significant interest, being the subject of several theoretical and experimental
studies~\cite{Gruhn_SF_B_T_M_M_C_K_B,CMFGBB,SC_CFDFOMSSB}.

Let us  define the reorganization energy precisely.
The ionic coordinates of any system depend on its electronic occupation. For instance, if an electron is removed from a
neutral molecule, such as in photoemission spectroscopy, its ionic coordinates will readjust to a new geometry due to the
local electron-phonon coupling~\cite{doi:10.1021/jp900157p,doi:10.1021/cr050140x}. Figure~\ref{FIG:ReorgEnDiagram}
shows two parabolic curves corresponding to the energy surface of the neutral molecule and that of the singly ionized
one as a function of some collective atomic coordinates. We define as $\lambda^0$ the energy difference between
the ground state geometry and the ground state geometry of the charged configuration~\cite{C0CS00198H}, when the
molecule is neutral. In contrast, $\lambda^+$ is the same quantity but calculated for the ionized system. The reorganization
energy, $\lambda$, for the molecule undergoing electron removal is defined as
\begin{equation}\label{equReOr}
\lambda=\lambda^0+\lambda^+\:,
\end{equation}
where similar definitions can be given for the case where the molecule receives an extra electron.

\begin{figure}
\centering
\includegraphics[width=\columnwidth]{Schematic.pdf}
\caption {Schematic diagram of the energy as a function of the ionic coordinates for a charged and a neutral molecule. The
reorganization energy is defined as $\lambda^0+\lambda^+$. }\label{FIG:ReorgEnDiagram}
\end{figure}

Theoretical approaches to compute the reorganization energy typically consist of either calculating the energy difference from the
adiabatic potential energy surface, or of indirectly evaluating the molecule's normal modes ~\cite{YX_WL_WC_LW_SZ}. Here we
adopt the former approach. For an isolated pentacene molecule, an electron removal can be simulated with unconstrained DFT and
therefore it does not require the aforementioned force terms. However, this approach is not viable for the study of reorganisation in
systems relevant to organic semiconductor devices, where organic molecules is typically adsorbed on metallic electrodes. When a
molecule is adsorbed on a metallic substrate and its highest occupied molecular orbital (HOMO) lies below the Fermi level, the hole
must be prevented from migrating to the energetically favourable location of the substrate. We achieve this by using cDFT to force
the hole onto the adsorbate.

cDFT has been widely applied to the study of charge transfer in organic compounds~\cite{Franke2012,doi:10.1021/acs.jctc.6b00815,doi:10.1063/1.4979895,doi:10.1021/acs.jctc.5b00057,C6SC04547B,PhysRevB.93.195208,doi:10.1021/acs.jctc.6b00564,doi:10.1021/acs.jctc.6b01085,doi:10.1080/00268976.2013.800243}.
Recently, cDFT has been used to estimate charge-transfer excitations in bulk pentance in the infinite-crystal limit~\cite{PhysRevB.93.165102}.
The present work utilises the same underlying linear-scaling cDFT implementation, itself an extension of a linear-scaling implementation of
DFT+$U$~\cite{PhysRevB.85.085107} using nonorthogonal generalized Wannier functions. Also relevant to this work is that cDFT
has been used to simulate removal or addition of electrons from adsorbed molecule in the context of calculating charge transfer
energies~\cite{PhysRevB.88.165112,PhysRevB.93.045130}. Here we use cDFT in conjunction with nonorthogonality Pulay forces
to calculate the reorganization energy of a pentacene molecule physisorbed on a flake of graphene. \rededit{The energy of a system as a function of its geometry can contain multiple local minima, and this is particularly  the case
for the incommensurate corrugated system at hand.
The proposed method, in conjunction with efficient sampling techniques like simulated annealing~\cite{Kirkpatrick671}, basin hopping~\cite{doi:10.1021/jp970984n}, etc., could be used to explore such
energy landscapes in the presence
of orbital-based constraints.} We note that a more complex system,
consisting of a film of weakly bound pentacene molecules adsorbed on highly oriented pyrolytic graphite (HOPG), has been the
subject of several theoretical and experimental studies \cite{KERA2009135,YH_NS_FH_KS_FR_OKK_UN,PP_CV_BJL}. It has
been shown, in the experimental work of reference~[\onlinecite{KERA2009135}], that the reorganization energy of
pentacene is there, remarkably, higher than that in the gas phase.

\section{Theoretical Problem: population analysis and forces based on nonorthogonal orbitals}

In cDFT, to date, real-space partitioning has prevailed over orbital-based population analysis methods.
Central to the viability of using more chemically motivated orbitals to define the constrained
population in cDFT, and perhaps hindering their adoption, is the proper treatment of their nonorthogonality.
In particular, historically there has been some uncertainty~\cite{2008JPCM...20F5205T,PhysRevB.73.045110}
as to how subspace populations should be defined in terms of nonorthogonal orbitals, which typically
(but not necessarily by any means) form a subset of the basis set for the Kohn-Sham states.
This uncertainty has previously been conclusively resolved within the context of DFT+$U$~\cite{ORPM}, and the correct
procedure has recently been pioneered in cDFT for calculating charge-transfer energies in solid pentacene~\cite{PhysRevB.93.165102}.
We will numerically investigate the performance of this tensorially consistent procedure  for cDFT in the present work.
A separate problem, which we also will touch upon in this work, is the arbitrary choice of the underlying projection orbitals
in terms of their particular spatial profile.

The canonical orbital-based population analyses in quantum chemistry are due to L\"{o}wdin and Mulliken, and these are both
unsuitable for cDFT.
cDFT population analyses based on orbitals that are globally L\"{o}wdin orthornormalized, meaning that the entire
basis set is orthonormalized before a subset is selected out, typically collect density contributions from all atoms in
the simulation cell, regardless of how distant they may be from the region of interest. Mulliken  population analysis,
constructed using the global orbital overlap matrix has the same problem~\cite{ORPM}. In a nutshell both methods
have the fundamental difficulty that the measured population is arbitrary with respect to linear transformations among
the selected subset of the orbitals (an example of broken \emph{tensorial invariance}).

A tensorially invariant population analysis~\cite{PhysRevB.93.165102,ORPM} instead gathers density contributions and
applies constraining potentials only within the region of interest. We will here demonstrate that this can provide very
reasonable electronic populations for a physisorbed molecule when using either pseudoatomic orbitals or generalized
Wannier functions. Physically-motivated orbitals can thus compete with real-space weight functions in cDFT, when treated
appropriately. Their use may be particularly advantageous in situations where the system or observable of interest does not
readily admit a real-space partitioning, such as when constraining the population of an atom in a crystal, or that of a group
of single-particle states based on their principal angular momentum character.

\section{Methodology}

\subsection{Constrained density-functional theory forces}

In DFT the ground state (GS) electron density, $\rho_0$, uniquely specifies all the GS properties of a system, including
its GS energy~\cite{HPKW}. This can thus be found by variationally minimizing an approximate energy functional, $E\left[\hat{\rho}\right]$,
where $\hat{\rho}$ is the density operator. In cDFT, instead, one seeks to find the GS of the system subject to a constraint,
for example the constraint that a given number of electrons is found in a particular subspace. This simple constraint
has the mathematical form
\begin{equation}\label{equ2_ReorgEn}
{\rm Tr} [\hat{\rho}\hat{\mathbb{P}} ] - N_\textit{c} = 0,
\end{equation}
where $\hat{\mathbb{P}}$ is projection operator for the subspace of interest and $N_c$ is the target number of electrons (here
`Tr' indicates the trace of the operator, computed over an appropriate basis set). In order to find the density corresponding to such
constrained ground state, one finds the stationary point~\cite{WVV,ORT} of the functional $W\left[\hat{\rho},V_\textit{c}\right]$,
where $V_\textit{c}$ is a Lagrange multiplier and
\begin{equation}\label{equ3}
W\left[\hat{\rho},V_\textit{c}\right]=E\left[\hat{\rho}\right]+V_\textit{c}\left({\rm Tr}[\hat{\rho}\hat{\mathbb{P}}]-N_\textit{c}\right).
\end{equation}
For a given $V_\textit{c}$ the Kohn-Sham potential is modified by the addition of the term $V_\textit{c} \hat{\mathbb{P}}$ and
$W \left[\hat{\rho},V_\textit{c} \right]$ is minimized as a functional of $\hat{\rho}$ as usual. Considering just the global
minima for each $V_\textit{c}$, $W$ can be regarded as a function $W\left(V_\textit{c}\right)$ of $V_\textit{c}$ alone~\cite{WVV}
(strictly speaking, constrained systems can be constructed where it is a multiple-valued non-function~\cite{ORT}).
The stationary points of $W\left(V_\textit{c}\right)$ yield the (potentially degenerate) ground state densities of the system subject to the
given constraint. In particular, the stability of a ground-state ensures that $W\left(V_\textit{c}\right)$ attains a maximum~\cite{ORT}
with respect to $V_\textit{c}$. At the stationary point $W\left[\hat{\rho},V_\textit{c}\right]=E\left[\hat{\rho}\right]$,
since Eq.~(\ref{equ3}) is satisfied.

In general, $E\left[\hat{\rho}\right]$ is not stationary at a non-trivially constrained density and, hence, the Hellmann-Feynman
theorem cannot be applied to $E\left[\hat{\rho}\right]$ alone. It is instead applied to $W\left[\hat{\rho},V_\textit{c}\right]$
in order to find the ionic force
\begin{equation}\label{equ4}
F_i=-\frac{dW}{d R_i}=
-\frac{\partial W}{\partial R_i}
- {\rm Tr} \left[ \frac{\partial W}{\partial \hat{\rho}} \frac{{\rm d} \hat{\rho}}{{\rm d} R_i} \right]
- \frac{\partial W}{\partial V_\textit{c} } \frac{{\rm d} V_\textit{c} }{{\rm d} R_i} ,
\end{equation}
where the index `$i$' is collective for the ion number and the Cartesian direction indexes. Here the term containing the trace
vanishes at any stable ground-state by virtue of the Hellmann-Feynman theorem~\cite{ORT}, and the final term vanishes at
the cDFT stationary points, i.e., where $\partial W / \partial V_\textit{c} = 0$.
The force is thus given, in practice,  by
\begin{equation}\label{equ5_ReOr}
F_i=
-\frac{\partial W}{\partial R_i} =
-\frac{\partial E\left[\hat{\rho}\right]}{\partial R_i}-V_\textit{c}{\rm Tr} \left[\hat{\rho} \frac{\partial \hat{\mathbb{P}}}{\partial R_i} \right]\:.
\end{equation}
The first term on the right hand side is the contribution from the conventional DFT external potential of the constrained
density~\cite{doi:10.1063/1.4728026},
while the second term, which we will denote by $F_i^\textit{c}$, is the  Pulay force due to the constraint.
Before evaluating this contribution, we must next discuss how the subspace projection operator $\hat{\mathbb{P}}$ is constructed.

\subsection{Tensorially invariant population analysis}

When defining $\hat{\mathbb{P}}$ in terms of nonorthogonal orbitals, such as atomic orbitals centred on atoms, let us label them
$\lvert \phi_m \rangle$, it is a commonplace and usually unnecessary practice to orthonormalize them by L\"{o}wdin transformation.
This generates orbitals of the form $ \lvert \tilde{\phi_j} \rangle = \sum_m \lvert \phi_m \rangle O^{-\frac{1}{2}}_{m j} $,
where  $\mathbf{O}$ is an orbital overlap matrix. The matrix fractional power is most easily calculated by diagonalizing $\mathbf{O}$,
taking the corresponding power of the eigenvalues, and by performing the inverse of the original diagonalizing transformation to
arrive at $\mathbf{O}^{-\frac{1}{2}}$.

In methods dealing with the population of orbital-based subspaces such as cDFT and DFT+$U$,  it has been shown~\cite{ORPM} to
be quite incorrect to use for $\mathbf{O}$ the overlap matrix $\mathbf{S}$ of any larger set that the projector orbitals $ \lvert \phi_m \rangle $
may be chosen from, since then the orthonormalized functions $ \lvert \tilde{\phi_j} \rangle $ extend across the larger subspace.
Instead, if the projection orbitals $ \lvert \phi_m \rangle $ used to span a cDFT subspace happen to be selected from a larger set of basis
orbitals (e.g. the one spanning the entire Kohn-Sham space), then the subspace overlap matrix $\mathbf{O}$ must be extracted as a sub-block
from the full overlap matrix $\mathbf{S}$ \emph{before} being diagonalized~\cite{PhysRevB.93.165102}.

As an example, let us imagine a bipartite system composed of natural but non-trivially overlapping source and drain regions
for a charge-transfer excitation to be accessed using cDFT. If the source-region orbitals $ \lvert \tilde{\phi_j} \rangle $ are built
using $\mathbf{S}$, then they will extend to some amount over the drain region, and vice-versa, in an uncontrolled manner.
This pathology will not arise if separate, smaller subspace overlap matrices $\mathbf{O}$ are defined for each of the source and
drain regions. This also ensures tensorial invariance and, in particular, physical occupancy eigenvalues  (i.e., $0 \le \lambda_j \le 1$)
for the projected density matrices of each constrained subspace~\cite{ORPM}.

By defining the subspace population as the trace over such orthonormalized functions, we obtain
\begin{align*}
\rm {Tr} \big[\hat{\rho}\hat{\mathbb{P}} \big]
&{}=\sum_{j }\braket{\tilde{\phi}_j |\hat{\rho}|\tilde{\phi}_j}\\
&{}=\sum_{m n}\braket{\phi_m|\hat{\rho}|\phi_n}\sum_{j} O^{-\frac{1}{2}}_{n j } O^{-\frac{1}{2}}_{j m}\:. \numberthis \label{equLOWD2}
\end{align*}
Equation (\ref{equLOWD2}) suggests a straightforward alternative approach, albeit one that is not available if the index
$j$ does not run over the same orbital count as $n$ and $m$ (such as when the delocalizing global matrix $\mathbf{S}$ is used).
Instead of performing a L\"{o}wdin orthonormalization, we may accept the nonorthogonality of the projectors and define the
subspace population as a tensor contraction over the nonorthogonal set of $ \ket{\varphi_m} $ and their biorthogonal \rededit{complements}
$\ket{\varphi^m}$, defined through $\braket{\varphi^m|\varphi_{n}}=\delta^m_{\; n}$. This gives the transformations
\begin{equation}\label{equ6}
 \ket{\varphi^m}=\ket{\varphi_{n}}O^{nm} \quad
 \Leftrightarrow \quad
 \ket{\varphi_m}=\ket{\varphi^{n}}O_{nm}\:,
\end{equation}
where we have adopted the Einstein summation convention for contracting over paired indices, and where $O^{mn}$ is an element
of the matrix $\mathbf{O}^{-1}$ and $O_{mn}=\langle \varphi_m \rvert \varphi_n\rangle$. If the functions $ \ket{\varphi_m} $ are chosen
to be localized over a particular spatial region then also the functions $\ket{\varphi^m}$ will be. The required subspace occupancy is
then given by
\begin{align*}
\textrm{Tr} \big[
\hat{\rho}\hat{\mathbb{P}}\big] &{} =
\textrm{Tr} \big[
\hat{\rho}\ket{\varphi^m}  \bra{\varphi_m}
 \big] =
\bra{\varphi_m}\hat{\rho}\ket{\varphi_{n}}O^{nm}\numberthis\:, \label{equ7_RO}
\end{align*}
which is equivalent to Eq.~(\ref{equLOWD2}). Next, we look at how the  Pulay force  of cDFT appears when we make this
simplification, i.e., when we use the contraction $\sum_j O^{-\frac{1}{2}}_{n j} O^{-\frac{1}{2}}_{j m}=O^{n m}$ \emph{before}
the ionic-position derivative is taken.

\subsection{The nonorthogonality Pulay forces}

A change in the degree of nonorthogonality between projecting orbitals centred on atoms is a natural occurrence in calculations
involving ionic displacements. In order to account for this, the final term of Eq.~(\ref{equ5_ReOr}) may be expanded, in view
of Eq.~(\ref{equ7_RO}), as
\begin{align*}
 F_i^\textit{c}  =&{} -V_\textit{c} \Bigg[ \braket{\frac{\partial\varphi_m}{\partial R_i}|\hat{\rho}|\varphi_{n}}O^{nm}+\braket{\varphi_{m}|\hat{\rho}|\frac{\partial\varphi_{n}}{\partial R_i}}O^{nm}+ \\
&{} \quad + \braket{\varphi_m|\hat{\rho}|\varphi_{n}}\frac{\partial O^{nm}}{\partial R_i} \Bigg]\:.\numberthis \label{equ8_Reorg}
\end{align*}
The first and the second term on the right-hand side represent the force due to the change in the projectors as a result of the ionic
displacements, while the third term represents that due to a change in the mutual overlap of the projectors. If the projectors are localized
orbitals centred on the atoms, then the third term is exclusively due to the relative motion of the atoms that define the subspace.
The first term may be written as ${\rm Tr}[\hat{\rho}\hat{X}]$, defining the operator
$\hat{X}=\ket{\varphi_{n}}O^{nm}\bra{\partial\varphi_m / \partial R_i}$. Similarly, the second term on the right-hand side in
Eq.~(\ref{equ8_Reorg}) is $\rm{Tr}[\hat{X^\dagger}\hat{\rho}]$. For the calculation of this latter see reference
[\onlinecite{PhysRevB.85.085107}].

In order to evaluate the third term we shall use the following matrix identity for invertible matrices $\mathbf{M}$,
\begin{align*}
\mathbb{0} =
  \frac{d}{dR_i} \left[ \mathbb{1} \right] &{}=
  \frac{d}{dR_i}\left[\mathbf{M}\mathbf{M}^{-1}\right]
=\frac{d\mathbf{M}}{dR_i}\mathbf{M}^{-1}+\mathbf{M}\frac{d\mathbf{M}^{-1}}{dR_i}\\
\Rightarrow  \frac{d\mathbf{M}^{-1}}{dR_i}
&{}=
- \mathbf{M}^{-1}\frac{d\mathbf{M}}{dR_i}\mathbf{M}^{-1}\:,\\
\end{align*}
where $\mathbb{0}$ is the null matrix. By applying this identity to the overlap matrix $\mathbf{O}$, the third term of Eq.~(\ref{equ8_Reorg})
can be rewritten as
\begin{align*}
  &{}\braket{\varphi_m|\hat{\rho}|\varphi_{n}}\frac{\partial O^{nm}}{\partial R_i}\\
  =-&{}\braket{\varphi_m|\hat{\rho}|\varphi_{n}}O^{n n'}\left[\braket{\frac{\partial\varphi_{n'}}{\partial R_i}|\varphi_{m'}}+\braket{\varphi_{n'}|\frac{\partial\varphi_{m'}}{\partial R_i}}\right]O^{m' m}\\
  =-&{}\braket{\varphi_{n'}|\frac{\partial\varphi_{m'}}{\partial R_i}}O^{m' m} \braket{\varphi_m|\hat{\rho}|\varphi_{n}}\braket{\varphi^{n}|\varphi^{n'}}+
  \textit{c.c.}\\
  =-&{}{\rm Tr}[\hat{X}^\dagger\hat{\rho}\hat{\mathbb{P}}]+   \textit{c.c.}\numberthis\:, \label{equ10}
\end{align*}
where the projectors obey $\hat{\mathbb{P}}^\dagger \hat{\mathbb{P}}= \hat{\mathbb{P}} \hat{\mathbb{P}}= \hat{\mathbb{P}}$.

If we now bring all the terms together, the nonorthogonality-respecting Pulay force will be given by the remarkably simple expression
\begin{align*}
F_{i}^\textit{c}
  =&{}-V_\textit{c} \mathrm{Tr}\big[\hat{\rho}\hat{X} +\hat{X}^{\dagger} \hat{\rho} - \hat{X}^\dagger\hat{\rho}\hat{\mathbb{P}}-\hat{\mathbb{P}} \hat{\rho}  \hat{X}\big] \\
  =&{}-2V_\textit{c} \Re \mathrm{Tr}\left[ \hat{\rho} \hat{X}
  \left(\hat{\mathbb{1}}-\hat{\mathbb{P}}\right)
 \right]\:.\numberthis \label{equ11}
\end{align*}
The final factor, $(\hat{\mathbb{1}}-\hat{\mathbb{P}})$, in this expression is a projector onto the space \rededit{\emph{complementary}} to the
constrained one. The effect of variable nonorthogonality thus becomes clear. It generates an extra projection factor that cancels any
component of the Pulay force associated with orbital derivatives that are not related to changes in the projected subspace. In other words it
cancels contributions related to changes that cannot cause a variation of the measured occupancy.
If the operator $\hat{X}$ applies a linear transformation among the projector orbitals, then $\hat{X} = \hat{X} \hat{\mathbb{P}}$ and the
Pulay force will vanish entirely. In contrast, if $\langle \partial \varphi_m / \partial R_i \rvert \varphi_n \rangle = 0$ for all $m$ and $n$,
then $ \hat{X} \hat{\mathbb{P}} =  \hat{\mathbb{0}} $ and the expression will reduce to the ordinary Pulay force.
It is possible that the projection factor in Eq.~(\ref{equ11}) is a useful addition to Pulay force calculations \emph{in general}, since even
when orbitals nonorthogonality is not expected to arise or vary, numerical noise may cause slight variations from the condition
$\langle \partial \varphi_m / \partial R_i \rvert \varphi_n \rangle = 0$. An example where this may arise is in force calculations
involving atom-centred pseudopotentials defined on a radial grid, which are projected onto a real or reciprocal-space Cartesian grid
prior to integration with Kohn-Sham states.

\subsection{Implementation and procedure for  calculation}\label{ProcedureForCalculation_RE}

We have implemented the nonorthogonality Pulay forces in the linear-scaling DFT code {\sc onetep}~\cite{CKSPDHAAMMCP},
which uses  strictly localized, variationally-optimized nonorthogonal generalized Wannier functions (NGWFs)~\cite{PhysRevB.66.035119,MOSTOFI2002788,PhysRevB.85.193101}, ${\ket{\phi_\mu}} $, as a basis set. The NGWFs are, in turn, expressed as a
linear combination of highly localized orthonormal psinc functions, which are essentially Fourier transforms of plane waves specified
with a maximum cutoff energy. For a given DFT calculation, {\sc onetep} optimizes the NGWFs using a conjugate-gradients (CG)
method in order to minimize the total energy. Within each iteration of such optimization, it minimizes~\cite{0953-8984-20-29-294207}
the total-energy functional with respect to the density kernel $K^{\alpha\beta}, $ which builds the single-particle density matrix by means
of $\rho(\mathbf{r},\mathbf{r'})=\phi_\alpha(\mathbf{r})K^{\alpha\beta}\phi_\beta(\mathbf{r'})$\cite{0953-8984-20-29-294207}. Thus, for a
geometry optimization in presence of a constraint of the form contained in Eq.~(\ref{equ2_ReorgEn}), we run the following nested optimization
loops,
\begin{enumerate}
\item Optimization of the ionic geometry,
\item Conjugate gradients optimization of the NGWFs ${\ket{\phi_\alpha}} $ within
ensemble DFT,
\item Conjugate gradients optimization of the Lagrange multiplier, $V_\textit{c}$,
\item  Optimization of the density kernel $K^{\alpha\beta}$ within ensemble DFT.
\end{enumerate}

\rededit{We note that, although we use the NGWFs as optimized basis functions and as cDFT projectors in this work, the expression for the Pulay forces remain valid for any nonorthogonal set of projector functions.} The scheme that we follow for calculating the reorganization energy of a pentacene molecule adsorbed on a flake of graphene
can be summarized as follows:
\begin{enumerate}
\item Optimize the geometry of the neutral system and calculate the GS energy with a DFT run. This gives the geometry
$G0$ and the energy $E^0_{@G0}$.
\item Run cDFT for singly ionized pentacene at the geometry $G0$ in order to obtain the energy $E^+_{@G0}$.
\item Run a constrained geometry optimization to find the nuclear coordinates for the charged pentacene and the corresponding energy.
This gives us a geometry $G+$ and an energy $E^+_{@G+}$.
\item Run DFT on neutral pentacene with geometry $G+$ to find the energy $E^0_{@G+}$ of the neutral configuration at the geometry
of the charged state.
\end{enumerate}

The reorganization energy $\lambda$ is then given by
\begin{align*}
\lambda &{}=\lambda^0+\lambda^+,\\
&{}=(E^0_{@G+}-E^0_{@G0})+(E^+_{@G0}-E^+_{@G+}).\numberthis \label{eqnReorgEqn}
\end{align*}

\rededit{Geometry relaxation is performed only on the pentacene molecule, keeping the graphene flake fixed. In other words, the reorganization energies so obtained correspond to pentacene only.} Our calculations have been performed with the Perdew-Burke-Ernzerhof (PBE)~\cite{PhysRevLett.77.3865} parameterization of the
generalized-gradient approximation of exchange-correlation functional and norm-conserving pseudopotentials. The NGWF cutoff radius
was set to 9~$a_0$. It was found that a very high plane-wave cutoff energy of $1500$~eV is needed to avoid small changes in energy due
to the egg-box effect. cDFT optimization is performed with conjugate gradient with the convergence threshold of $10^{-5}$~e/eV for the
Lagrange multiplier gradient. This translates to an error of $<4 \times 10^{-4}\%$ in the population of the pentacene molecule. Geometry
relaxation is performed with a quasi-Newton method~\cite{PFROMMER1997233} using a Broyden-Fletcher-Goldfarb-Shanno
algorithm~\cite{PhysRevB.83.195102} with Pulay corrected forces (including correction for any
residual NGWF non-convergence~\cite{doi:10.1063/1.4728026}) and an energy convergence threshold of $2.5 \times10^{-6}$ eV per
atom. Some additional features employed in our calculations are described in the following subsections.

A numerical evaluation of the orbitals used to construct the constrained pentacene subspace follows below, but as standard we have
adopted the well-established practice~\cite{PhysRevB.93.165102,PhysRevB.82.081102,Lukman,DNDmMKVIA,0953-8984-24-41-415603,PhysRevB.74.125120} of using  Wannier
functions centred on the appropriate atoms (in this case the pentacene carbon and hydrogen) for the projectors $\lvert \varphi_m \rangle$.
In particular, these were chosen as a subset of the NGWFs variationally-optimised for the valence manifold of the unconstrained, relaxed
neutral ground-state of the pentacene-graphene system, following the protocol  proposed in  Ref.~[\onlinecite{PhysRevB.82.081102}] and
first applied to cDFT in Ref.~[\onlinecite{PhysRevB.93.165102}].

\subsubsection*{Ensemble density-functional theory}
The occupation number of states in the vicinity of the Fermi level is ill-conditioned in the case of a high degree of degeneracy, as
in metals and near-metals like graphene. In other words, significant fluctuations in the occupation numbers and in the electron
density take place despite tiny energy changes. In these situations the number of self-consistent steps necessary for converging
the ground state can be large. In order to circumvent this problem, we employ the finite temperature ensemble DFT (and cDFT)
formalism~\cite{MVP} as implemented within \textsc{onetep}~\cite{ARSCKS}. Here, instead of the energy, one minimizes the
Helmholtz free energy
\begin{align*}
  &{}A[T,\{\epsilon_i\},\{\ket{\psi_i}\}]=\sum_{i}f_i\langle \psi_i|-\frac{1}{2}\nabla^{2}|\psi_i\rangle \numberthis \\
  &{}+\int d\mathbf{r} \; v_n(\mathbf{r})\rho(\mathbf{r})+J[\rho]+E_{xc}[\rho^{\alpha},\rho^{\beta}]-TS[\{f_i(\epsilon_i)\}]\;, \label{equFreeEn}
\end{align*}
where $S[\{f_i\}]$ is the entropy of the system given by~\cite{mandl1971statistical},
\begin{equation}\label{ENTROPY}
S[\{f_i\}]=-k_B\sum_i \left[f_i {\rm ln} f_i+ \left(1-f_i \right) {\rm ln} \left(1-f_i \right)\right]\;.
\end{equation}
Here, the occupation number $f_i(\epsilon_i)$ is that of the $i$-th KS state and it follows the Fermi-Dirac distribution
\begin{equation}\label{FD}
f_i(\epsilon_i)=\left(1-\exp\left[\frac{\epsilon_i-\mu}{k_\mathrm{B}T}\right]\right)^{-1}\:,
\end{equation}
with $\mu$ being the chemical potential, $k_\mathrm{B}$ the Boltzmann constant and $T$ the temperature. In all our calculations
we have used $T=$~300~K.

\subsubsection*{Correction for periodic boundary conditions}
Since {\sc onetep} uses the fast Fourier transform to solve the Poisson equation, it requires using periodic boundary conditions. For
isolated systems one then constructs artificial periodic replica  of the simulation cell. This gives rise to undesired interactions
between the cells. In order to correct such shortfall, we have used  the Martyna-Tuckerman scheme~\cite{MT} of replacing
the Coulomb interaction from the periodic images of the simulation cell with a minimum image convention technique. This essentially
adds an screening potential term to approximately cancel the Coulomb interactions from neighbouring cells~\cite{HDHS}. We used the
Martyna-Tuckerman parameter of 7.0~$a_0$ that is recommended in reference~[\onlinecite{MT}].

\subsubsection*{Dispersion correction}
Dispersion interactions, which are poorly accounted for in semi-local exchange and correlation functionals are expected to be dominant
between the pentacene molecule and the graphene flake. Hence, we use an empirical correction, $E_\mathrm{disp}(r_{ij})$, to the total
energy, in the form of a damped London term summing over all pairs of atoms $(i,j)$ with interatomic distance of $r_{ij}$, given by
\begin{equation}\label{DISPERSION}
E_\textrm{disp}(r_{ij})=-\sum_{i>j}f_\textrm{damp}(r_{ij})\frac{C_{6,ij}}{r_{ij}^6}\:,
\end{equation}
where $C_{6,ij}$ depends on the particular pair of atoms and the damping term is given by~\cite{MEPHTFSSEK}
\begin{equation}\label{ELSTNER}
f_\textrm{damp}(r_{ij})=(1-\exp(-c_\textrm{damp}(r_{ij}/R_{0,ij})^7))^4\:.
\end{equation}
The parameters, $c_\textrm{damp}$ and $R^{0}_{ij}$, used here have been generated and implemented previously in the \textsc{onetep}
code by fitting a set of $60$ complexes with significant dispersion~\cite{QHCKS}.

\section{Results}

\subsection{Test of the forces on isolated pentacene}

In order to demonstrate the role and necessity of using nonorthogonality Pulay corrections, we first present some tests on a very
simple system consisting of one isolated, charge-neutral pentacene molecule. We run three independent geometry relaxations,
namely
\begin{enumerate}
\item An unconstrained DFT geometry optimization starting from an idealized initial guess for the ionic geometry of the neutral molecule.
This provides a benchmark level of geometry optimization performance on the test system.
\item A geometry optimization with the same initial guess of  1., while applying a fixed constraint potential of strength $V_\textit{c}$ to
the pre-defined pentacene space and relaxing without the force correction for the derivative of projector overlap [i.e. by omitting
the last term on the right-hand side of Eq.~(\ref{equ8_Reorg})].
\item The same relaxation of 2., but including the exact expression of the Pulay forces given in Eq.~(\ref{equ8_Reorg}).
\end{enumerate}

\begin{figure}
\centering
\includegraphics[width=\columnwidth]{FIG2.pdf}
\caption {The maximum displacement of any atom, the change in energy per atom, and the maximum force on any atom,
plotted against the iteration number in a geometry relaxation calculation. The black, blue and red curves show the plots for
a regular DFT run, a constrained run without the properly corrected forces and one with the proper correction for forces,
respectively. The constrained calculations are separately performed with a fixed constant potential $V_\textit{c}=1$~eV
(left column) and $V_\textit{c}=2.5$~eV (right column). See main text for details.}\label{FIGForceTest}
\end{figure}

A fixed, minimal set of valence pseudo-orbitals (the initial guesses for the NGWFs prior to optimization, i.e.
H 1$s$ and C 2$p$ and 2$p$) were used to define the constrained subspace, with tensorially consistent population analysis.
In Fig.~\ref{FIGForceTest} we plot the maximum displacement, the change in energy per ion and the maximum force as a function
of the iteration number for the aforementioned calculations performed with two different $V_\textit{c}$, namely $1$~eV and $2.5$~eV.
For the $V_\textit{c}=$~1~eV the three calculations differ only slightly since the force correction is small. However, for $V_\textit{c}=2.5$~eV we
see that the behaviour of the calculation using the incorrect force (red line) differs significantly from the other two, especially for the
maximum force on any atom. In order to quantify the difference in force between the cDFT runs with and without force correction, we
calculate the root-mean-squared (RMS) difference between the two quantities, given by
\begin{equation}
\sqrt{\frac{1}{n}\sum_i\left(\frac{F_C^i-F_U^i}{F_C^i}\right)^2},
\end{equation}
where $F_C^i$ and $F_U^i$ are, respectively, the corrected and uncorrected, total ionic forces on the $i$-th iteration. Here, $n$ is
the total number of iterations and, clearly, the potential that generates these forces differs except upon the first iteration. The atom
with the largest force may also change from iteration to iteration. In percentage terms, the RMS force differences are a very significant
$121.73$~\% and $112.65$~\% for $1$~eV and $2.5$~eV constraint potentials, respectively.

\subsection{Reorganization energy of graphene-adsorbed pentacene}

\begin{figure}
\centering
\includegraphics[width=\columnwidth]{PUNCH}
\caption{The left-hand side panel shows the system of interest, namely a pentacene molecule adsorbed on a graphene flake.
The right-hand side one shows an isovalue plot of the HOMO of the neutral Kohn-Sham system. It is clear that the HOMO
is confined to the graphene flake, with most of its amplitude located at its edges.}\label{FIG:SYSTEM}
\end{figure}

In this section we present and discuss our results concerning the reorganization energy of pentacene molecules adsorbed on a
flake of graphene. The molecule is positioned above the graphene flake at its centre and is oriented parallel to it. We have performed
our calculations with two different shapes and sizes of hydrogen-passivated graphene flake, one containing 358 atoms (hereafter referred
to as the smaller flake) and another 474 (hereafter referred to as the larger flake). The geometry of the smaller flake has been relaxed in
isolation. However, for the larger flake we use the geometry of an infinite graphene sheet so that the positions of the carbon atoms are
symmetric with respect to each other, in order to better emulate an infinite graphene sheet. The system is shown in the left-hand side
panel of Fig.~\ref{FIG:SYSTEM}, while the right-hand side one shows a plot of the highest occupied molecular orbital (HOMO) of the
entire system. Since the HOMO is mostly localized on the graphene flake (at its edges), simply running a DFT calculation with one less
electron is not an option as an electron will be removed from the graphene flake. Thus we use cDFT to constrain a unit positive charge on the pentacene. \rededit{We emphasize that we do not treat the reorganization effect due to pentacene-graphene charge transfer, but rather
the photoemission reorganization effect, in which
an electron is removed from the
pentacene molecule. This leaves the
simulation cell with a net positive charge. The monopole
interactions between the periodic replica of the charged
unit cells are neutralized by the periodic boundary correction mentioned in section~\ref{ProcedureForCalculation_RE}.}

\subsubsection{Orbital-based population analysis}\label{SubSubsection_PopAn_RE}
In the cDFT calculations we intend to remove one electron from the pentacene molecule. It is therefore necessary to carry out
a population analysis for the uncharged ground state in order to find the number of electrons in the molecule and to define the
constraining potential. This population depends on the choice of projectors used to represent the subspace assigned to the molecule.
In {\sc onetep} it is possible to use as projectors the atomic pseudo-orbitals (generated from a self-consistent pseudo-atomic solver) or
the optimized NGWFs from a previous successful run (in our case a DFT run for the same system). In both cases only the NGWFs
associated with the relevant atoms, which here are all the pentacene atoms, are considered. Once the choice of projectors is made,
{\sc onetep} allows predominantly two kinds of population analysis on the set of target atoms. The first technique (the `Summed' analysis)
essentially calculates the populations on each individual atom and then sums them up. This population is defined as
\begin{align}\label{Summed_PopAn}
N_\textrm{Summed}=\sum\limits_{I}\sum\limits_{m m'}\bra{\varphi^I_{m}}\hat{\rho} \ket{\varphi^I_{m'}}O_I^{m'm}\:,
\end{align}
where $I$ is an atom in the desired set and $O_I^{m'm}$ are the elements of the inverse of the overlap matrix of the projectors
$\ket{\varphi^I_{m}}$ and $\ket{\varphi^I_{m'}}$ belonging to atom $I$ (this is very close to a Kronecker delta matrix in the case
of the pseudo-atomic orbitals). The second one (the `Unified' technique) calculates the tensorially invariant population
of the entire subspace  as
\begin{align}\label{Unified_PoPAn}
N_\textrm{Unified}=\sum\limits_{m m'}\bra{\varphi_m}\hat{\rho}\ket{\varphi_{m'}}O^{m'm}\:,
\end{align}
where the sum is over all the orbitals of the given subspace and the inverse overlap matrix is constructed accordingly~\cite{PhysRevB.93.165102,ORPM}.
The `Unified' technique is expected to be much more reliable, since the other double-counts the population shared by the projectors
belonging to different atoms. This is clearly seen in Fig.~\ref{fig:rPr}, which shows a plot of $\braket{r|\hat{\mathbb{P}}|r}$ for the neutral
pentacene molecule adsorbed on the graphene flake, where the positions $r$ lie on a plane passing close to all of the pentacene atoms.
Using the Summed scheme (top panel) we see significant positive values of $\braket{r|\hat{\mathbb{P}}|r}$ in the interstitial region between
the atoms, indicating the aforementioned double-counting. As expected, this is not present in the plot for the Unified scheme (bottom panel).

   \begin{table}
   \centering
    \begin{tabular}{ ccc}
    \hline \hline \vspace{0.5mm}
    Projector & Analysis & Population \\ \hline
    Atomic orbitals & Summed & 171.56\\
    Atomic orbitals & Unified & 100.74\\
    Optimized NGWFs & Summed & 172.72\\
    Optimized NGWFs & Unified & 102.11\\ \hline \hline
    \end{tabular}
     \captionsetup{justification=justified, singlelinecheck=false}
     \caption{Number of electrons on the pentacene molecule calculated by using different choices of projectors and for different population
     analysis methods. An isolated pentacene molecule has 102 valence electrons. Please see text in section~\ref{SubSubsection_PopAn_RE}
     for the definitions of `Summed' and `Unified'.}
       \label{table:PopulationAnalysis}
    \end{table}

In Tab.~\ref{table:PopulationAnalysis}, we tabulate the populations calculated with the different techniques/projectors on the pentacene
molecule, which is adsorbed on a flake of graphene. Noting that an isolated pentacene molecule has 102 valence electrons, we see that
the combination of optimized NGWFs with the Unified scheme reproduces this count to $0.1$\%, and  so we use this population analysis
for further calculations. The residual  $0.1$\% is due to hybridization with the graphene substrate (a very slight chemisorption effect).
We note that pseudo-atomic population analysis exhibits an under-count of approximately $1$\%, but that this is small compared to the error
of `Summed', or sometimes known as `on-site', population analysis. The significance of this result is that even pseudo-atomic orbitals can
provide a reasonable population analysis device for cDFT, if the nonorthogonality or equivalent L\"owdin treatment is tensorially invariant
(if it uses $\mathbf{O}$).

\begin{figure}
\centering
\subfloat[]
  \includegraphics[width=\columnwidth]{TC1_P.pdf}}%

\subfloat[]
 \includegraphics[width=\columnwidth]{TC4_P.pdf}}%
\caption{Plot of $\braket{r|\hat{\mathbb{P}}|r}$ for the pentacene molecule adsorbed on graphene in the neutral state. The top and the
bottom panels correspond respectively to the `Summed' analysis, which calculates population on individual atoms separately before adding
them up, and the `Unified' analysis, which calculates population of the entire subspace as a whole, respectively. In the case of the Summed
method, significant brightness in the interstitial space between atoms indicates double-counting in the region of orbital overlap. Clearly, this
is not the case for the Unified method.}\label{fig:rPr}
\end{figure}

\subsubsection{Calculation of the reorganization energy}

Once the population of the molecule, $N$, is determined, the target population for the cDFT calculation is defined as
$N_\textit{c} = N \times 101/102$. Fig~\ref{FIG:DensityPlot} shows the charge density on the system after the removal of an
electron from the molecule. As seen in the picture, a molecule with a net positive charge induces a negative charge in the region
of the graphene flake immediately beneath the molecule. This is the image charge.

\begin{figure}
\centering
\subfloat[]
  \fbox{\includegraphics[width=\columnwidth]{denpotC1_copy.pdf}}%
}

\subfloat[]
  \fbox{\includegraphics[width=\columnwidth]{denpotC2_copy.pdf}}%
}
\caption{Plot of isovalues of the change in charge density upon the removal of an electron from the molecule as calculated with cDFT.
Blue and red colors denote positive and negative charge densities, respectively.}\label{FIG:DensityPlot}
\end{figure}

We follow the steps outlined in the subsection~\ref{ProcedureForCalculation_RE} to calculate the reorganization energy of the
pentacene molecule adsorbed on the graphene flake. \rededit{Since the final energy of a {\sc onetep} calculation is dependent, albeit very weakly, on the initial NGWFs, we ensure that both the calculations used for computing each instance of $\lambda^0$ or $\lambda^+$ use optimized NGWFs of as similar a provenance as possible.} The main problem with such calculation is the existence of multiple configurational
local minima differing only slightly in energy. The local minimum that a structural relaxation converges to depends largely on the
initial geometry. Therefore we find the reorganization energy corresponding to the two local minima (one for the uncharged system and
another for the charged one).

As the opposite image charge formed on the flake results in a Coulomb attraction between the molecule and the flake, in the charged
state geometry $G_+$, the molecule is closer to the flake than in the uncharged geometry $G_0$. We also
notice that the directions of the in-plane displacements of the atoms of the pentacene molecule upon charging are very similar for the
isolated molecule and for the molecule adsorbed on the graphene flake, as it can be seen in Fig.~\ref{fig:DISPLACEMENTS}. Furthermore,
the average bond-length of the relaxed pentacene molecule is smaller for the charged case, for both the isolated and the adsorbed molecule.
This indicates a shrinking of the molecule on electron emission. Such change in the average bond-length is larger for the isolated pentacene
than for the adsorbed one, as indicated by length of the arrows in Fig.~\ref{fig:DISPLACEMENTS}. This can be attributed to the steric effects
due to the presence of graphene.
However, as mentioned earlier, one must keep in mind that these properties can, in principle, be specific
to the pair of local geometry minima pertaining the calculation. For a different pair of minima, these values could be different in principle.

   \begin{table}
   \centering
    \begin{tabular}{ cccccc}
    \hline \hline \vspace{0.5mm}
    Cutoff energy & flake & \hspace{2.5mm} $\lambda^0$ \hspace{2.5mm} & \hspace{2.5mm} $\lambda^+$ \hspace{2.5mm} & \hspace{2.5mm} $\lambda$ \hspace{2.5mm} & \hspace{0.5mm} $\Delta V_\textit{c}$
    \hspace{1.5mm} \\ \hline
    900 eV & none & 29 & 27 & 56 & N.A.\\
    900 eV & smaller & \rededit{23} & \rededit{26} & \rededit{49} & \rededit{44}\\
    900 eV & larger & \rededit{20} & \rededit{20} & \rededit{39} & \rededit{50}\\
    1500 eV & none & 29 & 27 & 56 & N.A.\\
    1500 eV & smaller & \rededit{25} & \rededit{25} & \rededit{51} & \rededit{45}\\
    1500 eV & larger & \rededit{17} & \rededit{23}  & \rededit{40} & \rededit{33}\\ \hline \hline
    \end{tabular}
     \captionsetup{justification=justified, singlelinecheck=false}
     \caption{Reorganization energies (corresponding to local minima in the geometry), of a pentacene molecule as a function of the
     cutoff energy and the size of the graphene flake. $\Delta V_\textit{c}$ denotes the difference in the cDFT Lagrange multipliers corresponding
     to the two different geometries. All energies are in meV. The smaller and the larger flakes contain 358 and 474 atoms
     at the optimized and idealized positions, respectively.}
       \label{table:ReorganizationEnergy}
    \end{table}

In Tab.~\ref{table:ReorganizationEnergy} we summarize our results for the reorganization energy for two different cutoff-energies and
different sizes of the graphene flake. We have also included the reorganization energy of an isolated pentacene molecule (flake=none)
for comparison. Note that our results for isolated pentacene matches with that obtained with MP2 method in an earlier theoretical
study~\cite{Gruhn_SF_B_T_M_M_C_K_B}. As mentioned in Eq.~(\ref{equReOr}) here, $\lambda^0$, $\lambda^+$ and $\lambda$ refer
to the reorganization energy contributions from the uncharged molecule, the positively charged molecule, and the total reorganization
energy, respectively.

\rededit{Since the reorganization energy is very small in general, minute fluctuations (per atom) arising due to diverse local geometry minimum or differences in the  NGWF initial state  can change the results considerably. As a result of exhaustive calculations using different NGWF restart protocols, we estimate the root mean square value of error caused by such deviations to be approximately $6$~meV for each instance of $\lambda^0$ or $\lambda^+$. Therefore, in Tab.~\ref{table:ReorganizationEnergy}, we  focus predominantly on the general trend in the results, which we consider to be quite robust, rather than the precise values.
An surprising effect to observe here is that while the
total reorganization energy $\lambda$ appears to be
insensitive to changes in the kinetic cutoff
energy, relative to its separate components
$\lambda^0$ and $\lambda^+$. It is not possible to
conclude that this is more generally the case based
on the available evidence.
The take home message of the table is} that the reorganization energy of the isolated molecule is generally greater than that of the same molecule on graphene. This can be attributed to steric effects for the latter case, namely to the fact that an adsorbed molecule has less freedom for ionic relaxation.

\rededit{The reorganization energy is lower for the larger flake. We attribute this to  two possible mechanisms: (i)  the freedom of ionic motion of the molecule may be more restricted for a larger substrate; (ii) since, as mentioned earlier, the bond lengths in the smaller flake are not all equal, adsorption on this flake is likely to result in a more uneven energy landscape for the pentacene molecule.} It is worth noting that we have analysed the different contributions due to Hartree, exchange and correlation, pseudopotentials, and kinetic energy
to the reorganization energy. However, the relatively small rereorganization energy turns out to be the result of the substantial cancellation
of large variations in these individual terms. It is noteworthy that experimental studies~\cite{KERA2009135,YH_NS_FH_KS_FR_OKK_UN}
on a rather different system of graphene-adsorbed pentacene, namely a thin film of pentacene deposited on HOPG, conversely exhibits an
increase in reorganization energy with respect to the isolated pentacene molecule. This points to the possibility that intermolecular relaxation
in the film contributes to the reorganization energy and more than compensates for the effects of steric hindrance.

\rededit{Here we note that, since, strictly speaking, the polarizability of the neutral molecule is different from that of the charged one, using the same form of empirical vdW correction for the molecule-flake interface in both cases may introduce some bias in the numerical results. To obtain an estimate for such error, we calculate, without using any vdW correction, the reorganization energy of pentacene adsorbed on the smaller flake using plane-wave cutoff of $900$~eV. We see that the results so obtained ($\lambda^0=23$~meV and $\lambda^+=29$~meV) are similar to those obtained with vdW corrections, and that the difference is
within the range of fluctuations caused by local minima and in the NGWF restart protocol.  We infer that the inclusion of the vdW corrections does not alter the reorganization energy significantly.}

We finally note that, since the Lagrange multiplier $V_\textit{c}$ for one-electron removal may be interpreted as an unscreened approximate
subspace-local ionization potential, and since the extent of the screening may be assumed to be independent of small changes in the ionic
geometry, so the difference, $\Delta V_\textit{c}$, between the converged Lagrange multipliers for the charged pentacene in geometries
$G_0$ and $G_+$ can be taken as an approximation for the reorganization energy. Also, since this quantity is evaluated explicitly only
on the basis of the occupancy of the adsorbate, we may expect it to be relatively free (that is, compared to the true reorganization
energy) from numerical errors in the optimized ionic positions of distant atoms in the graphene flake. Consequently, in
Tab.~\ref{table:ReorganizationEnergy}, we find that $\Delta V_\textit{c}$ is slightly less dependent on the nature of the substrate than the true
reorganization energy is but, in contrast, it seems to be too sensitive to the plane-wave energy cutoff for practical utility.

\begin{figure}
\subfloat[]
  \fbox{\includegraphics[width=\columnwidth]{Force_1.pdf}}%
}
\vspace{-0.620cm}
\subfloat[]
  \fbox{\includegraphics[width=\columnwidth]{Force_2.pdf}}%
}
\caption{Pentacene molecular geometry. The arrows show the directions and magnitudes of the in-plane displacement of the atoms in
response to the removal of one electron. The top and the bottom figures correspond to an isolated pentacene and one deposited on a
graphene flake, respectively. The graphene substrate introduces an effective steric hindrance, which reduces the reorganization effect
and energy}\label{fig:DISPLACEMENTS}
\end{figure}

\section{Conclusion}
We have presented a method for calculating self-consistent forces in conjunction with constrained DFT in first principles calculations
employing atom-centred functions. We have investigated a very accurate population analysis constructed over Wannier functions
and a tensorially consistent treatment of nonorthogonality. This is shown to yield an exact expression for force containing a Pulay term for
the change in nonorthogonality, which circumvents the need for overlap matrix diagonalisation and is compatible with complex-valued orbitals.
We have implemented this expression for the force in the DFT code {\sc onetep} and have shown that the contribution to the force arising
from the change in mutual overlap of the nonorthogonal projector orbitals of the subspace exerts significant influence on the geometry relaxation.

In order show a novel practical application of such forces, we perform a hyper-accurate geometry optimisation with numerous extra features to
capture the reorganization energy of a pentacene molecule adsorbed on a flake of graphene. We have argued that the Lagrange multiplier itself
can be used to provide a local estimate of the reorganization energy in systems, where the principal change to the system is spatially localised.
Since the geometry of such system has multiple local minima closely related in energy, the reorganization energy can, in principle, be calculated
only over such local minima. These depend on the initial geometry. We show that for the minima obtained in our calculations, the reorganization
energy of the molecule adsorbed on a graphene flake is typically smaller than that of the isolated molecule, a fact that is consistent with a steric hindrance effect.

\section*{ACKNOWLEDGEMENTS}

This work is supported by the European Research Council project \textsc{Quest}.
We acknowledge and thank G. Teobaldi and N. D. M. Hine for their implementation and automation of cDFT in \textsc{ONETEP},
D. Turban for extending the population analysis to encompass orbitals across multiple atomic centres, and C.-K. Skylaris and
his team for their prior implementation of the dispersion correction, boundary condition correction, and ensemble DFT in that package.
The authors  acknowledge the DJEI/DES/SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support. We also acknowledge Trinity Research IT for the maintenance of the Boyle cluster on which further calculations were performed.

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text:
The latest news and the coverage of news, events, videos, tweets and more from the U.S. Marine Corps.
Category Artillery Aviation Base or Station BioPhoto Career Ceremonies/Events Combat Combat Support Commandant of the Marine Corps Community Relations Deployment Education Environmental Expeditionary Family Historical Humanitarian Joint Operations Marine Corps Wide Medal of Honor Medal of Honor - Kyle Carpenter Operation Enduring Freedom Operation Iraqi Freedom Operational Personal Profile Policy Recreation Recruiting Safety Sergeant Major of the Marine Corps Sports Technology Training Veterans FRO JCISFA
Unit 10th Marine Regiment 11th Marine Expeditionary Unit 11th Marine Regiment 12th Marine Corps District 12th Marine Regiment 13th Marine Expeditionary Unit 15th Marine Expeditionary Unit 1st Air Naval Gunfire Liaison Company 1st Battalion, 11th Marines 1st Battalion, 5th Marine Regiment 1st Dental Battalion 1st Marine Aircraft Wing 1st Marine Corps District 1st Marine Division 1st Marine Expeditionary Brigade 1st Marine Logistics Group 1st Marine Special Operations Battalion 22nd Marine Expeditionary Unit 24th Marine Expeditionary Unit 26th Marine Expeditionary Unit 2nd Air Naval Gunfire Liaison Company (ANGLICO) 2nd Battalion 2nd Battalion 23rd Marines 2nd Dental Battalion 2nd Marine Aircraft Wing 2nd Marine Division 2nd Marine Expeditionary Brigade 2nd Marine Logistics Group 2nd Marine Regiment 31st Marine Expeditionary Unit 3D Law Enforcement Battalion 3rd Marine Aircraft Wing 3rd Marine Division 3rd Marine Expeditionary Brigade 3rd Marine Logistics Group 3rd Marine Regiment 4th Marine Corps District 4th Marine Division 4th Marine Regiment 5th Battalion, 11th Marines 5th Marine Expeditionary Brigade 6th Marine Corps District 6th Marine Regiment 8th Engineer Support Battalion 8th Marine Corps District 8th Marine Regiment 9th Marine Corps District Adjutant Administration and Resource Managment Assistant Commandant of the Marine Corps Chemical Biological Incident Response Force Combat Logistics Battalion 31 Combat Logistics Company 21 Combat Logistics Regiment 2 Combat Logistics Regiment 25 Combat Logistics Regiment 27 Combined Arms Training Center Camp Fuji Command Element, Marine Forces Central Command Forward Commandant of the Marine Corps Community of Interest Defense Logistics Agency Defense Media Activity Deployment Processing Command-East Deputy Commandant of Information Director of the Marine Corps Staff Division of Public Affairs Expeditionary Energy Office Field Medical Training Battalion-East Field Medical Training Battalion-West Ground Combat Element Integrated Task Force Headquarters Marine Corps Human Resources and Organizational Management I Marine Expeditionary Force I MEF Headquarters Group I MEF Information Group II Marine Expeditionary Force II MEF Headquarters Group II MEF Information Group III Marine Expeditionary Force III MEF Information Group III MEF/MCIPAC Consolidated Public Affairs Office Inspector General of the Marine Corps Installations and Logistics Marine Air Control Group 28 Marine Aircraft Group 14 Marine Aircraft Group 26 Marine Aircraft Group 29 Marine Aircraft Group 31 Marine Aviation Marine Barracks Marine Corps Air Facility Marine Corps Air Ground Combat Center Twentynine Palms Marine Corps Air Station Beaufort Marine Corps Air Station Camp Pendleton Marine Corps Air Station Cherry Point Marine Corps Air Station Futenma Marine Corps Air Station Iwakuni, Japan Marine Corps Air Station Iwakuni-Japanese Marine Corps Air Station Miramar Marine Corps Air Station Miramar-EMS Marine Corps Air Station New River Marine Corps Air Station Yuma Marine Corps Base Camp Blaz Marine Corps Base Camp Butler Marine Corps Base Camp Lejeune Marine Corps Base Camp Pendleton Marine Corps Base Hawaii Marine Corps Base Quantico Marine Corps Blount Island Command Marine Corps Civil-Military Operations School Marine Corps Combat Development Command Marine Corps Combat Service Support School Marine Corps Defense Services Organization Marine Corps Embassy Security Group Marine Corps Engineer School Marine Corps Engineer School Marine Corps Forces Africa Marine Corps Forces Central Command Marine Corps Forces Cyberspace Command Marine Corps Forces Europe Marine Corps Forces North Marine Corps Forces Reserves Marine Corps Forces South Marine Corps Forces Special Operations Command Marine Corps Helicopter Squadron One Marine Corps Installations Command, MCICOM Marine Corps Installations East Marine Corps Installations Pacific Marine Corps Installations West Marine Corps Institute Marine Corps Junior Reserve Officer Training Corps Marine Corps Logistics Base Albany Marine Corps Logistics Base Barstow Marine Corps Logistics Command Marine Corps Mountain Warfare Training Center Marine Corps Recruit Depot, Parris Island Marine Corps Recruit Depot, San Diego Marine Corps Recruiting Command Marine Corps Security Cooperation Group Marine Corps Security Force Regiment Marine Corps Support Facility New Orleans Marine Corps Systems Command Marine Corps Tactical Systems Support Activity Marine Corps Training and Education Command Marine Corps University Marine Corps Warfighting Laboratory Marine Expeditionary Brigade-Afghanistan Marine Fighter Attack Squadron 251 Marine Forces Command Marine Rotational Force - Darwin Marine Wing Support Squadron 371 Multi National Force - West Officer Candidate School Okinawa Marines PEO Land Systems Plans, Policies and Operations Programs and Resources Ready Marine Corps Recruiting Station New York Recruiting Station Pittsburgh Recruiting Station Twin Cities Safety School of Infantry-East School of Infantry-West Sergeant Major of the Marine Corps Staff Judge Advocate TF 51/5 The Official United States Marine Corps Public Website The United States Marine Drum and Bugle Corps Train the Trainer School Training Command U.S. Marine Corps Forces, Japan U.S. Marine Corps Forces, Korea U.S. Marine Corps Forces, Pacific U.S. Marine Corps Forces, U.S. Strategic Command United States Marine Band United States Navy Wounded Warrior Regiment
Theme Force Design Education and Training Core Values Command and Leadership Warfighting
Tag: Carlton Sauls
Korean War Survivors Break Ground on 'Chosin Few' Memorial at DFW National Cemetery
1/12/2022 - https://www.nbcdfw.com/news/local/korean-war-survivors-break-ground-on-chosin-few-memorial-at-dfw-national-cemetery/2856459/
First US Marine Corps F-35C squadron deploys on USS Abraham Lincoln
1/07/2022 - https://www.navyrecognition.com/index.php/naval-news/naval-news-archive/2022/january/11215-first-us-marine-corps-f-35c-squadron-deploys-on-uss-abraham-lincoln.html
US Marines Live-Test Medium-Range Interceptor Prototype
12/23/2021 - https://www.thedefensepost.com/2021/12/23/marines-interceptor-missile-test/
Marine Corps conduct field training exercise in Japan
12/21/2021 - https://homelandprepnews.com/stories/75222-marine-corps-conduct-field-training-exercise-in-japan/
Biden awards Congressional Gold Medal to Lawrence Marine, 12 other service members killed in evacuation from Afghanistan
12/17/2021 - https://www.bostonherald.com/2021/12/16/biden-awards-congressional-gold-medal-to-lawrence-marine-12-other-service-members-killed-in-evacuation-from-afghanistan/amp/
RT @2ndMLG: We are aware of a vehicle rollover in Jacksonville, North Carolina, involving service members with 2nd MLG. We are working clos…
@usmc 7 hours ago Follow @usmc
Jim "Horse Collar" Smith, a Marine Corps Raider who served in both World War II and the Korean War, passed away in… https://t.co/WBFoTKSFiT
@usmc 11 hours ago Follow @usmc
An F-35C Lightning II aircraft with Marine Fighter Attack Squadron (VMFA) 314, @3rdmaw, lands on the flight deck of… https://t.co/GLEdRArbTL
#Marines with the @22nd_MEU load gear and personnel onto a landing craft, air cushion aboard @camp_lejeune, Jan. 15… https://t.co/9wfXYzBWJ7
@usmc 1 day ago Follow @usmc
#OTD, we honor the life and legacy of Dr. Martin Luther King Jr. He is remembered as one of the most significant le… https://t.co/Q2z2qdPKnW
@usmc 2 days ago Follow @usmc

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: antisamy does not encode @ I am using antisamy 1.5 to prevent XSS.
I saw issue when input was
firstname,lastname<name@mail.com> or firstname,lastname<name@mail.com testing>

Result after Antisamy scan is same for both above case
firstname,lastname<name>

I have below directive in policy file
<directive name="onUnknownTag" value="encode"/>

Is there a place in policy file I can update to encode @ ?

redpajama_set_name: RedPajamaStackExchange


Recently I've been rolling out a lot of fresh pasta.
And baking ovens full of bread.
And enjoying pizza with a young friend.
And driving by wheat fields that will soon be harvested.
It never ceases to amaze me what can be done with some flour and water.
← Prosciutto e melone, does it get any better than this?


text:
Google imagines environment-aware mobile adverts
The patent potentially paves the way for a mobile phone fitted with sensors. If you have ever stood in the rain wondering where the nearest umbrella shop is, then the latest Google patent may interest you. The search giant has secured intellectual rights to a system that would serve ads based on environmental conditions. Google said forward-looking patents were useful for its portfolio, but it had no current plans to act on it. But privacy advocates have warned it could set a dangerous precedent.
Data theft: Hacktivists 'steal more than criminals'
Hacktivists stole more data from large corporations than cybercriminals in 2011, according to a study of significant security incidents. The annual analysis of data breaches by Verizon uncovered a huge rise in politically motivated attacks. Verizon found that 58% of all the data stolen during breaches in 2011 was purloined by these groups. Hacktivists were hard to defend against, it said, as their attack strategies were much harder to predict. The Verizon report catalogued 855 incidents around the world in which 174 million records were stolen.
Report: Mobile Devices Boost News Consumption
If you're anything like me, mobile devices have transformed the way you consume the news. I'll often fish out my iPhone and pull up New York Times headlines when waiting in line for just about anything. The bulk of the magazine journalism I read, too, I tend to read on my phone. The Instapaper add-on is one of just three I keep handy in my Chrome browser; I'm constantly clicking it, pushing long-form stories to my iPhone, which then becomes a personalized magazine of sorts for trips on the subway. A new study from the Pew Research Center's Project for Excellence in Journalism reveals that more and more Americans are consuming media on their tablets and smartphones. The picture isn't all rosy, however. "For news, the new era brings mixed blessings," writes Pew.
Rumor: A $149 Google Nexus Tablet?
The rumors are coming from all angles. Let's start with the most audacious one: that a forthcoming Google tablet might retail for as low as $149. That comes via a site called Android and Me, which cites a supply chain source calling the tablet "a done deal." That's an interesting price, undercutting the Kindle Fire and Nook Tablet by 50 bucks. If it were comparable with those two devices in terms of specs, it might be hard for many consumers to justify shelling out for either of the former. (Then again, it's easy to imagine Amazon slashing its own prices the instant it began to detect real competition; the Kindle Fire becomes a real moneymaker by serving as a portal to Amazon's own content.) Android and Me classifies that $149 figure as a "rumor," however, and I'm not aware of that site getting other big scoops in the past. It will be interesting to see if the site's claims are borne out. CNET's Brooke Crothers, a smart fellow when it comes to hardware, deems the rumor credible enough or at least compelling enough to reference in a recent post, as have other tech bloggers of repute.
Just How Much Is Your Privacy Worth?
By Nic Fleming, Technology Review
Most of us would shy away from making purchases in a foreign country if we didn't know the exchange rate. Yet, if privacy is the true currency of the Internet, as many argue, millions of us are doing that very thing every day. Meanwhile, Internet giants amend their privacy policies in ways that allow them to harvest and sell even more of our personal data. While privacy campaigners protest, users generally vote with their clicks and carry on regardless. So should we conclude the Internet generation is happy to trade its privacy for free or cheaper Web services? Not according to Nicola Jentzsch of the German Institute of Research in Berlin, and colleagues, who last week published research showing that most people prefer to protect their personal data when given a choice and that a significant proportion are willing to pay extra to do so.
TVs and Tablets to Get the "Retina Display" Treatment
A manufacturing technique being adopted by companies that make gadgets for some of the biggest names in consumer tech will help them significantly improve the resolution of TV and tablet displays later this year. Applied Materials, which makes electronics manufacturing equipment, has introduced machines that make it feasible to use an advanced approach for making displays—previously limited to R&D—at a large scale. This will enable consumer electronics companies to put screens with much higher resolution into many gadgets, Applied Materials says.
Big Data for the Rest of Us, in One Start-Up
By QUENTIN HARDY, NY Times
The best insight into the current state of the Big Data business may be a five-person start-up in Palo Alto, Calif. While the industry mostly gathers lots of data, or stores it in new cloud-based databases, the start-up, ClearStory Data, is building the biggest possible base of data consumers. ClearStory, which was formed last summer, is making software for ordinary business professionals. These customers will be able to blend their own corporate data with the large amounts of publicly available data, in search of new statistical insights. There just aren't enough statisticians, the company figures, to address the demand corporations will have for Big Data.
http://bits.blogs.nytimes.com/2012/03/19/all-about-big-data-in-one-startup/?src=me&ref=technology
Google Inc (GOOG) – YouTube Alone Could be Worth $45.7 Billion
by Eliot Turner, Value Walk
Want to invest in one of the best, most innovative startups in the world with taking none of the risk associated with a startup, and more potential upside than many of the most popularly watched private market web names like Facebook? Look no further than the strongest brand hiding behind the Google Inc (NASDAQ:GOOG) name: YouTube. YouTube is turning into a huge business, and were it a standalone start-up, the company would easily be one of the most valuable Internet companies and one of the most hyped. Instead we hear little about YouTube's business other than the obligatory question and non-answer answer on each Google quarterly conference call about when/if/how much money YouTube will make.
http://www.valuewalk.com/2012/03/google-inc-goog-youtube/
The Snails of War
By JAMES GORMAN, New York Times
The electric snail is here. There's an electric cockroach too. A snail with implanted biocatalytic electrodes connected with crocodile clips to the external circuitry. Both are early experimental forays in a new line of research aimed at creating tiny, self-powered animal/machine hybrids as an alternative to tiny robots. Instead of starting from scratch and having to solve all those pesky movement problems that plague roboticists, some researchers have asked, why not start out with living creatures that already know how to walk and fly?
http://www.nytimes.com/2012/03/21/science/the-snails-of-war-and-other-robotics-experiments.html?_r=1&ref=technology
Windows 8 may have October launch date
The initial rollout will include devices running Intel Corp. and ARM Holdings Plc chips, making good on Microsoft's promise to support both standards, said the people, who declined to be named because the plans are confidential. In embracing ARM technology, Microsoft is using the same kind of processors as Apple Inc.'s iPad. Still, there will be fewer than five ARM devices in the debut, compared with more than 40 Intel machines. The timing would let Microsoft target Christmas shoppers with the new software, which works with touch-screen devices as well as laptops and desktop PCs. The Redmond, Washington-based company, which hasn't announced timing for the Windows 8 release, aims to take back sales lost to the iPad and reinvigorate the sluggish PC market. Apple released the third version of the iPad this month, posing an even stiffer challenge to Microsoft.
http://www.washingtonpost.com/business/technology/windows-8-may-have-october-launch-date/2012/03/20/gIQA3Ci8PS_story.html
Employers ask job seekers for Facebook passwords
by MANUEL VALDES and SHANNON MCFARLAND, Associated Press
When Justin Bassett interviewed for a new job, he expected the usual questions about experience and references. So he was astonished when the interviewer asked for something else: his Facebook username and password. Bassett, a New York City statistician, had just finished answering a few character questions when the interviewer turned to her computer to search for his Facebook page. But she couldn't see his private profile. She turned back and asked him to hand over his login information. Bassett refused and withdrew his application, saying he didn't want to work for a company that would seek such personal information.
http://www.ydr.com/business/ci_20215796/employers-ask-job-seekers-facebook-passwords
The robots are coming! Better get used to it
by Stephen Shankland, CNET news.com
Six times in the last month I've been struck by the increasing utility of robots performing tasks that a human otherwise would. I can't imagine the number will be going down, either. The most recent example was Amazon's $775 million acquisition of Kiva Systems, a company that automates warehouse operations with robots. "Kiva's technology is another way to improve productivity by bringing the products directly to employees to pick, pack, and stow," said Dave Clark, vice president of global customer fulfillment at Amazon, in a statement. In other words, robots do a lot of the grunt work to make the warehouse run faster. Amazon knows a lot about operating at large scale, and robots that might not make sense for a small company are a good match for huge warehouses wired directly to a huge e-commerce operation.
http://news.cnet.com/8301-30685_3-57400957-264/the-robots-are-coming-better-get-used-to-it/?tag=mncol;topStories
New York Times cuts free reads in half
by Don Reisinger, CNET news.com
The New York Times has cut the number of free online articles that readers are allowed to access per month in half. The publishing company today said that starting in April readers will be able to access 10 stories for free each month. The New York Times previously allowed its readers to access 20 free stories online. The move is a not-so-subtle attempt on the Times' part to push more of its readers to digital subscriptions. Those digital paid subscriptions have proven somewhat popular, the Times said. In the last year since they've been available, 454,000 subscriptions have been purchased for access to The New York Times and the International Herald Tribune.
http://news.cnet.com/8301-13506_3-57400710-17/new-york-times-cuts-free-reads-in-half/
Apple on new iPad heat issue: It's not as hot as you think
Some customers say Apple's new iPad is running hotter than its predecessor. But the Cupertino, Calif.-based company says it's just right. "The new iPad delivers a stunning Retina display, A5X chip, support for 4G LTE plus 10 hours of battery life, all while operating well within our thermal specifications," an Apple representative told CNET today. "If customers have any concerns, they should contact AppleCare." All Things Digital was first to report of Apple's response to heat claims regarding its newly released tablet.
http://news.cnet.com/8301-13506_3-57400794-17/apple-on-new-ipad-heat-issue-its-not-as-hot-as-you-think/
Khan Academy for the Masses – ShowMe Boasts 1.5M Lessons
by Startl
ShowMe, the startup with the ultimate iPad app and corresponding web platform, turns the iPad into a video whiteboard allows teachers to record lessons while drawing on the touchscreen whiteboard. The recorded video lesson can then be shared on the app and web where learners can browse video lessons on everything from math and physics to finance, history and the arts at their own pace. ShowMe has over 400k downloads since summer 2011 and with over 1.5 million lessons is taking the Khan Academy concept mainstream. ShowMe's technology powers Princeton Review's SAT Prep app.
http://startl.org/blog/2012/03/18/khan-academy-for-the-masses-showme-boasts-1-5m-lessons/
New iPad: 10 Lessons Learned During the First Weekend
By: Don Reisinger, eWeek
3. I don't think iPad 2 owners should upgrade
I have several friends and family that currently own the iPad 2. And as one might expect, they wanted to find out if they should dump the old option to get the new one. I told them without thinking twice that jumping to the new iPad wouldn't make much sense. Sure, the Retina Display is great and the LTE is a welcome addition, but they're not worth another $629 and up. Current iPad 2 owners should stick with their favored tablet.
http://www.eweek.com/c/a/Mobile-and-Wireless/New-iPad-10-Lessons-Learned-During-the-First-Weekend-409429/
Dell's Windows 8 Tablets Will Target iPad
Dell wants to pull an Apple in the tablet market. "We have a road map for tablets that we haven't announced yet," Dell chief commercial officer Steve Felice told Reuters March 16. "We don't think that this market is closed off in any way." Those announcements will apparently come in the second half of 2012, suggesting a holiday release for whatever Dell has tucked up its collective sleeve. Dell will concentrate its tablet efforts on Windows 8, Microsoft's upcoming operating system also due later in the year. Although Apple's iPad has made steady inroads into the enterprise, Dell apparently believes that its experience in areas such as security and interoperability will allow it to claim the allegiances of a significant number of businesses.
http://www.eweek.com/c/a/Mobile-and-Wireless/Dells-Windows-8-Tablets-Will-Target-iPad-783013/
NetZero Offers Low-Cost 4G Wireless Service
NetZero Wireless, a subsidiary of United Online Inc. announced the launch of NetZero 4G mobile broadband, protected Internet service for notebooks, iPads and other tablets, and netbooks. The service, which launches this week in more than 80 cities nationwide, including New York, Los Angeles, Chicago, Houston, Philadelphia, San Francisco, Washington, D.C., and Miami, lets consumers or small and midsize businesses (SMBs) create a personal Internet connection without being tied to unsecure public hotspots at places like coffee shops, airports and hotels. The company's 4G mobile broadband data plans start at just $9.95 per month. Additionally, customers are not required to sign a contract and can upgrade their data plan at any time. Each plan delivers 4G service with download speeds of up to 10M bps and upload speeds of up to 1.5M bps. All data plans, including the free plan, require the purchase of one of two access devices: the NetZero 4G HotSpot and the NetZero 4G Stick.
http://www.eweek.com/c/a/Mobile-and-Wireless/NetZero-Offers-Free-4G-Wireless-Service-459981/
Free mobile apps 'drain battery faster'
Free mobile apps which use third-party services to display advertising consume considerably more battery life, a new study suggests. Researchers used a special tool to monitor energy use by several apps on Android and Windows Mobile handsets. Findings suggested that in one case 75% of an app's energy consumption was spent on powering advertisements. Report author Abhinav Pathak said app makers must take energy optimisation more seriously. Free applications typically have built-in advertisements so developers can make money without having to charge for the initial app download.
Startups Aim to Make Coding Fun
For Jacob Arriola, a business development manager for a Spanish media company in Los Angeles, learning to program wasn't a necessity. But figuring it might help with his job, he started using an online code-tutorial service called Treehouse in January. After three months with the paid service, he's earned several dozen badges for completing programming quizzes and challenges, and watching coding-related video lessons. Arriola is one of a growing number of non-techies turning to Web-based sites to learn how to code, either for fun or in hopes of advancing their job prospects. And while the basic concept isn't new, the execution is. The addition of video-game elements like badges and points is helping startups such as Treehouse take off.
Android Ads Could Attack, Study Warns
To guard against malicious behavior, apps that run on Android smart phones must ask politely for permission to do things like access your personal information, track your location, or transmit data via the Internet. But once they have approval, these apps can share the permissions with the advertising libraries they use to serve up ads, creating serious potential privacy and security vulnerabilities, researchers have found. Combing through 100,000 apps selected randomly from Google Play (the erstwhile Android Market), a team of researchers at North Carolina State University found that 48,139 of the ad libraries used by these apps tracked the user's GPS location; 18,575 tracked the identity of the phone (its IMEI number); 4,190 let advertisers track the user via GPS; and 4,047 accessed the device's phone number.


H.E. Dato Abd Razak met the President of Turkey Badminton Federation, Mr. Murat Ozmekik at the latter's office in Kecioren Municipality, Ankara. 6 February 2019.
H.E. Dato' Abd Razak met the President of Turkey Badminton Federation, Mr. Murat Ozmekik at the latter's office in Kecioren Municipality, Ankara. 6 February 2019.
H.E Dato' Abd Razak Abdul Wahab, was awarded "Ambassador of the Year" at the illustrious 7th International Buhara Media Award Gala Night that was convened at Sheraton Ankara Hotel on 7 November 2018. Congratulations H.E Dato' Ambassador!
MALAYSIA My Second Home -Apply Now!


If this is the first blog you are reading then welcome! If you are reading this because you are unfortunate enough to be friends with me on Facebook then it's nice to see you back, sorry for strong-arming you into returning.
Ok the last one about my parents isn't true (hopefully) but you get the picture.
I resolve to try and not talk about this as much from now on and thank you for your patience. FYI – some people reading this don't live in Manchester! Apparently I'm a "hit" in India (6 views baby!) and to the one person in Iceland who has seen my blog – hallo.
Before I get too carried away and imagine myself sipping a chai latte in Greenwich Village whilst pondering the deep injustices of the world and preparing my next Pulitzer acceptance speech I have to remind myself that I have only written 2 blogs. The Hunger Games it ain't. Chances of me winning any literary awards or moving to New York for that matter are about the same as the chances of me sprouting wings or becoming an astronaut or not doing my stupid rap when I am drunk (Yes it happened again – I hate myself!). Plus I hate the taste of chai – it tastes like socks.
Here we are then. The third date. This could be make or break for us. If it makes you feel better so far this is probably the best third date I have had in a long time (or the only third date I've had in a long time but whatever – I'm a career girl *gulps red wine*).
When I started writing for your amusement and my own sanity I swore I wouldn't make this another "twenty-something single gal" blog. Mainly because I am inching my way towards thirty – aaa. But also other people have done it and done it better. The first Bridget Jones film was released 13 years ago! Renee has moved on and I think we should too.
This being said we are at the start of wedding season and this can sometimes turn even the most sensible of girls into a dribbling snivelling wreck.
We have all been there at some point in our lives. Currently I'd like to think I'm pretty happy being single but honestly – who cares?
So single wedding guests one and all I implore you to follow this advice. Rather than seeing weddings as another opportunity to feel sorry for ourselves and the fact that we might die alone I am going to appreciate it for what it is. An amazing opportunity to get all my very best friends in the same room looking slightly less dishevelled than normal with a cheesy DJ and lashings of wine.
A wedding is not the time to feel down. It isn't about me at all. It is about my friends making a lifelong commitment to each other and paying for me to have a free buffet while they are at it. Not only do I feel honoured that they want me to be there but I'm flippin grateful for the invite – Vol-au-vent anyone?
So girls (and guys) when you are at a wedding, don't feel sorry for yourself. Don't cry when you have had too much toasting fizz. Be happy. Laugh lots. Appreciate the moment and, most importantly, dance like an idiot.


text:
package com.github.quintans.ezSQL.toolkit.utils;

import java.util.function.Consumer;

public class Result<T> {
    private boolean success;
    private T value;

    public static <R> Result<R> of(R value) {
        return new Result<>(value, true);
    }

    public static <R> Result<R> fail() {
        return new Result<>(null, false);
    }

    public static <R> Result<R> fail(R value) {
        return new Result<>(value, false);
    }

    public Result(T value, boolean success) {
        this.success = success;
        this.value = value;
    }

    public boolean isSuccess() {
        return success;
    }

    public T get() {
        return value;
    }

    public void onSuccess(Consumer<T> consumer){
        if(this.success) {
            consumer.accept(value);
        }
    }

    public void onFailure(Consumer<T> consumer){
        if(!this.success) {
            consumer.accept(value);
        }
    }
}

redpajama_set_name: RedPajamaGithub


text:
Memorial Congregational Church of Sudbury, MA
No matter who you are or where you are on lifes journey, you are welcome here!
All are welcome. Really!
Affliliated Ministries
MCC in Pictures
Youth Music
Sudbury Bell Ringers
Covenant Band
Annual Concert Series
Renaming Ceremony
Sign up to help
Food Packaging – March 1, 2020
Help on Sundays
Spotlight: Church Floats Message Across Sudbury
Originally posted at http://www.macucc.org/newsdetail/spotlight-church-floats-a-message-across-sudbury-5287461
Fourth of July fireworks and parades usually generate a lot of noise and attention. This month Memorial Congregational Church, UCC, Sudbury (MCC) used the opportunity of the town's parade to make some noise and draw attention to the "Be the Church" message.
Church members created a float that was a replica of the church building — complete with a detailed steeple and bell tower, and a rainbow flag. Marchers accompanied the float with handheld signs highlighting the individual statements from the "Be the Church" banner that is also displayed in front of the church.
"We had to find a way to combine the parade's theme, 'Celebrate the American Dream,' with the message we wanted to share about our church," said Pastor Tom O'Brien. "I was planning to preach a sermon series on the UCC's 'Be the Church' campaign so the members wanted to highlight those statements. We had recently placed a banner on the outside of the church and we felt the words spoke to who we are as a church."
Eight people worked about 20 hours to design and build the float over two weekends. Many hours went into creating the octagonal bell tower out of cardboard and the weather vane out of tinker toys. Costs were fairly minimal as the team tried to use materials that were around or donated. A pop-up tent was purchased, but will be used for other church events. Flowers were added as a finishing touch.
Eleven adults marched with signs, while an additional eleven children rode the float or marched with the adults. All along the route, parade goers recognized the church and made many positive comments about the banner statements that included "Care for the Poor," Protect the Environment," and "Forgive Often."
Many in the community were then able to connect the 'Be the Church' message to the congregation. "There were remarks from some that the statements were powerful while others expressed that they were glad such a church was in their town," said O'Brien. "Our message seemed very well-received."
Members of the church felt that it was important to seize this opportunity to let the town know what their church represented. "While much of the media portrays Christians as anti-LGBT or Christianity as a list of 'Thou Shall Nots,' we wanted to show that MCC, and the United Church of Christ, believe that we are called to speak out for the oppressed and lift up the lowly.
"This was a fun way for us to share the gospel as we understand it."
26 Concord Rd.
(across from Goodnow Library)
Food Packaging on March 1, 2020 11:00 am
Trivia Night is Back but with a twist – ZERO WASTE on March 14, 2020 5:30 pm
Songs of the Season
Meditation on hope from Rev. Gail Wright
Destroyed, Dis-remembered, Disregarded
Come Back to God.
On Toxic Masculinity
Sign up to keep up to date with church events
Copyright © 2020 Memorial Congregational Church of Sudbury, MA. Powered by WordPress. Theme: Spacious by ThemeGrill.


Revenue from tourism rose 10.8 per cent year-on-year in May, to €224.1 million, compared with €201.1 million in 2013, the statistical service said on Friday.
Proceeds from tourism in the first five months of the year also rose 8.6 per cent year-on-year to €475.5 million.
May saw 293,181 tourist arrivals who stayed on the island an average 10 days. Average spending was around €764 per person, the statistical service said.
In May last year, 276,244 tourists spent around €731 per person during an average stay of 9.3 days.
Germans topped the list of spenders in May 2014, averaging around €901 per person with an average stay of 10.6 days. However, only 8,564 German tourists visited Cyprus compared with 88,426 Russians who spent €874 per person. The average stay for Russian tourists was 9.2 days.
The statistical service said 106,063 British tourists visited Cyprus in May, spending an average 750 per person during the 11.4 days they stayed on the island.


text:
Harry Partch (Oakland (California), 24 de juny de 1901 - San Diego (California), 3 de setembre de 1974) fou un compositor estatunidenc. Pioner de la música aleatòria, el microtonalisme i de la utilització no estàndard dels instruments musicals tradicionals, com la creació del kitara, Quadrangularus Reversum. Partch va ser una de les principals figures de l'avantguarda de la post-guerra. Però les principals influències de Partch provenen de les cultures orientals.

Discografia

Album
 The World of Harry Partch (Columbia Masterworks MS 7207 & MQ 7207, 1969, out of print) "Daphne of the Dunes", "Barstow", and "Castor & Pollux", conducted by Danlee Mitchell under the supervision of the composer.
 Delusion of the Fury (LP Columbia Masterworks M2 30576, 1971; CD Innova 406, 2001) "Delusion of the Fury", conducted by Danlee Mitchell under the supervision of the composer and "EXTRA: A Glimpse into the World of Harry Partch", composer introduces and comments on the 27 unique instruments built by him.
 Enclosure II (early speech-music works) (Innova 401)
 Enclosure V ("On a Greek Theme") (Innova 405)
 Enclosure VI ("Delusion of the Fury") (Innova 406)
 The Seventeen Lyrics of Li Po (Tzadik, 1995). ASIN B000003YSU.
 Revelation In The Courthouse Park (Tomato Records TOM-3004, 2003)

Video
 Enclosure I (Innova 400, VHS) Four films by Madeline Tourtelot
 Enclosure IV (Innova 404, VHS) "Delusion", "Music of HP"
 Enclosure VII (Innova 407, DVD) "Delusion", "Dreamer", Bonus Album, "Revelation"
 Enclosure VIII (Innova 399, DVD) Four Films by Madeline Tourtelot: "Music Studio," "Windsong," "U.S. Highball," and "Rotate the Body in All Its Planes," with "The Music of Harry Partch" KEBS-TV documentary, "Barstow" and "Castor and Pollux".
 Musical Outsiders: An American Legacy - Harry Partch, Lou Harrison, and Terry Riley. Directed by Michael Blackwood. (1995)

Bibliografia
 Blackburn, Philip (1998). Harry Partch: Enclosure III. Saint Paul: Innova. .
 Gilmore, Bob (1998). Harry Partch, A Biography, New Haven: Yale University Press.
 Partch, Harry (1974). Genesis of a Music. New York: Da Capo Press. .
 Partch, Harry (1991). Bitter Music: Collected Journals, Essays, Introductions and Librettos, Champaign: University of Illinois Press.

Referències

Enllaços externs
 www.harrypartch.com
 Corporeal Meadows

Compositors estatunidencs del segle XX
Persones de San Diego
Naixements del 1901
Morts a San Diego
Marimbistes estatunidencs
Violistes estatunidencs
Morts d'infart de miocardi
Compositors californians
Percussionistes estatunidencs
Músics d'Oakland

redpajama_set_name: RedPajamaWikipedia


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