# List of My Publications

# 2009

# Approaching the Hartree-Fock Limit by Perturbative Methods

### Jia Deng, Andrew T.B. Gilbert, Peter M.W. Gill, J Chem Phys 130 (2009) 231101

We describe perturbative methods for improving finite-basis Hartree-Fock calculations toward the complete-basis limit. The best method appears to offer quadratic error reduction and preliminary numerical applications demonstrate that remarkably accurate Hartree-Fock energies can be obtained.

# Self-Consistent-Field Calculations of Core Excited States

### Nicholas A. Besley, Andrew T. B. Gilbert and Peter M. W. Gill J Chem Phys 130 (2009) 124308

The accuracy of core excitation energies and core electron binding energies computed within a Δself-consistent-field framework is assessed. The variational collapse of the core excited state is prevented by maintaining a singly occupied core orbital using an overlap criterion called the maximum overlap method. When applied to a wide range of small organic molecules, the resulting core excitation energies are not systematically underestimated as observed in time-dependent density functional theory and agree well with experiment. The accuracy of this approach for core excited states is illustrated by the calculation of the pre-edge features in X-ray absorption spectra of plastocyanin, which shows that accurate results can be achieved with Δself-consistent-field calculations when used in conjunction with uncontracted basis functions.

# Rydberg States of the Helium Atom

### Jia Deng, Andrew T. B. Gilbert, Peter M. W. Gill Int J Quant Chem 109 (2009) 1915

Using the recently introduced maximum overlap method and
Hartree-Fock Perturbation Theory (HFPT), we compute
Hartree-Fock (HF) wavefunctions for triplet 1s *n*s
states of the helium atom. Comparison with near-exact
results from Nakatsuji's free ICI method reveals that HF
theory provides a simple route to accurate energies of these
Rydberg states, especially for large *n*.

# The role of exchange in systematic DFT errors for some organic reactions

### David R. B. Brittain, Ching Yeh Lin, Andrew T. B. Gilbert, Ekaterina I. Izgorodina, Peter M. W. Gilla and Michelle L. Coote Phys Chem Chem Phys 11 (2009) 1138

Serious (up to 87 kJ/mol) systematic DFT errors in a series of isodesmic reactions are found to be due to the DFT exchange component, and can be largely corrected by substitution of the DFT exchange energy with the Fock exchange energy.

# Resolutions of the Coulomb operator: II. The Laguerre generator

### Peter M. W. Gill and Andrew T. B. Gilbert Chem Phys 356 (2009) 86

We discuss a resolution of the Coulomb operator,
r_{12}^{-1} = |φ_{i}
〉〈φ_{i}|, into a one-particle
basis. We show that the Laguerre polynomials generate a
resolution with attractive computational properties and we
apply it to the calculation of Coulomb and exchange energies
in hydrogenic ions, the H_{2} molecule, and the Be
atom. Rapid convergence is observed in all cases and a
theoretical reason for this is discussed.

# 2008

# Self-consistent field calculations of excited states using the Maximum Overlap Method (MOM)

### ATB Gilbert, NA Besley, PMW Gill, J Phys Chem A 112 (2008) 13164

We present a simple algorithm, which we call the maximum overlap method (MOM), for finding excited-state solutions to self-consistent field (SCF) equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rather than the lowest energy, solution. The resulting excited-state solutions can be treated in the same way as the ground-state solution and, in particular, derivatives of excited-state energies can be computed using ground-state code. We assess the performance of our method by applying it to a variety of excited-state problems including the calculation of excitation energies, charge-transfer states, and excited-state properties.

# A generalized Poisson equation and short-range self-interaction energies

### SA Varganov, ATB Gilbert, PMW Gill J Chem Phys 128 (2008) 241101

We generalize the Poisson equation to attenuated Newtonian potentials. If the attenuation is at least exponential, the equation provides a local mapping between the density and its potential. We use this to derive several density functionals for the short-range self-interaction energy.

# Resolutions of the Coulomb operator

### SA Varganov, ATB Gilbert, E Deplazes, PMW Gill J Chem Phys 128 (2008) 201104

We discuss a generalization of the resolution of the
identity by considering one-body resolutions of two-body
operators, with particular emphasis on the Coulomb operator.
We introduce a set of functions that are orthonormal with
respect to 1/r_{12} and propose that the resulting
"resolution of the Coulomb operator",
r^{-1}_{12} = |φ_{i}⟩⟨φ_{i}|.
We generalize the Poisson equation to attenuated Newtonian
potentials. If the attenuation is at least exponential, the
equation provides a local mapping between the density and
its potential. We use this to derive several density
functionals for the short-range self-interaction energy.

# Calculating molecular vibrational spectra beyond the harmonic approximation

### CY Lin, ATB Gilbert, PMW Gill Theor Chem Acc 120 (2008) 23

We present a new approach for calculating anharmonic corrections to vibrational frequency calculations. The vibrational wavefunction is modelled using translated Hermite functions thus allowing anharmonic effects to be incorporated directly into the wavefunction whilst still retaining the simplicity of the Hermite basis. We combine this new method with an optimised finite-difference grid for computing the necessary third and fourth nuclear derivatives of the energy. We compare our combined approach to existing anharmonic models - vibrational self-consistent field theory (VSCF), vibrational perturbation theory (VPT), and vibrational configuration interaction theory (VCI) - and find that it is more cost effective than these alternatives. This makes our method well-suited to computing anharmonic corrections for frequencies in medium-sized molecules.

# 2007

# BFW: A density functional for transition metal clusters

### MA Addicoat, GF Metha, MA Buntine, ATB Gilbert, PMW Gill J Phys Chem A 111 (2007) 2625

Ionization potentials (IPs) or electron affinities (EAs) for transition metal clusters are an important property that can be used to identify and differentiate between clusters. Accurate calculation of these values is therefore vital. Previous attempts using a variety of DFT models have correctly predicted trends, but have relied on the use of scaling factors to compare to experimental IPs. In this paper, we introduce a new density functional (BFW) that is explicitly designed to yield accurate, absolute IPs for transition metal clusters. This paper presents the numerical results for a selection of transition metal clusters and their carbides, nitrides, and oxides for which experimental IPs are known. When tested on transition metal clusters, the BFW functional is found to be significantly more accurate than B3LYP and B3PW91.

# Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations

### HL Woodcock, M Hodoscek, ATB Gilbert, PMW Gill, HF Schaefer, BR Brooks J Comput Chem 28 (2007) 1485

A hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy function with Hartree- Fock, density functional theory (DFT), and post-HF (RIMP2, MP2, CCSD) capability has been implemented in the CHARMM and Q-Chem software packages. In addition, we have modified CHARMM and Q-Chem to take advantage of the newly introduced replica path and the nudged elastic band methods, which are powerful techniques for studying reaction pathways in a highly parallel (i.e., parallel/parallel) fashion, with each pathway point being distributed to a different node of a large cluster. To test our implementation, a series of systems were studied and comparisons were made to both full QM calculations and previous QM/MM studies and experiments. For instance, the differences between HF, DFT, MP2, and CCSD QM/MM calculations of H2O...H2O, H2O...Na+ , and H2O...Cl- complexes have been explored. Furthermore, the recently implemented polarizable Drude water model was used to make comparisons to the popular TIP3P and TIP4P water models for doing QM/MM calculations. We have also computed the energetic profile of the chorismate mutase catalyzed Claisen rearrangement at various QM/MM levels of theory and have compared the results with previous studies. Our best estimate for the activation energy is 8.20 kcal/mol and for the reaction energy is -23.1 kcal/mol, both calculated at the MP2/6-31+G(d)//MP2/6-31+G(d)/C22 level of theory.

# 2006

# A point-charge model for electrostatic potentials based on a local projection of multipole moments

### ATB Gilbert, PMW Gill, Mol Simul 32 (2006) 1249

We introduce a method for obtaining atomic point-charges that yield accurate representations of the electrostatic potentials (ESP) of large systems. The method relies on a decomposition of the density and subsequent projection of the multipole moments of the density components onto neighbouring atomic sites. The resulting local multipole-derived charges (LMDCs) are well-defined, do not require sampling of the ESP at grid points around the molecule and provide a good description of the electrostatic potential. This local approach circumvents the numerical problems that arose in our original method which was designed to find the optimal atomic charge representation of the ESP of a system outside the electron density.

# Advances in methods and algorithms in the Q-Chem 3.0 program package

### Yihan Shao, Laszlo Fusti Molnar, Yousung Jung, Jorg Kussmann, Christian Ochsenfeld, Shawn T. Brown, Andrew T.B. Gilbert, Lyudmila V. Slipchenko, Sergey V. Levchenko, Darragh P. O'Neill, Robert A. DiStasio Jr, Rohini C. Lochan, Tao Wang, Gregory J.O. Beran, Nicholas A. Besley, John M. Herbert, Ching Yeh Lin, Troy Van Voorhis, Siu Hung Chien, Alex Sodt, Ryan P. Steele, Vitaly A. Rassolov, Paul E. Maslen, Prakashan P. Korambath, Ross D. Adamson, Brian Austin, Jon Baker, Edward F. C. Byrd, Holger Dachsel, Robert J. Doerksen, Andreas Dreuw, Barry D. Dunietz, Anthony D. Dutoi, Thomas R. Furlani, Steven R. Gwaltney, Andreas Heyden, So Hirata, Chao-Ping Hsu, Gary Kedziora, Rustam Z. Khalliulin, Phil Klunzinger, Aaron M. Lee, Michael S. Lee, WanZhen Liang, Itay Lotan, Nikhil Nair, Baron Peters, Emil I. Proynov, Piotr A. Pieniazek, Young Min Rhee, Jim Ritchie, Edina Rosta, C. David Sherrill, Andrew C. Simmonett, Joseph E. Subotnik, H. Lee Woodcock III, Weimin Zhang, Alexis T. Bell, Arup K. Chakraborty, Daniel M. Chipman, Frerich J. Keil, Arieh Warshel, Warren J. Hehre, Henry F. Schaefer III, Jing Kong, Anna I. Krylov, Peter M. W. Gill, Martin Head-Gordon, Phys Chem Chem Phys 8 (2006) 3172

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

# 2005

# An optimal point-charge model for molecular electrostatic potentials

### AC Simmonett, ATB Gilbert, PMW Gill, Mol Phys 103 (2005) 2789

Motivated by the Legendre expansion of the electrostatic potential (ESP), we propose a method for obtaining atomic point-charges for a molecule based on reproducing the low-order multipole moments of the system. The resulting multipole-derived charges (MDCs) are well defined, do not require sampling of the ESP at grid points around the molecule and provide excellent reproduction of the electrostatic potential. No constraints are placed on the magnitude of the atomic charges.

# Decay behavior of least-squares coefficients in auxiliary basis expansions

### PMW Gill, ATB Gilbert, SW Taylor, G Friesecke, M Head-Gordon, J Chem Phys 123 (2005) 061101

Many quantum chemical methods, both wave function and
density based, rely on an expansion of elements of the
electron density in an auxiliary basis. However, little is
known about the analytical behavior of the expansion
coefficients and, in particular, about their rate of decay
with distance. We discuss an exactly solvable model system
and characterize the expansion coefficients for various
fitting metrics and various dimensionalities of the
auxiliary basis. In the case of Coulomb fitting, we find
that the decay rate depends critically on the effective
dimensionality D of the auxiliary basis, varying from
O(r^{-1}) to O(r^{-3}) to
O(e^{-ζr}) for D=1, 2, or 3.

# 2004

# Charge-transfer transitions in protein circular dichroism spectra

### A.T.B. Gilbert, J.D. Hirst, J Mol Struct: THEOCHEM 675 (2004) 53

Two peptide dimers (N-acetyl-glycine-N'methylamide and a hydrogen-bonded dimer of N-methylacetamide) were considered as models for charge-transfer transitions in proteins. Electronic structure calculations at the CASSCF and CASPT2 levels of theory were performed to determine the transition densities and excitation energies for these systems in two separate configurations. These transition properties were incorporated within the matrix method which couples the individual monomer transitions in a protein. The effects of including the charge-transfer transitions on circular dichroism spectra were considered for ideal α-helix and β-sheet structures.

# Extracting stoms from molecular electron densities via integral equations

### Andrew T.B. Gilbert, Peter M.W. Gill and Stephen W. Taylor, J Chem Phys 120 (2004) 7887

The observation that a molecular electron density is close to the superposition of its constituent atoms leads naturally to the idea of modeling a density by a sum of nuclear-centered, spherically symmetric functions. The functions that are optimal in a least-squares sense are known as Stewart atoms. Previous attempts to construct Stewart atoms by expanding them in an auxiliary basis have been thwarted by slow convergence with respect to the size of the auxiliary basis used. We present a method for constructing Stewart atoms via convolution integrals which bypasses the need for an auxiliary basis, and is able to produce highly accurate approximations to Stewart atoms.

# 2003

# Electronic circular dichroism of proteins from first principles calculations

### Jonathan D. Hirst, Karl Colella, Andrew T.B. Gilbert, J Phys Chem B 107 (2003) 11813

The circular dichroism (CD) spectra of 47 proteins in
the far-ultraviolet have been calculated from first
principles, using a parameter set derived from ab initio
calculations on N-methylacetamide. These spectra agree well
with experimental data, as shown by the Spearman rank
correlation coefficients of 0.86, 0.80, and 0.94 between the
computed and experimental intensities at 190, 208, and 220
nm, respectively. The computed spectra are most accurate for
proteins that have a high α-heical content and are
least accurate for a class of β-sheet-rich proteins,
which have some irregular structure and are known as
β-II proteins. To address the lack of resolution
between the two negative peaks around 208 and 220 nm in the
calculated spectra of α-helcal proteins, narrower
bandwidths have been explored. Other factors were
investigated, including the dielectric constant of the
protein, higher energy transitions of the amide chromophore,
and the orientation of the ππ^{*} electric
transition dipole moment vector. Combining some of these
aspects made it possible to obtain accurate spectra with the
desired resolution between the negative peaks. Although not
fully quantitative, the first-principles calculations of
protein CD presented in this study are the most accurate
reported to date.

# 2002

# Flow oriented linear dichroism to probe protein orientation in membrane environments

### Alison Rodger, Jascindra Rajendra, Rachel Marrington, Malin Ardhammar, Bengt NordÃ© Jonathan D. Hirst, Andrew T. B. Gilbert, Timothy R. Dafforn, David J. Halsall, Cheryl A. Woolhead, Colin Robinson, Teresa J. T. Pinheiro, Jurate Kazlauskaite, Mark Seymour, Niuvis Perez, Michael J. Hannon, J. Phys. Chem. B 4 (2002) 4051

Processes occurring on or in membranes are essential in most biological systems, and the study of these processes has been engendering an increasing interest for a long time, as has the creation of artificial lipid membrane systems. Studies of, for example, membrane transport and membrane protein function call for a thorough knowledge of molecular interactions within the membrane, between the lipids themselves and between lipids and other species (proteins, drugs, and ions). To this end, the locations and orientations of molecules bound to the membrane can give important information. However, to date no simple experimental method has been established to achieve this for membrane bound proteins. In this work we report the first flow linear dichroism (LD) study of proteins bound to liposomes. Flow LD of molecules bound to the bilayer of shear-deformed liposomes is one of the few direct methods potentially available for the study of the orientation of membrane guest molecules, provided that the molecules of interest have significant absorption in the visible and near-UV regions.

# 2000

# Rapid evaluation of two-center two-electron integrals

### Peter M.W. Gill, Andrew T.B. Gilbert, Terry R. Adams, J Comp Chem 21 (2000) 1505

We present optimal formulae for two-center two-electron replusion integrals (ERIs) over Cartesian Gaussian basis functions. Floating-point operations (flop) counts reveal that two-center ERIs are often an order of magnitude cheaper than their four-center analogues.

# Q-Chem 2.0: A high-performance ab initio electronic structure program package

### Jing Kong and Christopher A. White and Anna I. Krylov and David Sherrill and Ross D. Adamson and Thomas R. Furlani and Michael S. Lee and Aaron M. Lee and Steven R. Gwaltney and Terry R. Adams and Christian Ochsenfeld and Andrew T. B. Gilbert and Gary S. Kedziora and Vitaly A. Rassolov and David R. Maurice and Nikhil Nair and Yihan Shao and Nicholas A. Besley and Paul E. Maslen and Jeremy P. Dombroski and Holger Daschel and Weimin Zhang and Prakashan P. Korambath and Jon Baker and Edward F. C. Byrd and Troy Van Voorhis and Manabu Oumi and So Hirata and Chao-Ping Hsu and Naoto Ishikawa and Jan Florian and Arieh Warshel and Benny G. Johnson and Peter M. W. Gill and Martin Head-Gordon and John A. Pople, J. Comp. Chem 21 (2000) 1532

Q-Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function-based methods. A review of the technical features contained within Q-Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance.

# Methods for constructing Stewart atoms

### A.T.B. Gilbert, A.M. Lee, P.M.W. Gill, J Mol Struct: THEOCHEM 500 (2000) 363

We compare four methods for generating Stewart atoms, the spherically-symmetric nuclear-centred functions whose sum best fits a given electron density. We find that projecting a molecular density onto an atom-centred basis is a more subtle and difficult problem than is generally recognized and we conclude that new approaches, based on integral equations, may be more satisfactory than traditional projection methods.

# 1999

# Decomposition of exchange-correlation energies

### Andrew T.B. Gilbert, Peter M.W. Gill, Chem Phys Lett 312 (1999) 511

We discuss a function Q(x) that decomposes a locally defined exchange-correlation energy of a system into contributions from each value of the reduced density gradient x. We outline a method for constructing these functions for molecular systems and give examples of these for the Dirac exchange energy of some simple molecules. Graphs of the Q(x) functions show which values of the reduced gradient are the most important energetically. We use the curves to construct an ab initio gradient-corrected exchange functional which yields the exact energy for a new model reference density. The performance of this functional when applied to chemical systems is examined.