Recent extensions of the DMol3 local orbital density functional method for band structure calculations of insulating and metallic solids are described. Furthermore the method for calculating semilocal pseudopotential matrix elements and basis functions are detailed together with other unpublished parts of the methodology pertaining to gradient functionals and local orbital basis sets. The method is applied to calculations of the enthalpy of formation of a set of molecules and solids. We find that the present numerical localized basis sets yield improved results as compared to previous results for the same functionals. Enthalpies for the formation of H, N, O, F, Cl, and C, Si, S atoms from the thermodynamic reference states are calculated at the same level of theory. It is found that the performance in predicting molecular enthalpies of formation is markedly improved for the Perdew–Burke–Ernzerhof [Phys. Rev. Lett. 77, 3865 (1996)] functional.

From molecules to solids with the DMol3 approach

Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M(Z−28)+-core orbitals of the second row transition elements and the M(Z−60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Nonrelativistic and quasirelativistic ab‐initio pseudopotentials representing the Ne‐like X(Z−10)+ cores (X=Sc–Zn) of the first row transition metals and optimized (8s7p6d1f )/[6s5p3d1f ]‐GTO valence basis sets for use in molecular calculations have been generated. Excitation and ionization energies of the low lying states of Sc through Zn from numerical HF‐ as well as SCF‐ and CI(SD)‐pseudopotential calculations using the derived basis sets differ by less than 0.1 eV from corresponding all‐electron results.

Energy‐adjusted ab initio pseudopotentials for the first row transition elements

We present the first global parameterization and validation of a novel charge model, called AM1-BCC, which quickly and efficiently generates high-quality atomic charges for computer simulations of organic molecules in polar media. The goal of the charge model is to produce atomic charges that emulate the HF/6-31G* electrostatic potential (ESP) of a molecule. Underlying electronic structure features, including formal charge and electron delocalization, are first captured by AM1 population charges; simple additive bond charge corrections (BCCs) are then applied to these AM1 atomic charges to produce the AM1-BCC charges. The parameterization of BCCs was carried out by fitting to the HF/6-31G* ESP of a training set of >2700 molecules. Most organic functional groups and their combinations were sampled, as well as an extensive variety of cyclic and fused bicyclic heteroaryl systems. The resulting BCC parameters allow the AM1-BCC charging scheme to handle virtually all types of organic compounds listed in The Merck Index and the NCI Database. Validation of the model was done through comparisons of hydrogen-bonded dimer energies and relative free energies of solvation using AM1-BCC charges in conjunction with the 1994 Cornell et al. forcefield for AMBER.(13) Homo- and hetero-dimer hydrogen-bond energies of a diverse set of organic molecules were reproduced to within 0.95 kcal/mol RMS deviation from the ab initio values, and for DNA dimers the energies were within 0.9 kcal/mol RMS deviation from ab initio values. The calculated relative free energies of solvation for a diverse set of monofunctional isosteres were reproduced to within 0.69 kcal/mol of experiment. In all these validation tests, AMBER with the AM1-BCC charge model maintained a correlation coefficient above 0.96. Thus, the parameters presented here for use with the AM1-BCC method present a fast, accurate, and robust alternative to HF/6-31G* ESP-fit charges for general use with the AMBER force field in computer simulations involving organic small molecules.

Fast, efficient generation of high-quality atomic charges. AM1-BCC model: II. Parameterization and validation

Quasi-relativistic energy-adjusted ab initio pseudopotentials for the elements of groups 13–17 up to atomic number 53 (I) are presented together with corresponding energy-optimized valence basis sets. Test calculations for atomic excitation and ionization energies show the reliability of the derived pseudopotentials and basis sets.

Ab initio energy-adjusted pseudopotentials for elements of groups 13-17

A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin–orbit operators for the elements Rb through Xe. Particular attention was given to the partitioning of the core and valence space and, where appropriate, more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with contraction coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was examined by comparing computed atomic excitation energies with accurate all‐electron relativistic values. The spin–orbit operators were tested in calculations on selected atoms.

Abinitio relativistic effective potentials with spin–orbit operators. III. Rb through Xe

A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin‐orbit operators for the atoms K through Kr. Particular attention was given to the partitioning of the core and valence space, and where appropriate more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with expansion coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was determined by comparing computed atomic excitation energies with accurate all‐electron relativistic values. In all cases the maximum error was found to be less than 0.1 eV. The reliability of the spin‐orbit operators was also considered.

Abinitio relativistic effective potentials with spin‐orbit operators. II. K through Kr

Publisher Summary This chapter focuses on the recommended method for the inclusion of spin-orbit coupling and other relativistic effects for molecules containing heavy elements, considering computational complexity and accuracy factors that is one based on ab initio REPS. The calculation of accurate wave functions for systems containing heavy elements requires addressing the difficulties of the treatment of large numbers of electrons and the subtleties of electron correlation. This is not intended as a general review of relativity in chemistry or quantum mechanics, nor even of effective potential procedures, but is rather a critical discussion, including a limited number of applications, of the background, approximations, and implications of techniques developed by the present authors and collaborators and colleagues. The underlying assumption behind all methods for defining effective core potentials (EP) is the frozen core approximation. That is, the intrinsic reliability of core-valence separability. However, substantial savings are not realized by this approximation alone because of the radical oscillations of the valence orbitals in the region near the nuclei. An accurate procedure for performing calculations that incorporate spinorbit and other relativistic effects, and that represents intermediate coupling states for molecules containing heavy atoms, is based on A-S coupling in conjunction with the use of the ab initio REP-based spin-orbit operator and extended configuration interaction.

Spin-Orbit Coupling and Other Relativistic Effects in Atoms and Molecules

Ab initio calculations including relativistic effects for Ag2, Au2, AgAu, AgH, and AuH

Author Institution: Laboratoire de Chimie Quantique, E. R. 139 du CNRS, Institut Le Bel, Universit\'{e} Louis Pasteur; Department of Chemistry, The Ohio State University

R. B. Ross

Papers

Abinitio relativistic effective potentials with spin–orbit operators. III. Rb through Xe

Abinitio relativistic effective potentials with spin‐orbit operators. II. K through Kr

Spin-Orbit Coupling and Other Relativistic Effects in Atoms and Molecules

Ab initio calculations including relativistic effects for Ag2, Au2, AgAu, AgH, and AuH

Ab initio calculations of dirhenium complexes using relativistic effective core potentials