Michael W. Schmidt

General atomic and molecular electronic structure system

A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines.

Effective convergence to complete orbital bases and to the atomic Hartree--Fock limit through systematic sequences of Gaussian primitives

Optimal starting points for expanding molecular orbitals in terms of atomic orbitals are the self‐consistent‐field orbitals of the free atoms and accurate information about the latter is essential for the construction of effective AO bases for molecular calculations. For expansions of atomic SCF orbitals in terms of Gaussian primitives, which are of particular interest for applications in polyatomic quantum chemistry, previous information has been limited in accuracy. In the present investigation a simple procedure is given for finding expansions of atomic self‐consistent‐field orbitals in terms of Gaussian primitives to arbitrarily high accuracy. The method furthermore opens the first avenue so far for approaching complete basis sets through systematic sequences of atomic orbitals. It is shown that, for expansions of atomic SCF orbitals in terms of even‐tempered Gaussian primitives, the energy‐ optimized exponents are simple analytic functions of the number of primitives used in the expansions.With the h...

Advances in electronic structure theory: GAMESS a decade later

Publisher Summary This chapter focuses on the new developments in electronic structure theory during the past decade. These developments include new methods in quantum mechanics, including approaches for extrapolating to the full CI and complete basis set limits, novel methods for CASSCF calculations, new coupled cluster techniques, methods for evaluating non-adiabatic and relativistic interactions, new approaches for distributed parallel computing, and QM/MM methods for describing solvent effects and surface science. It is useful to note in this regard that GAMESS is a general-purpose suite of electronic structure and QM/MM methods (including open-and closed-shell Hartree–Fock which has been essentially ignored here) that can be run on virtually any computer, cluster, massively parallel system, or for that matter a desktop Mac or PC. Indeed, GAMESS is used at many universities as an educational tool, making use of its graphical back end MacMolPlt. GAMESS and MacMolPlt can be downloaded at no cost from www.msg.ameslab.gov, with only a simple license required.

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

Abstract The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave-function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a “formal minimal basis” of valence, orbitals on the constituent atoms. These configurations span a “full reaction space”, and MC SCF optimization of the orbitals in terms of an extended set of quantitative basis orbitals determines the full optimized reaction space (FORS). Basic justifications, methodological specifics and sample applications are discussed.

Spin-orbit coupling in molecules: chemistry beyond the adiabatic approximation

An extensive introduction to spin-orbit coupling (SOC) is presented, starting from a discussion of the phenomenological operators and general chemical importance of SOC to studies of chemical reactions. Quantitative SOC operators are discussed, and the symmetry properties of the SOC Hamiltonian important for understanding the general features of SOC are summarized. Comparison of the one- and two-electron contributions to SOC is given, followed by a discussion of commonly used approximations for the two-electron part. Applications of SOC to studies using effective and model core potentials have been analysed. The theoretical discussion is illustrated with numerous practical examples, including diatomic molecules (with an emphasis on hydrides) and some examples for polyatomic molecules. The fine structure of the SOC interaction (vibrational dependence) for some diatomic molecules has been elucidated.

Ab initio vibrational state calculations with a quartic force field: applications to H2CO, C2H4, CH3OH, CH3CCH, and C6H6.

For polyatomic molecules, n-mode coupling representations of the quartic force field (nMR-QFF) are presented, which include terms up to n normal coordinate couplings in a fourth-order polynomial potential energy function. The computational scheme to evaluate third-and fourth-order derivatives by finite differentiations of the energy is fully described. The code to generate the nMR-QFF has been implemented into GAMESS program package and interfaced with the vibrational self-consistent field (VSCF) and correlation corrected VSCF (cc-VSCF) methods. As a demonstration, fundamental frequencies have been calculated by the cc-VSCF method based on 2MR-QFF for formaldehyde, ethylene, methanol, propyne, and benzene. The applications show that 2MR-QFF is a highly accurate potential energy function, with errors of 1.0-1.9% relative to the experimental value in fundamental frequencies. This approach will help quantitative evaluations of vibrational energies of a general molecule with a reasonable computational cost.

Are atoms sic to molecular electronic wavefunctions? II. Analysis of fors orbitals

Abstract Electronic wavefunctions that describe molecules in the full optimized reaction space (FORS) are multiconfigurational wavefunctions which are invariant under non-singular linear transformations of the occupied molecular orbitals. They offer therefore a considerably wider scope for orbital interpretations than the single-configuration Hartree-Fock approximation. For example they can be analyzed in terms of natural MOs and in terms of localized MOs. The latter turn out to be remarkably atomic in character and a new localization procedure can be formulated which yields atom-adapted molecular orbitals. These have the character of minimal-basis-set AOs that are optimally adapted to the molecular environment and furnish an unambigious atomic population analysis. On the other hand, chemically adapted molecular orbitals can be defined by an appropriate compromise between natural orbitals and localized orbitals. The freedom to use, as configuration-generating molecular orbitals, atom-adapted FORS MOs as well as chemically adapted FORS MOs makes FORS wavefunctions particularly suitable for chemical interpretations. The ensuing analysis establishes the minimal basis set (in molecule-adapted form) as a theoretically sound concept for the understanding of accurate molecular wavefunctions. An illustrative example is discussed.

Are atoms intrinsic to molecular electronic wavefunctions? III. Analysis of FORS configurations

Abstract The interpretation of configurational bases in the full reaction space depends on the type of FORS MOs from which they are generated. Configurations constructed from atom-adapted FORS MOs have the character of valence bond structures and can be transformed into antisymmetrized products of atomic state functions. Configurations based on natural FORS MOs can be used to advantage to generate that part of the full reaction space which dominates the orbital optimization. Configurational mixing in the full reaction space can be predicted using the minimal basis set of the free-atom SCF AOs. Illustrative examples are given. The FORS model can be improved through the intra-atomic correlation correction.

The Distributed Data Interface in GAMESS

The Distributed Data Interface to permit storage of large data arrays in the aggregate memory of distributed memory, message passing computer systems is described. The design of this relatively small library is discussed, in regard to its implementation over SHMEM, MPI-1, or socket based message libraries. The good performance of a MP2 program using DDI is demonstrated on both PC and workstation cluster computers, and some details of the resulting message traffic are presented.

A natural orbital diagnostic for multiconfigurational character in correlated wave functions

The natural orbitals and their corresponding occupation numbers are constructed for several interesting problems to demonstrate that the existence of negative natural orbital occupation numbers for single reference correlation methods provides a simple diagnostic for the need for a multiconfigurational description of the wave function.