The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures.

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g.

Atoms and bonds in molecules as synergisms of interactions between electrons and nuclei.

The molecular electronic wave functions are expressed in quasi-atomic form. The corresponding global energy expression exhibits the unified resolution of the various modes of chemical bonding in terms of physical interactions. The bonding patterns in several molecules is elucidated.

Atoms and interatomic bonding synergism inherent in molecular electronic wave functions.

The chemical model of matter consists of atoms held together by bonds. The success of this model implies that the physical interactions of the electrons and nuclei in molecules combine into compound interactions that create the bonding. In the quantum mechanical description, the modified atoms in molecules and the bonding synergism are contained in the molecular electronic wave function.

Multiple Bonding in Rhodium Monoboride. Quasi-atomic Analyses of the Ground and Low-Lying Excited States.

The bonding structures of the ground state and the lowest five excited states of rhodium monoboride are identified by determining the quasi-atomic orbitals in full valence space MCSCF wave functions and the interactions between these orbitals. A quadruple bond, namely two π-bonds and two σ-bonds, is identified and characterized for the XΣ ground state, in agreement with a previous report (Cheung . 2020, 11, 659-663).

Why is SiH Not Linear? An Intrinsic Quasi-Atomic Bonding Analysis.

The molecular energy of SiH geometric structures increases in the order dibridged < -bent < linear, in contrast to acetylene, CH, for which the linear structure is the global minimum. In this study, the intra-atomic (antibonding) and bonding contributions to the total molecular energy of these valence isoelectronic molecules are computed by expressing the density matrices of the full valence space multiconfiguration self-consistent field wave function in terms of quasi-atomic orbitals. The analysis shows that the -atomic contributions to the molecular energy become favorable in the order dibridged → -bent → linear for both CH and SiH.

Recent developments in the general atomic and molecular electronic structure system.

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory.

Quasi-Atomic Bond Analyses in the Sixth Period: II. Bond Analyses of Cerium Oxides.

The role of the 4f orbitals in bonding is examined for the molecules cerium monoxide and cerium dioxide that have cerium formally in the +2 and +4 oxidation states, respectively. It is shown that the 4f orbitals are used primarily for polarization of the 5d orbitals when cerium is in the lower oxidation state, while the 4f orbitals play a significant role in chemical bonding via 5d/4f hybridization when cerium is in the +4 oxidation state.

Quasi-Atomic Bond Analyses in the Sixth Period: I. Relativistic Accurate Atomic Minimal Basis Sets for the Elements Cesium to Radon.

Full-valence relativistic accurate atomic minimal basis set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic basis sets are developed and subsequently used to form the AAMBS orbitals. By virtue of the use of a saturated basis, properties computed based on the AAMBS orbitals are basis set independent.

The Virial Theorem and Covalent Bonding.

A long-held view of the origin of covalent binding is based on the notion that electrostatic forces determine the stability of a system of charged particles and that, therefore, potential energy changes drive the stabilization of molecules. A key argument advanced for this conjecture is the rigorous validity of the virial theorem. Rigorous in-depth analyses have however shown that the energy lowering of covalent bonding is due to the wave mechanical drive of electrons to lower their kinetic energy through expansion.

Quasi-Atomic Bonding Analysis of Xe-Containing Compounds.

The origin of bonding in the rare-gas-containing molecules HXeCCH, HXeCCXeH, and HXeOXeH is explored using a quasi-atomic orbital (QUAO) analysis. The QUAOs provide qualitative and quantitative data about bonding through transformations of the density matrix. Bond orders, kinetic bond orders, and the extent of transfer of charge are analyzed.

Identification and Characterization of Molecular Bonding Structures by ab initio Quasi-Atomic Orbital Analyses.

The quasi-atomic analysis of ab initio electronic wave functions in full valence spaces, which was developed in preceding papers, yields oriented quasi-atomic orbitals in terms of which the ab initio molecular wave function and energy can be expressed. These oriented quasi-atomic orbitals are the rigorous ab initio counterparts to the conceptual bond forming atomic hybrid orbitals of qualitative chemical reasoning. In the present work, the quasi-atomic orbitals are identified as bonding orbitals, lone pair orbitals, radical orbitals, vacant orbitals and orbitals with intermediate character.

Dispersion Interactions in QM/EFP.

The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved.

Relativistic ab Initio Accurate Atomic Minimal Basis Sets: Quantitative LUMOs and Oriented Quasi-Atomic Orbitals for the Elements Li-Xe.

Valence virtual orbitals (VVOs) are a quantitative and basis set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored ab initio accurate atomic minimal basis sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a minimal basis set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment.

Intrinsic Resolution of Molecular Electronic Wave Functions and Energies in Terms of Quasi-atoms and Their Interactions.

A general intrinsic energy resolution has been formulated for strongly correlated wave functions in the full molecular valence space and its subspaces. The information regarding the quasi-atomic organization of the molecular electronic structure is extracted from the molecular wave function without introducing any additional postulated model state wave functions. To this end, the molecular wave function is expressed in terms of quasi-atomic molecular orbitals, which maximize the overlap between subspaces of the molecular orbital space and the free-atom orbital spaces.

Correlation Energy Extrapolation by Many-Body Expansion.

Accounting for electron correlation is required for high accuracy calculations of molecular energies. The full configuration interaction (CI) approach can fully capture the electron correlation within a given basis, but it does so at a computational expense that is impractical for all but the smallest chemical systems. In this work, a new methodology is presented to approximate configuration interaction calculations at a reduced computational expense and memory requirement, namely, the correlation energy extrapolation by many-body expansion (CEEMBE).

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study.

The metastable ring structure of the ozone 1(1)A1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two (1)A1 states. In the present work, valence correlated energies of the 1(1)A1 state and the 2(1)A1 state were calculated at the 1(1)A1 open minimum, the 1(1)A1 ring minimum, the transition state between these two minima, the minimum of the 2(1)A1 state, and the conical intersection between the two states.

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. II. Strongly Correlated MCSCF Wave Functions.

A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular minimal basis set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms.

A Comprehensive Analysis in Terms of Molecule-Intrinsic Quasi-Atomic Orbitals. IV. Bond Breaking and Bond Forming along the Dissociative Reaction Path of Dioxetane.

The quantitative analysis of molecular density matrices in terms of oriented quasi-atomic orbitals (QUAOs) is shown to yield detailed conceptual insight into the dissociation of dioxetane on the basis of ab initio wave functions. The QUAOs persist and can be followed throughout the reaction path. The kinetic bond orders and the orbital populations of the QUAOs quantitatively reveal the changes of the bonding interactions along the reaction path.

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. III. The Covalent Bonding Structure of Urea.

The analysis of molecular electron density matrices in terms of quasi-atomic orbitals, which was developed in previous investigations, is quantitatively exemplified by a detailed application to the urea molecule. The analysis is found to identify strong and weak covalent bonding interactions as well as intramolecular charge transfers. It yields a qualitative as well as quantitative ab initio description of the bonding structure of this molecule, which raises questions regarding some traditional rationalizations.

Seniority number description of potential energy surfaces: Symmetric dissociation of water, N2, C2, and Be2.

The present study further explores the concept of the seniority number (Ω) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of Ω in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of Ω in addressing also dynamic electron correlation in addition to the static correlation.

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion.

An analysis based on the variation principle shows that in the molecules H2 (+), H2, B2, C2, N2, O2, F2, covalent bonding is driven by the attenuation of the kinetic energy that results from the delocalization of the electronic wave function. For molecular geometries around the equilibrium distance, two features of the wave function contribute to this delocalization: (i) Superposition of atomic orbitals extends the electronic wave function from one atom to two or more atoms; (ii) intra-atomic contraction of the atomic orbitals further increases the inter-atomic delocalization. The inter-atomic kinetic energy lowering that (perhaps counter-intuitively) is a consequence of the intra-atomic contractions drives these contractions (which per se would increase the energy).

A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions.

Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods.

The dispersion interaction between quantum mechanics and effective fragment potential molecules.

A method for calculating the dispersion energy between molecules modeled with the general effective fragment potential (EFP2) method and those modeled using a full quantum mechanics (QM) method, e.g., Hartree-Fock (HF) or second-order perturbation theory, is presented.

Accurate potential energy curve for B2. Ab initio elucidation of the experimentally elusive ground state rotation-vibration spectrum.

The electron-deficient diatomic boron molecule has long puzzled scientists. As yet, the complete set of bound vibrational energy levels is far from being known, experimentally as well as theoretically. In the present ab initio study, all rotational-vibrational levels of the X (3)Σ(g)(-) ground state are determined up to the dissociation limit with near-spectroscopic accuracy (<10 cm(-1)).