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., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

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. So far, only part of this information has been recovered from the wave function. Notably, the atoms have remained unidentified in the wave function. One reason is that conventional energy decomposition analyses formulate separate model wave functions, independent of the actual wave function, to represent "prepared atoms" and preconceived interactions and, then, intuitively catenate the parts. In the present work, the embedded modified atoms and the inherent physical synergisms between them are determined by a unified derivation entirely from the actual molecular valence space wave function. By means of a series of intrinsic orbital and configurational transformations of the wave function, the energy of formation of a molecule is additively resolved in terms of intra-atomic energy changes, interference energies, and quasi-classical, non-classical, and charge-transfer Coulombic interactions. The analysis furnishes an algorithm for the quantitative resolution of the energy of formation, which enables analyses elucidating reaction energies.

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 X1Σ+ ground state, in agreement with a previous report (Cheung J. Phys. Chem. Lett. 2020, 11, 659-663). However, in all excited states, the bonding is predicted to be weaker because, in these states, one of the σ-bonding interactions has a small magnitude. In the a3Δ and A1Δ states, the bond order is between a triple and quadruple bond. In the b3Σ+ state, the Rh-B linkage is a triple bond. In the c3Π and B1Π states, the atoms are linked by a double bond due to an additional weakening of the two π-bonds. The decreases in the predicted bond strengths are reflected in the decreases of the predicted binding energies and in the increases of the predicted bond lengths from the X1Σ+ ground state to the c3Π and the B1Π excited states. Notably, the 5pσ orbital of rhodium, which is vacant in the ground state of the atom, plays a significant role in the molecule.

Why is Si2H2 Not Linear? An Intrinsic Quasi-Atomic Bonding Analysis.

The molecular energy of Si2H2 geometric structures increases in the order dibridged < trans-bent < linear, in contrast to acetylene, C2H2, 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 intra-atomic contributions to the molecular energy become less favorable in the order dibridged → trans-bent → linear for both C2H2 and Si2H2. By contrast, the inter-atomic bonding contributions become energetically more favorable in that order for both C2H2 and Si2H2. The two systems differ as follows. For Si2H2, the antibonding intra-atomic energy changes that occur when the dibridged molecule reconstructs into the trans-bent and linear structures prevail over the interatomic interactions that induce bond formation. In contrast, for C2H2, the interatomic interactions that create bonds prevail over the intra-atomic energy changes that occur when the dibridged molecule reconstructs into the trans-bent and linear structures. The intra-atomic energy changes that occur in these systems are related to the hybridization of the heavy atoms in an analogous manner to the hybridization of C in CH4 from (2s)2(2p)2 to sp3 hybrid orbitals.

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. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

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. In molecules, the AAMBS orbitals can be used to construct valence virtual orbitals (VVOs) that provide chemically meaningful ab initio lowest unoccupied molecular orbitals (LUMOs) with basis set independent orbital energies. The optimized occupied molecular orbitals complemented with the VVOs form a set of full-valence molecular orbitals. They can be transformed into a set of oriented quasi-atomic orbitals (QUAOs) that provide information on intramolecular bonding via an intrinsic density analysis. In the present work, the development of the AAMBS for the sixth row is presented.

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.

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. Since the virial theorem applies only to systems with Coulombic interaction potentials, its relevance as a foundation of the electrostatic view is tested here by calculations on analogues of the molecules H2+ and H2, where all 1/ r interaction potentials are replaced by Gaussian-type potentials that yield one-electron "atoms" with realistic stability ranges. The virial theorem does not hold in these systems, but covalent bonds are found to form nonetheless, and the wave mechanical bonding analysis yields analogous results as in the case of the Coulombic potentials. Notably, the key driving feature is again the electron delocalization that lowers the interatomic kinetic energy component. A detailed discussion of the role of the virial theorem in the context of covalent binding is given.

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. Localized molecular orbitals formed from the QUAOs provide additional insights about the relative polarity of bonds formed by xenon. The analysis suggests significant covalent bonding for Xe-Y (Y = C, O) as well as Xe-H, with both bonds using the same pσ-type orbital on Xe. These covalent interactions are established by substantial charge shifts from Xe to Y as well as to H. Accordingly, a covalent three-center four-electron bond links the atoms H-Xe-Y. On the basis of the analysis, electrostatic interactions do not play a significant role in the Xe-Y or Xe-H bonding.