Molecule intrinsic minimal basis sets. II. Bonding analyses for Si4H6 and Si2 to Si10

Analysis of bonding motifs in unusual molecules I: planar hexacoordinated carbon atoms

The bonding structures of CO3Li3+ and CS3Li3+ are studied by means of oriented quasi-atomic orbitals (QUAOs) to assess the possibility of these molecules being planar hexacoordinated carbon (phC) systems. CH3Li and CO32- are employed as reference molecules. It is found that the introduction of Li+ ions into the molecular environment of carbonate has a greater effect on the orbital structure of the O atoms than it does on the C atom. Partial charges computed from QUAO populations imply repulsion between the positively charged C and Li atoms in CO3Li3+. Upon the transition from CO3Li3+ to CS3Li3+, the analysis reveals that the substitution of O atoms by S atoms inverts the polarity of the carbon-chalcogen σ bond. This is linked to the difference in s- and p-fractions of the QUAOs of C and S, as element electronegativities do not explain the observed polarity of the CSσ bond. Partial charges indicate that the larger electron population on the C atom in CS3Li3+ makes C-Li attraction possible. Upon comparison with the C-Li bond in methyllithium, it is found that the C-Li covalent interactions in CO3Li3+ and CS3Li3+ have about 14% and 6% of the strength of the C-Li covalent interaction in CH3Li, respectively. Consequently, it is concluded that only CS3Li3+ may be considered to be a phC system.

Quasi-atomic orbital analysis of halogen bonding interactions

A quasi-atomic orbital analysis of the halogen bonded NH3⋯XF complexes (X = F, Cl, Br, and I) is performed to gain insight into the electronic properties associated with these σ-hole interactions. It is shown that significant sharing of electrons between the nitrogen lone pair of the ammonia molecule and the XF molecule occurs, resulting in a weakening of the X-F bond. In addition, the N-X bond shows increasing covalent character as the size of the halogen atom X increases. While the Mulliken outer complex NH3⋯XF appears to be overall the main species, the strength of the covalent interaction of the N-X bond becomes increasingly similar to that of the N-X bond in the [NH3X]+ cation as the size of X increases.

Orbital contraction and covalent bonding

According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H₂ ⁺ and H₂. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H₂, Li₂, B₂, C₂, N₂, O₂, F₂, CO, P₂, and Cl₂ and the polyatomics CH₃-CH₃, CH₃-SiH₃, CH₃-OH, and C₂H₅-C₂H₅ (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.

The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

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.

Substituent Effects on the Quantum Interference of Two-Center One-Electron Bonds: [B2X6]- (X = H, F, Cl, CN, OH, CH3, and OCH3)

The interference energy analysis (IEA) provided by the generalized product function energy partitioning (GPF-EP) method was applied to investigate the influence of the neighboring atoms on the nature of the two-center one-electron (2c1e) bonds in the anion dimers of BX₃ species (X = H, F, Cl, CN, OH, CH₃, and OCH₃). The species were studied at the GVB-PP(6/12).SC(1,2)/6-31**G++ level of calculation. The IEA has revealed that there is a balance between two main factors determining the chemical stability of the species. Quantum interference acts as the sole stabilizing effect in the formation of the chemical bonds, particularly as the result of the drop in kinetic energy, and the electronegativity of the substituent has a direct influence on the magnitude of this effect. The quasi-classical energy is responsible for the destabilizing factors, mainly the group bulkiness, and the "electron-withdrawing" effect in the case of the cyano group.

A deep neural network for molecular wave functions in quasi-atomic minimal basis representation

The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts to answer this question have, among other methods, given rise to semi-empirical quantum chemistry in minimal basis representation. We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [K. T. Schütt et al., Nat. Commun. 10, 5024 (2019)] for electronic wave functions in an optimized quasi-atomic minimal basis representation. For five organic molecules ranging from 5 to 13 heavy atoms, the model accurately predicts molecular orbital energies and wave functions and provides access to derived properties for chemical bonding analysis. Particularly for larger molecules, the model outperforms the original atomic-orbital-based SchNOrb method in terms of accuracy and scaling. We conclude by discussing the future potential of this approach in quantum chemical workflows.

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.

The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees

Atomic partial charges are among the most commonly used interpretive tools in quantum chemistry. Dozens of different 'population analyses' are in use, which are best seen as proxies (indirect gauges) rather than measurements of a 'general ionicity'. For the GMTKN55 benchmark of nearly 2,500 main-group molecules, which span a broad swathe of chemical space, some two dozen different charge distributions were evaluated at the PBE0 level near the 1-particle basis set limit. The correlation matrix between the different charge distributions exhibits a block structure; blocking is, broadly speaking, by charge distribution class. A principal component analysis on the entire dataset suggests that nearly all variation can be accounted for by just two 'principal components of ionicity': one has all the distributions going in sync, while the second corresponds mainly to Bader QTAIM vs. all others. A weaker third component corresponds to electrostatic charge models in opposition to the orbital-based ones. The single charge distributions that have the greatest statistical similarity to the first principal component are iterated Hirshfeld (Hirshfeld-I) and a minimal-basis projected modification of Bickelhaupt charges. If three individual variables, rather than three principal components, are to be identified that contain most of the information in the whole dataset, one representative for each of the three classes of Corminboeuf et al. is needed: one based on partitioning of the density (such as QTAIM), a second based on orbital partitioning (such as NPA), and a third based on the molecular electrostatic potential (such as HLY or CHELPG).

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.

Benchmark of correlation matrix renormalization method in molecule calculations

We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.

Covalent Bonding in the Hydrogen Molecule

This work addresses the continuing disagreement between two schools of thought concerning the mechanism of covalent bonding. According to Hellmann, Ruedenberg, and Kutzelnigg, covalent bonding is a quantum mechanical phenomenon whereby lowering of the kinetic energy associated with electron sharing, i.e., delocalization, is the key stabilization mechanism. The opposing view of Slater, Feynman, and Bader has maintained that the source of stabilization is electrostatic potential energy lowering due to electron density redistribution to binding regions between nuclei. Following our study of H₂⁺ we present an analogous detailed study of H₂ where bonding involves an electron pair with repulsion and correlation playing a significant role in its properties. We use a range of different computational approaches to study and reveal the relevant contributions to bonding as seen in the electron density and corresponding kinetic and potential energy distributions. The energetics associated with the more complex electronic structure of H₂, when examined in detail, clearly agrees with the analysis of Ruedenberg; i.e., covalent bonding is due to a decrease in the interatomic kinetic energy resulting from electronic delocalization. Our results support the view that covalent bonding is a quantum dynamical phenomenon requiring a properly quantized kinetic energy to be used in its description.

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. A program determines the bonding characteristics of all quasi-atomic orbitals in a molecule on the basis of their occupations, bond orders, kinetic bond orders, hybridizations and local symmetries. These data are collected in a record and provide the information for a comprehensive understanding of the synergism that generates the bonding structure that holds the molecule together. Applications to a series of molecules exhibit the complete bonding structures that are embedded in their ab initio wave functions. For the strong bonds in a molecule, the quasi-atomic orbitals provide quantitative ab initio amplifications of the Lewis dot symbols. Beyond characterizing strong bonds, the quasi-atomic analysis also yields an understanding of the weak interactions, such as vicinal, hyperconjugative and radical stabilizations, which can make substantial contributions to the molecular bonding structure.

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 density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme.

Electronic structure and transport of a carbon chain between graphene nanoribbon leads

The electronic structure and transport property of a carbon chain between two graphene nanoribbon leads are studied using an ab initio tight-binding (TB) model and Landauer's formalism combined with a non-equilibrium Green's function. The TB Hamiltonian and overlap matrices are extracted from first-principles density functional calculations through the quasi-atomic minimal basis orbital scheme. The accuracy of the TB model is demonstrated by comparing the electronic structure from the TB model with that from first-principles density functional theory. The results of electronic transport on a carbon atomic chain connected to armchair and zigzag graphene ribbon leads, such as different transport characters near the Fermi level and at most one quantized conductance, reveal the effect of the electronic structure of the leads and the scattering from the atomic chain. In addition, bond length alternation and an interesting transmission resonance are observed in the atomic chain connected to zigzag graphene ribbon leads. Our approach provides a promising route to quantitative investigation of both the electronic structure and transport property of large systems.

A first-principles divide-and-conquer approach for electronic structure of large systems and its application to graphene nanoribbons

We demonstrate an efficient and accurate first-principles method to calculate the electronic structure of a large system using a divide-and-conquer strategy based on localized quasi-atomic minimal basis set orbitals recently developed. Tight-binding Hamiltonian and overlap matrices of a large system can be constructed by extracting the matrix elements for a given pair of atoms from first-principles calculations of smaller systems that represent the local bonding environment of the particular atom pair. The approach is successfully applied to the studies of electronic structure in graphene nanoribbons. This provides a promising way to do the electronic simulation for large systems directly from first principles.

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

The recently introduced method of correlation energy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F(2) molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 A to 8 A, the equilibrium distance being 1.412 A. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.

Correlation energy extrapolation by intrinsic scaling. V. Electronic energy, atomization energy, and enthalpy of formation of water

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390+/-0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh.

Toward a physical understanding of electron-sharing two-center bonds. I. General aspects

In 1916, Lewis and Kossel laid the empirical ground for the electronic theory of valence, whose quantum theoretical foundation was uncovered only slowly. We can now base the classification of the various traditional chemical bond types in a threefold manner on the one- and two-electron terms of the quantum-physical Hamiltonian (kinetic, atomic core attraction, electron repulsion). Bond formation is explained by splitting up the real process into two physical steps: (i) interaction of undeformed atoms and (ii) relaxation of this nonstationary system. We aim at a flexible bond energy partitioning scheme that can avoid cancellation of large terms of opposite sign. The driving force of covalent bonding is a lowering of the quantum kinetic energy density by sharing. The driving force of heteropolar bonding is a lowering of potential energy density by charge rearrangement in the valence shell. Although both mechanisms are quantum mechanical in nature, we can easily visualize them, since they are of one-electron type. They are however tempered by two-electron correlations. The richness of chemistry, owing to the diversity of atomic cores and valence shells, becomes intuitively understandable with the help of effective core pseudopotentials for the valence shells. Common conceptual difficulties in understanding chemical bonds arise from quantum kinematic aspects as well as from paradoxical though classical relaxation phenomena. On this conceptual basis, a dozen different bond types in diatomic molecules will be analyzed in the following article. We can therefore examine common features as well as specific differences of various bonding mechanisms.

Structure and stability of oxygen adsorption on Si(n) (n = 5-10) clusters

The structures, binding energies, and electronic properties of one oxygen atom (O) and two oxygen atoms (2O) adsorption on silicon clusters Si(n) with n ranging from 5 to 10 are studied systematically by ab initio calculations. Twelve stable structures are obtained, two of which are in agreement with those reported in previous literature and the others are new structures that have not been proposed before. Further investigations on the fragmentations of Si(n)O and Si(n)O2 (n = 5-10) clusters indicate that the pathways Si(n)O --> Si(n-1) + SiO and Si(n)O2 --> Si(n-2) + Si2O2 are most favorable from thermodynamic viewpoint. Among the studied silicon oxide clusters, Si8O, Si9O, Si5O2 and Si8O2 correspond to large adsorption energies of silicon clusters with respect to O or 2O, while Si8O, with the smallest dissociation energy, has a tendency to separate into Si7 + SiO. Using the recently developed quasi-atomic minimal-basis-orbital method, we have also calculated the unsaturated valences of the neutral Si(n) clusters. Our calculation results show that the Si atoms which have the largest unsaturated valences are more attractive to O atom. Placing O atom right around the Si atoms with the largest unsaturated valences usually leads to stable structures of the silicon oxide clusters.

Fast localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates

We present here an algorithm for computing stable, well-defined localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates. The algorithm is very fast, limited only by diagonalization of two matrices with dimension the size of the number of virtual orbitals. Furthermore, we require no more than quadratic (in the number of electrons) storage. The basic premise behind our algorithm is that one can decompose any given atomic-orbital (AO) vector space as a minimal basis space (which includes the occupied and valence virtual spaces) and a hard-virtual (HV) space (which includes everything else). The valence virtual space localizes easily with standard methods, while the hard-virtual space is constructed to be atom centered and automatically local. The orbitals presented here may be computed almost as quickly as projecting the AO basis onto the virtual space and are almost as local (according to orbital variance), while our orbitals are orthonormal (rather than redundant and nonorthogonal). We expect this algorithm to find use in local-correlation methods.

Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine

The method of extrapolation by intrinsic scaling, recently introduced to obtain correlation energies, is generalized to multiconfigurational reference functions and used to calculate the binding energies of the diatomic molecules C2, N2, O2, and F2. First, accurate approximations to the full configuration interaction energies of the individual molecules and their constituent atoms are determined, employing Dunning's correlation consistent double-, triple- and quadruple zeta basis sets. Then, these energies are extrapolated to their full basis set limits. Chemical accuracy is attained for the binding energies of all molecules.