On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

Calculation of excited states of H2O and NH3 by the one-center expansion approximation

The potential energy curves with respect to the bond angle are calculated for some excited and ionized states of the H₂O and NH₃ molecules by the use of the one-center expansion SCF MO and the improved virtual orbital approximations. The calculated equilibrium bond angles and force constants of bending motion are in good agreement with the experimental results.     

Systematic regularities of molecular SCF energies

New formulae for the approximate computation of total molecular energies are developed based on ab initio calculations of n-alkanes. Their application to various kinds of molecules reveals that good expectation values for total molecular energies can be obtained by considering only the one-electron terms h _i and the nuclear repulsion energy. It is further shown that very good agreement with SCF total energies is obtained by a relationship which connects the total energy with the sum of inner-shell (core) orbital energies. The results turn out to be better than those obtained using Ruedenberg's approximation, which takes both inner-shell and valence-shell orbital energies into account.     

Ab-Initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H₃C? NO₂ bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H₃C? NO₂ bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H₃C? NO₂ bond dissociation energies.     

Bonding/antibonding character of “lone pair” molecular orbitals from their energy derivatives; consequences for experimental data

The derivative of molecular orbitals (MO) energies with respect to a bond length (dynamic orbital force [DOF]) is used to estimate the bonding/antibonding character of valence MOs along this bond, with a focus on lone pair MOs, in a series of small molecules: AH (A = F, Cl, Br), AH₂ (A = O, S, Se), AX₃ (A = N, P, As; X = H, F), and H₂CO. The HOMO DOF agrees with the calculated variation of bond length and force constant in the corresponding ground state cation, and of bond length variation by protonation. These results also agree with available experimental data. It is worthy to note that the p‐type HOMOs in AH and AH₂ are found bonding. The lone pair MO is bonding in NH₃, while it is antibonding in PH₃, AsH₃, and AF₃.     

The Bonding Nature of the Canonical Molecular Orbitals in Simple Diatomic Molecules

The bonding nature of the canonical molecular orbitals 2σg, 2σu and 3σg in the molecules N₂,O₂, F₂ and the related analogous molecular orbitals in the molecules P₂ and CO, is analysed using Weinhold's natural bond orbital set. When the canonical molecular orbitals can be well localized into natural bond orbitals, the covalent bond can be completely attributed to the bonding type natural bond orbitals. The decomposition of canonical molecular orbitals into the natural bond orbital basis then gives the weighted bond order as the component of the bonding portion in the canonical molecular orbital. The weighted bond order results match the photoelectron spectroscopy assignment quite satisfactorily.     

Bond types of molecular orbitals and the photoelectron spectrum

The vibrational structures of the photoelectron spectra for diatomic molecules can be accounted for in terms of the slope of the orbital energy curve in the conventional correlation diagram with respect to internuclear distance. The vibrational structures of the photoelectron spectra for simple polyatomic molecules HCN, C₂H₂, and AH₂ type of hydrides can also be accounted for in terms of the slopes of the orbital energy curves in the correlation diagrams with respect to angles, as well as distances. Among all correlation diagrams, the slopes in the distance correlation diagram are related to the criterion for bond type—the positive for “bonding,” the negative for “antibonding,” while slopes with small magnitudes for “nonbonding.” The Fock matrix elements within the bond orbital basis provide heuristic and systematic rationalization of the slopes for the orbital energy curves. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 53–65, 2001     

The inner-sphere reorganization energies for AH2 + AH (A = Al,Si, P,S) electron self-exchange reactions in electron-transfer processes from ab initio calculations

This article presents an application of the accurate calculation scheme proposed recently for the inner-sphere reorganization energies of molecules of the type AH₂ (A = Al, Si, P, and S). A reasonable extension has been made. The inner-sphere reorganization energies for the title thermal electron self-exchange reactions are calculated in terms of ab initio MO self-consistent field method (HFSCF ) at different basis-set levels (6-31G **, 6-31 + G **, DZ , and DZP ) and the involved parameters are also determined. These calculated results have been calibrated by comparing optimized molecular geometrical parameters and corresponding energy properties with the experimental findings or other theoretical values. An approximation, in which the contribution from the bond length–bond angle to the potential energy surface is neglected, is adopted in constructing the calculation formulas via the function model. Its adequacy is discussed. Agreement among different calculation schemes is analyzed. © 1995 John Wiley & Sons, Inc.     

Basis set and correlation effects on computed positive ion hydrogen bond energies of the complexes AHn · AHn + 1+1: AHn = NH3, OH2, and FH

Basis set expansion and correlation effects on computed hydrogen bond energies of the positive ion complexes AH_n · AH_{n + 1}⁺¹, for AH_n = NH₃, OH₂ and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms is the single most important enhancement of split-valence plus polarization basis sets for computing hydrogen bond energies. Basis set enhancement effects appear to be additive in these systems. The correlation energy contribution to the stabilization energies of these complexes is significant, with the second order term being the largest term and having a stabilizing effect. The third order term is smaller and of opposite sign, while the fourth order term is smaller yet and stabilizing. As a result, computed MP4 stabilization energies are bracketed by the MP2 and MP3 energies. The overall effect of basis set enhancement is to decrease hydrogen bond energies, whereas the addition of electron correlation increases stabilization energies.     

Possible improvements of the interaction energy calculated using minimal basis sets

Interaction energies for H₂O·H₂O, H₂O·F^– and H₂O·CH₄ have been calculated using the LCAO MO SCF method with minimal basis sets, and employing the counterpoise method to eliminate the basis set superposition error. The results compare favourably with those obtained using extended basis sets. It is shown that for H₂O·H₂O and for the benzene-carbonyl cyanide complex a large part of the dispersion energy can easily be obtained as a sum of bond-bond dispersion energies calculated from a London-type formula using experimental values of the bond polarizability tensors. By considering the interaction between a water and a glycine molecule it is also shown that the dispersion energy plays an important role in the hydration of organic molecules.On leave from the Quantum Chemistry Laboratory, Institute of Basic Problems of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland     

Quantum chemical studies of propene,ethylene, acetylene and dihydrogen reactivity in the insertion reaction into the titanium-alkyl bond

Using the ab initio method of SCF MO LCAO

1 SCF MO LCAO: Self-consistent field molecular orbital linear combination of atomic orbitals.

in a valency-splitted basis of the Gaussian functions we have studied the addition of various monomers (C₃H₈, C₂H₄, C₂H₂) and dihydrogen to the titanium-alkyl bond in the complex H₂TiCH₃. The structure of transition states in the insertion reaction, heats of π-complex formation and activation energies for the insertion of the coordinated monomers have been calculated. The calculation results show that the reactivity decreases in the order C₂H₂ > C₂H₄ > C₃H₈ > H₂. According to the results obtained, the energy of the π^*-antibonding orbital of monomers can serve as an index of relative reactivity in the insertion reaction into the metal-alkyl bond.     

Electronic charge density and mean kinetic energy of lithium orbitals in LiH,LiH+, Li2, Li2+, LiH2+, and Li2H+

The electron density near the lithium nucleus in the species LiH, LiH⁺, Li₂, Li₂⁺, LiH₂⁺, and Li₂H⁺ was analyzed by transforming the SCF molecular orbitals into a sum of atomic contribnutions, for both core and valence orbitals. These “hybrid-atomic” orbitals were used to compare: electron densities, orbital polarizations, and orbital mean kinetic energies with the corresponding lithium atom quantities. Core-orbital electron densities at the lithium nucleus were observed to increase by up to 0.5% relative to the lithium atom 1s orbital. Lithium cores also exhibited polarization but, surprisingly, in the direction away from the internuclear region. Similar dramatic changes were seen in the electron densities of the valence orbitals of lithium: The electron density at the nucleus for these orbitals increased two-fold for homonuclear species and twenty-fold for heteronuclear triatomic species relative to the electron density at the nucleus in lithium atom. The polarization of the valence orbital electronic charge, in the vicinity of the lithium nucleus, was also away from the internuclear region. The mean “hybrid-atomic” orbital kinetic energies associated with the lithium atom in the molecules also showed changes relative to the free lithium atom. Such changes, accompanying bond formation, were relatively small for the lithium core orbitals (within 0.2% of the value for lithium atom). The orbital kinetic energies for the lithium valence electrons, however, increased considerably relative to the lithium atom: By a factor of about 2 in homonuclear diatomics, by a factor of 7 in heteronuclear diatomics, and by a factor of 11 in the triatomic species. In summary, the total electronic density (core plus valence) at the lithium nucleus remained remarkably constant for all of the species studied, regardless of the effective charge on lithium. Thus, the drastic changes noted in the individual lithium orbitals occurred in a cooperative fashion so as to preserve a constant total electron density in the vicinity of the lithium nucleus. In all cases, bond formation was accompanied by an increase in the orbital kinetic energy of the lithium valence orbital. We suggest that these two observations represent important and significant features of chemical bonding which have not previously been emphasized.     

Valence type vacant orbitals for configuration interaction calculations

A method is proposed to determine the valence type vacant orbitals, which are suitable for CI calculations and for the initial guess orbitals in MC SCF calculations. The method was applied to calculate the ionization energies of series of molecules and to draw the potential energy curves of various states of N₂ and N⁺₂.     

An application of the virial theorem to study AH2 structures II. Use of CNDO/2 wavefunctions

The simple form for the virial theorem for polyatomic molecules takes the form W=–t _i where t _i is an orbital kinetic energy. It is applied to study shapes of molecules of AH₂ type. Kinetic-energy-versus-angle diagrams are constructed with CNDO/2 wavefunctions that satisfy the virial theorem. The shapes of the molecules can be explained with the aid of the diagrams.     

An extended-valence MC SCF procedure: determination of the dissociation energies of C2, N2, O2, and F2

A series of MC SCF calculations have been carried out on C₂, N₂, O₂, and F₂ with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O₂ and F₂ than for C₂ and N₂. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.     

X-ray spectra and core hole energy curves of some diatomic molecules

Soft X-ray emission spectra of the molecules CO, N₂, NO and O₂ are examined for the purpose of deriving information on their core hole energy curves. Molecular force constant and equilibrium bond lengths are determined for the core hole species C*O and N₂*, and a qualitative analysis is made for CO*, N*O, NO* and O₂*. The results show that differences of equilibrium geometries between the core hole states and the ground states are very well reproduced (better than 1 pm) by SCF calculations within the Hartree-Fock formalism. Inclusion of anharmonicity in the Franck-Condon analysis gives a small but significant effect on the best fitted value for the core hole state bond lengths (about 0.5 pm). Oxygen is binding energies determined from the X-ray spectra are shown to agree with ESCA data, in most cases within a few tenths of an eV. Calculated ΔSCF transition energies reproduce the experimental data within a few eV.     

A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

Cooperative enhancement of water binding to antiparallel β‐sheet models: Analysis by ab initio calculations

The cooperative enhancement of water binding to the antiparallel β‐sheet models has been studied by quantum chemical calculations at the MP2/6‐311++G**//MP2/6‐31G* level. The binding energies of the two antiparallel β‐sheet models consisting of two strands of diglypeptide are calculated by supermolecular approach. Then water molecules are gradually bonded to the diglypeptide by N? H···OH₂ and C?O···HOH hydrogen bonds. Our calculation results indicated that the hydrogen bond length and the atom charge distribution are affected by the addition of H₂O molecules. The binding energy of antiparallel diglypeptide β‐sheet models has a great improvement by the increasing of the hydrogen bond cooperativity and the more H₂O molecules added the more cooperativity enhancement can be found. The orbital interactions are calculated by natural bond orbital analysis, and the results indicate that the cooperative enhancement is closely related to the orbital interaction. © 2012 Wiley Periodicals, Inc.