Restricted Hartree-Fock Wave Functions Research Articles

Synthesis, crystallographic, quantum chemical and molecular docking studies of 4-benzoyl-1,2,3,11a-tetrahydro-6H-chromeno[3,2-e]imidazo[1,2-a]pyridin-6-one

The synthesis of pyridine derivatives is an active area of research in the development of new drugs. In view of the above importance, a novel compound with fused rings of derivatives of biologically active imidazole, pyridine and chromanone was synthesized. The crystal structure was analysed by single crystal X-ray diffraction method. The quantum chemical parameters of the molecule in the gaseous state were calculated by semi-empirical method using restricted Hartree-Fock wavefunction. The physicochemical properties such as druglikeness and bioactive scores were predicted to understand the drug transport and receptor interactions. Molecular docking studies were performed to analyze the binding of this compound with various bacterial and fungal pathogens. This study points out the potential of this compound to act as an antimicrobial agent. Comparison with related compounds shows that the addition of more number of biologically active groups enhances the activity.

The nature of the chemical bond and the role of non-dynamical and dynamical correlation in Be2.

In the spin-coupled generalized valence bond (SCGVB) description of Be2, there is a pair of electrons in highly overlapping "inner" orbitals corresponding to a traditional σ bond, but this bond is compromised by Pauli repulsion arising from its overlap with a second "outer" pair. The presence of this outer pair of electrons leads to a repulsive potential energy curve at long range and a bound, but metastable molecule at short range. To obtain further insights into the nature of the bond in Be2, we determined the non-dynamical and dynamical correlation contributions to the potential energy curve of Be2 using four different choices for the zero-order wave function: Restricted Hartree-Fock (RHF), SCGVB, valence-CASSCF(4,4), and valence-CASSCF(4,8). The SCGVB and valence-CASSCF(4,4) wave functions yield similar breakdowns of the total correlation energy, with non-dynamical correlation being the more important contribution. For the RHF and valence-CASSCF(4,8) wave functions, dynamical correlation is critical, without which the potential energy curve is purely repulsive. High accuracy calculations on the HBen-1Be-BeBen-1H molecule as a function of n (n = 1-6) suggest that the intrinsic strength of a Be-Be σ bond uncompromised by Pauli repulsion is on the order of 62-63 kcal/mol, and its length is 2.13-2.14 Å, ∼60 kcal/mol stronger and ∼0.35 Å shorter than in Be2.

On-Top Pair Density as a Measure of Left-Right Correlation in Bond Breaking.

To better understand left-right electron correlation and the effect of bond breaking on the on-top pair density, analytic expressions for the total density, the on-top pair density, and the ratio of the on-top pair density to the square of the total density were derived for H2 for both a restricted Hartree-Fock wave function and a complete active space self-consistent-field wave function with two electrons in two active orbitals. These quantities are compared for the two wave functions for various points in space around the molecule as functions of internuclear distance. At some points in space, in the CASSCF(2,2) wave function, electron correlation, perhaps counterintuitively, increases the probability that two electrons are at the same point in space. At the Coulson-Fischer point, the on-top pair density for the complete active space wave function starts to rapidly approach zero, and this can be taken as an indicator of bond breaking.

Singlet and triplet instability theorems.

A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.

On the nodal structure of single-particle approximation based atomic wave functions

The nodal structures of atomic wave functions based on a product of spatial orbitals, namely, restricted, unrestricted, and generalized valence bond wave functions, are shown to be equivalent. This result is verified by fixed node-diffusion Monte Carlo simulations for atoms up to Ne. Also for a molecular system, Li(2) at the equilibrium geometry, a multideterminantal generalized valence bond wave function does not improve the nodal surfaces of a restricted Hartree-Fock wave function.

FCPAC: Fast calculation of partial atomic charges using strictly localized molecular orbitals

Most force fields of molecular mechanics use constant partial atomic charges whereas it is now admitted that those charges strongly vary with the environment. Charge variations are particularly important in hydrogen bonds where polar entities come close together. Moreover, organizing H-bonds in networks, like in secondary structures of proteins, go with cooperative effects which lead to an overall electrostatic stabilization of the system. This is why variable atomic charges are required to correctly mimic these effects. Different methods of charge calculation were developed, most use polarizable dipole or electronegativity equalization. In this work, we propose a semi-empirical method (fast calculation of partial atomic charges (FCPAC)) which derives partial atomic charges from strictly localized molecular orbitals. The approximations enable to treat molecular systems with hundreds of atoms within reasonable delays. Results reported here show that charges calculated with FCPAC are similar to charges derived from Mulliken’s population analysis of a restricted Hartree–Fock wave function using the split valence basis set 6-31G and including polarization orbitals p and d respectively for hydrogen and heavy atoms, RHF/6-31G(d,p). Comparison with ab initio calculation was also performed on a system composed of five formamide molecules disposed in the same geometry as peptide bonds in an α helix. Charges variations are similar and suggest that FCPAC is suitable for quantitative estimation of cooperative effects.

Electronic correlation in cyclic polyenes. Performance of coupled-cluster methods with higher excitations

In this paper we consider the electrically neutral annulenes CMHM (M=6,10,14,18) and their cations CMHM4+ (M=10,14,18), having the cyclic geometry corresponding to the CM point group, and described by the electronic Hamiltonian of the Pariser–Parr–Pople (PPP) model (in which the strength of electronic correlations is controlled by the magnitude of the resonance integral β). We study the ground-state electronic-correlation effects in these systems by means of the single-reference coupled-cluster (CC) theory employing the restricted Hartree–Fock wave function as the reference. It is known that the basic CC technique—the coupled cluster singles and doubles (CCSD) method (for the annulenes equivalent to the CCD method)—breaks down in the strongly correlated regime of annulenes. In this paper we analyze the performance of the standard extensions of the CCD method, taking into account the connected triple (T) and/or quadruple (Q) excitations in the CC operator T̂: the CCDT, CCDQ, and CCDTQ methods. For comparison we use some modifications of the CCD method that emulate the coupling between the D and Q excitations: the ACP and ACPQ methods. Whenever available, the full configuration-interaction results serve as the reference. We study not only the ground-state correlation energies, but also the quality of the CC amplitudes corresponding to the double excitations, as well as the magnitude of quasidegeneracy effects. Our results provide evidence that not only the CCD, but also the CCDT, CCDQ, and CCDTQ methods break down when the correlation effects become sufficiently strong. This indicates a failure of the standard CC theory (in which the CCD method is gradually augmented by taking into account the T, Q etc. excitations) in the strongly correlated regime of the PPP annulene model.

Ab initio cluster study of the bilayer manganite La 2−2 xSr 1+2 xMn 2O 7

We have performed complete active space self-consistent field (CASSCF) cluster calculations for (MnO 6) 9− and (MnO 6) 8− complexes in the background potential appropriate for the bilayer manganite La 2−2 x Sr 1+2 x Mn 2O 7 at x=0.40. While the ground state of the (MnO 6) 9− complex is well-described by a restricted Hartree–Fock wavefunction, contributions from configurations with holes in oxygen orbitals are significant in the (MnO 6) 8− ground state wavefunction. Surprisingly, the CASSCF calculations including sufficient oxygen orbitals in the active space yields a doubly degenerate E (of the C 4v point group) as the ground state.

The performance of the density functional theory on reaction pathways requiring the multideterminantal description

The density functional theory (DFT) methods have been applied for cases known to require the multireference description. The DFT calculations are based on the restricted single determinantal wavefunction. Methods applied to the dissociation process of NH 4 + lead to the improper dissociation limit characteristic for computational schemes based on the restricted Hartree-Fock wavefunction (Hartree-Fock, MP2). The results for nitromethane to methyl nitrite rearrangement indicate its dependence on the energy functional choice.

On the Chemical Interpretation of the One‐Electron Density Matrix of Some Ionic Solids: LiH, LiF, and LiFHF

AbstractTwo‐dimensional cuts through one‐electron density matrices of three ionic solids in the position representation were calculated from restricted Hartree–Fock wavefunctions. The basis‐set quality was assessed by comparison of calculated Compton profiles/reciprocal form factors with experimental ones. The off‐diagonal regions of the density matrix contain the main information about chemical bonding in the crystal. The decomposition of the total density matrix into band contributions shows that the valence band always dominates in those regions. Furthermore, one‐electron density matrices of small subunits of the crystal and of symmetrically orthogonalised crystal wavefunctions were calculated. Their similarity and differences with respect to the solid are discussed.

Effective core potential study of transition metal and lanthanide catalyzed hydrogen exchange

An effective core potential study of H2 activation by the sigma-bond metathesis mechanism is reported for a range of simple Cl2MH catalyst models: M=Sc, Y, La, Lu, Zr+, B, and Al. Several points of interest are noted. Effective core potentials methods allow the study of metals from the transition, lanthanide and main group series with near equal facility. A single-determinant wavefunction is found to be sufficient for a qualitatively correct description of the ground and transition states in these reactions; changes in optimized geometries are minimal upon inclusion of correlation at the multiconfiguration self-consistent field (MCSCF) level. Calculated barriers are the highest using restricted Hartree-Fock (RHF) and multiconfiguration self-consistent field wavefunctions and lowest using Møller-Plesset second-order perturbation theory and second-order configuration interaction (SOCI) methods. Trends as a function of metal species on H2 activation barriers are consistent for all wavefunctions employed. As MP2 and RHF wavefunctions are most amenable to larger, more experimentally relevant systems, the use of RHF wavefunctions to determine stationary point geometries followed by MP2 calculations to assess their relative energies seems to be an attractive theoretical approach for computational investigations of hydrogenation and important related reactions.

Comparison and assessment of different forms of open shell perturbation theory

Existing methods for the calculation of the correlation energy of open shell atoms and molecules using Mo/ller–Plesset perturbation theory are discussed with special emphasis on recent advances in methods based on the restricted Hartree–Fock wave function. The convergence of the Mo/ller–Plesset series is examined to high order for a number of small systems and it is shown that some of the methods offer significant advantage over traditional unrestricted Mo/ller–Plesset theory. The optimized bond length and vibrational frequencies of CN, NO, and O2 are also compared for second and fourth order Mo/ller–Plesset theory, and again it is found that the same methods give much better results than the corresponding unrestricted results. Further supporting calculations are presented on the electron affinity of CN and the dissociation energy of HCN. The new methods involve relatively minor adaptation of existing unrestricted Mo/ller–Plesset (UMP) codes, and in the light of their superior performance are recommended instead of UMP theory for open shell molecules.

The 14N Nuclear Quadrupole Coupling in E- and Z-C-Cyanomethanimine; its Prediction from Restricted Hartree-Fock Wave Functions and its Experimental Determination by High Resolution Microwave Spectroscopy

Abstract The 14N hyperfine multiplets of low-7 rotational transitions of the E and Z isomers of HN = CH - C ≡ N, produced by flash pyrolysis from (CH3)2N -C ≡ N as precursor, were observed and analysed. The quadrupole coupling constants determined are (c-axis perpendicular to the molecular plane): The observed hfs multiplets were predicted with reasonable accuracy from RHF/6-311G** field gradients, once the latter had been scaled appropriately to compensate partly for the typical errors in the RHF-wave functions. The hitherto unmeasured 14N hyperfine multiplets of the related pyruvonitriles, H - N = C(CH3) - C ≡ N, are predicted.

Time-dependent Hartree–Fock simulations of the dynamics of polyatomic molecules

The use of the time-dependent Hartree–Fock method for performing molecular-dynamics simulations of polyatomic systems is explored. The theory is outlined for closed-shell restricted Hartree–Fock wave functions which employ the neglect of diatomic differential overlap approximation. The motions of the nuclei are treated classically. If the starting electronic wave function for a simulation obeys the time-independent variational principle then trajectories calculated with the algorithm stay very close to those obtained with a method in which the wave function obeys the time-independent variational principle at all times.

Ab initio calculations of g values of free radicals by finite perturbation theory

A theoretical method for evaluating the g tensor of free radicals was developed on the basis of the finite perturbation theory (FPT) and the open-shell restricted Hartree-Fock wavefunction, and ab initio calculations were performed for several free radicals. Calculations were also carried out by using the sum-over-state perturbation theory (SOS-PT); both FPT and SOS-PT methods gave similar accuracy for g values. The spin-other-orbit coupling term was important in the ab initio FPT calculation.

Influence of an external uniform electric field on harmonic vibrational frequencies. Analytic energy second derivatives for closed-shell restricted Hartree–Fock wave functions with an applied uniform electric field

Expressions are given for analytic determination of energy second derivatives of closed-shell restricted Hartree–Fock (RHF) wave functions under the effect of an external uniform electric field. In this way, harmonic vibrational frequencies can be computed. Application of the theoretical method to the methane molecule is presented, and comparison with the induced changes in vibrational bands of its experimental infrared spectrum is carried out.

Ab initio study of 2-silaallyl cation and anion. Some attributes of silicon-containing .pi.-conjugated systems

2-Silaallyl cation and anion, closed-shell 1 A 1 states, have been examined by using ab initio single determinantal restricted Hartree-Fock wave functions. Integrated projected electron populations indicate significant polarization of both σ and π SiC bonds

The Hartree-Fock dissociation of F2

We examine the stability of the restricted Hartree-Fock (RHF) wave function for F2 in the vicinity of the equilibrium internuclear distance (R=R e ) and the shape of the unrestricted Hartree-Fock (UHF) potential energy curve for the same system. The results depend on the basis set: With a split valence plus polarization basis, 6-31G(d), the RHF wave function is unstable at R e , and the UHF potential curve is purely dissociative. When the basis is extended to 6-311+G(3d) or 6-311+G(3df), the RHF wave function becomes stable, and the UHF potential curve acquires a local maximum for R slightly (∼0.02 a) greater than R e . The local maximum, however, is only 0.1 kcal/mol higher than the local minimum at R=R e .

Calculation of spin-orbit coupling constants in diatomic molecules with restricted Hartree—Fock wavefunctions

A complete computer program has been developed for the non-empirical calculation of spin-orbit coupling constants in linear molecules. This program can be used to obtain all kinds of integrals about spin-orbit Hamiltonian. The method was used to calculate the spin-orbit coupling constants of NS(X 2π) and SiF(X 2π). Excellent agreement between experimental and calculated values was obtained provided that the core polarization was included.

Analytic evaluation and basis set dependence of intensities of infrared spectra

Equations are presented for the analytic determination of dipole moment derivatives with respect to nuclear coordinates for closed-shell, open-shell unrestricted, and open-shell restricted Hartree–Fock wave functions. The efficient evaluation of these derivatives and the resulting infrared intensities simultaneously with determination of the vibrational frequencies is discussed. Intensities are presented for a selection of test molecules with a wide variety of basis sets. It is concluded that basis sets of double-zeta polarized or higher quality usually give correct qualitative information about the ordering of the intensities, while smaller basis sets may not even predict the most intense mode correctly. Quantitative accuracy using the larger basis sets seems to be limited primarily by the use of the double harmonic approximation.