Semiempirical Hamiltonian Research Articles

Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene π‐electron models

AbstractMethods accounting for correlation effects in quasi‐one‐dimensional π‐electron systems and based on the restricted Hartree–Fock (RHF) single determinantal reference state are briefly reviewed as well as their role in the bond length alternation (or dimerization) problem in polyactylene‐like systems, as described by the semiempirical Hamiltonians of the Pariser–Parr–Pople (PPP) type. Particular attention is given to the π‐electron model of cyclic polyene homologous series CNHN, N = 2n = 4v + 2, v = 1,2,…, which can be regarded as an idealized model of one‐dimensional metallic‐like systems with imposed Born–von Kármán boundary conditions when N ∞. These models provide a useful bridge between the typical aromatic systems, represented by benzene (N = 6) π‐electron model, and long linear polyenic chains, since the properties of these systems hardly change once a sufficiently large N (˜26 or 30) is reached. It is shown that due to the quasidegenerate character of the RHF reference employed, and the related prominence of connected quadruply excited cluster components in the exact wave function, most of the standard technieques suffer a singular behavior break down entirely for large enough systems, particularly in the strongly correlated regime. The approximate coupled pair theory that accounts for quadruply excited clusters (ACPQ method) is shown to be free of these shortcomings and is extended to include also approximately the effects of connected triexcited cluster components. These results are compared with other recently examined approximate methods accounting for the tri‐ and quadruply excited clusters and the proposed ACPQ+T(ACPQ) procedure is shown to provide the best results in the whole range of the coupling constant.

Electronic structure and properties of strained polymers: 1. Methods for polyethylene

The modulus and strain-dependent frequency spectrum of polyethylene have been computed from a cluster of C 6H 12 units using the semi-empirical AM1 Hamiltonian and unrestricted Hartree—Fock wavefunctions. The computed modulus substantially exceeds experimental values, a result which derives from neglect of electron correlation in the calculations. Good qualitative and quantitive agreement with reported strain-dependent frequencies is found, suggesting that the method describes cubic anharmonicity in the bonding while systematically overestimating components of the Hessian.

Static second-order polarizability calculations for large molecular systems

A procedure to calculate all second-order polarizability tensor elements in static fields has been developed. The calculations are based on semiempirical Hamiltonians (MNDO) that include shaped electric fields. The technique has been applied to mono-, di-, and trisubstituted benzenes incorporating nitro, methyl, and primary and secondary amino groups.

Static second-order polarizabilities of aminobenzophenones and nitrobenzophenones

Static-field theoretical studies on molecular second-order polarizabilities (β) of benzophenone derivatives were performed. Calculations were based on the use of shaped electric fields and semiempirical Hamiltonians. Either an electron-donating (amine) or an electron-withdrawing (nitro) substituent was incorporated into a phenyl ring of benzophenone; the phenyl rings of benzophenone were oriented either coplanar or perpendicular to the carbonyl. The change in charge transfer with respect to the electrophilic character of the carbonyl group was monitored to determine its effect on the molecular second-order polarizability. Calculations were performed for all constitutional isomers of the two benzophenone derivatives.

Atomic charges derived from semiempirical electrostatic potentials; an interaction energy method

A method for calculating molecular electrostatic potentials using the semiempirical MNDO and AM1 Hamiltonians is presented. The electrostatic potential within the semiempirical framework is obtained as the first-order interaction energy between a unit positive charge (i.e. a hydrogen nucleus) and the molecule. The atomic charge distributions derived from such electrostatic potentials are of similar quality to those obtained as expectation values of the Coulomb potential operator using semiempirical wavefunctions derived from the MNDO or AM1 density matrices. The method requires trivial amounts of computer time and therefore should be well suited for deriving atomic charge models of large biological molecules for use in molecular mechanics and molecular dynamics simulations.

Quantum chemical vibrational analysis of the chromophore of bacteriorhodopsin

Vibrational spectra of the retinal chromophore in bacteriorhodopsin (BR) are interpreted by a quantum chemical vibrational analysis. The chromophore is represented by a semiempirical MNDO Hamiltonian (modified neglect of diatomic overlap) that describes all valence electrons using Hartree-Fock wave functions. The main sources of errors in a description based on the MNDO force field are identified. The authors show that the errors are mainly due to the neglect of the effects of electron correlation. A proper understanding of vibrational spectra of the BR chromophore can be obtained only if effects of electron correlation are taken into account.

The half‐projected Hartree‐Fock model for computing thermally “forbidden” pericyclic reactions and biradical processes. I. Formulation and results for some singlet biradical species

AbstractThe possible use of a half‐projected Hartree‐Fock (HPHF) wave function correlating a single pair of electrons, being defined as a linear combination of two unrestricted Slater determinants which are identical except that all the α and β spin functions are interchanged, is investigated in relation to the computation of the potential energy surfaces involving singlet biradical or biradical‐like species. The results of calculations, within the framework of the MINDO/3 semiempirical Hamiltonian, for a number of prototypical biradical molecules indicate that, in general, the HPHF model provides a geometrical and energetical description that is equivalent to that obtained from a conventional two‐configuration self‐consistent‐field wave function.

On the connection between semiempirical molecular orbital theories and effective hamiltonians: A constrained variational point of view

AbstractThe idea of interpreting the semiempirical MO theories from a constrained variational point of view is explored. A density‐based approach is developed for calibrating the parameters of useful semiempirical Hamiltonians of molecular electronic structure theory. Results of some numerical experiments with model Hamiltonians of constrained variational origin are reported.

GaAs Total Energy Tight Binding Hamiltonians for use in Molecular Dynamics

ABSTRACTA self-consistent non-orthogonal semi-empirical tight binding Hamiltonian is proposed for GaAs, or any sp system, which is simple, reliable, transferable, accurate and fast to evaluate. Matrix elements are functions of charges, distances between atoms and simple cosines of angles between s and p-electron densities and interatomic vectors which maintain the simplicity of Slater-Koster parameterizations. The tight binding scheme is fit against a large data base of local density functional derived total energies for systems of differing coordination and geometry. The Hamiltonian fulfills the correct Virial constraint, invokes the physically correct relationship between overlap and kinetic energy matrix elements and defines charges via Mulliken or Löwdin schemes. Such Hamiltonians will allow the reliable simulation of statistical mechanically interesting systems of order hundred or more atoms over physically useful periods of time of order tens to hundreds of thousands of time steps within not unreasonable supercomputer budgets.

On the strength of electron correlations in high-T c superconducting copper oxides

We analyze the strength of electronic correlations in the half-filled antibonding Cu−O orbitals of high-Tc superconducting copper oxides by considering a Cu12O 17 n− cluster withn=8 or 10, respectively. The correlated ground state is calculated by the method of the local approach (LA) in a version which allows the treatment of stronger correlated electrons. As mean-field basis a semiempirical Hamiltonian of the ZDO (zero differential overlap) type has been adopted. It is found that the correlations are particularly strong in the Cu 3dx2−y2 orbitals. The nonintegral orbital occupation allows for valence fluctuations between Cu+ and Cu2+ in spite of the remarkable correlations. According to the present model excess holes are located at the oxygen sites. The theoretical findings are compared with the results of spectroscopic investigations. The present electronic-structure analysis allows for a straighforward rationalization of previous experimental measurements. The strong connection between the importance of electronic correlations and the symmetry properties of the electronic wave function is emphasized.

New parametric analysis of the optical spectra of U4+ in ThSiO4

Crystals of ThSiO4–U4+ were grown by the flux method. Absorption and emission spectra were recorded from 4000 to 30 000 cm−1 at liquid helium and various higher temperatures. The transitions were assigned and fit to a semiempirical Hamiltonian with adjustable parameters via a least squares procedure. The crystal field parameters for U4+ in ThSiO4 were compared to those for U4+ in other hosts.

Reinterpretation of the absorption spectrum of UCl 4 single crystal

The absorption spectra of UCl 4 single crystals have been measured from 4000 to 30 000 cm −1 at temperatures ranging from 4.2 K to room temperature. The transitions were assigned by comparing the strong absorption features of UCl 4 to those of ThCl 4:U 4+. The energy levels were fitted to a semiempirical Hamiltonian in D 2d symmetry. A r.m.s. deviation of 60 cm −1 in the fit to 26 assigned levels was achieved using the following set of parameters (cm −1): F 2 = 42 561 ± 235; F 4 = 39 440 ± 634; F 6 = 24 174 ± 185; ξ = 1805 ± 8; α = 31 ± 1; β = −576 ± 168; (γ = 1200); B 2 0 = −903 ± 151; B 4 0 = 766 ± 220; B 4 4 = −3091 ± 185; B 6 0 = −1619 ± 482; B 6 4 = −308 ± 280.

The electronic structure of organometallic complexes of the f elements—XIV. Quantitative interpretation of the luminescence and magnetochemical properties of Cp 3Pr·CNC 6H 11

The 3 P 0 → 3 H 5 transition can be observed in the low temperature pre-resonance luminescence spectrum of the cyclobexylisocyanide adduct of tris (η 5-cyclopentadienyl)-praseodymium(III). The previously assigned crystal field splitting pattern, completed by the levels which are derived from the 3 H 5 term, was fitted to the parameters of a semiempirical Hamiltonian with an rms deviation of 34.5 cm −1 for 48 levels. From the eigenvalues and eigenfunctions obtained, the experimentally determined temperature dependence of the paramagnetic susceptibility could be reproduced by introducing orbital reduction factors between 0.975 and 1.0. The experimental temperature dependence of the 1H-NMR shift of the α proton of the cyclohexyl ring could be simulated by considering only the dipolar contribution.

The electronic structure of organometallic complexes of the ƒ elements—XI. Absorption spectrum and parameterization of the crystal field splitting pattern of a methyltetrahydrofuran adduct derived from tris(η5-cyclopentadienyl)-praseodymium(III)

The low temperature absorption spectrum of tris(η5-cyclopentadienyl)-praseodymium(III) dissolved in a 2-methyltetrahydrofuran glass has been measured. The observed transitions, along with the previously reported magnetic circular dichroism transitions, have been assigned and fitted to the parameters of a semiempirical Hamiltonian with an r.m.s. deviation of 27.2cm−1 for 40 levels. The experimental and calculated magnetic susceptibility of Cp3Pr·butyl acetate (which has an optical spectrum very similar to that of Cp3Pr·MeTHF) as a function of temperature are also given.

Crystal field analysis of Tm3+ and Yb3+ in YPO4 and LuPO4

The optical and near infrared absorption of dilute Tm3+ and Yb3+ impurities in YPO4 and LuPO4 single crystals have been measured at liquid helium and nitrogen temperatures. For Tm3+, the spectral region from 5 000 to 38 000 cm−1 was examined and Zeeman spectra were obtained in the visible region. The observed transitions were assigned and fit to a semiempirical Hamiltonian with adjustable parameters via a least-squares procedure. Satisfactory fits and good agreement between the calculated and measured g values were obtained. For Yb3+, there are more parameters than experimental levels, so ζ, B20, B40, and B44 were adjusted, while B60 and B64 were fixed at the values found for Tm3+. Energy levels and Zeeman splittings calculated with these parameters are in good agreement with the measured quantities.

On the importance of orbital relaxation and correlation in the photoelectron spectra of transition metal complexes

Orbital reorganisation energies in the photoelectron spectra of 15 transitional metal complexes with Ti, V, Cr, Mn, Fe, Co, Ni and Zn as 3d centres have been determined by means of the Green's function formalism. Computational background for the present investigation is an improved semi-empirical INDO Hamiltonian. Detailed results and comparisons with experimental data are given for four representative 3d complexes with V, Mn, Fe and Ni atoms. A self-energy approximation has been employed in the second order of perturbation that allows the decomposition of the net reorganisation energies into orbital relaxation, the loss of ground-state correlation and the variation of the electronic correlation in the cationic hole state as the many-body response to the relaxation energy. The magnitude of these corrections is studied as a function of the localisation properties of the corresponding orbital wavefunctions. Outer valence ionisation energies for delocalised ligand electrons can be assigned on the basis of the canonical molecular orbital energies of the electronic ground state (Koopmans' theorem). Relaxational procedures (e.g. Delta SCF formalism) are a suitable approximation in the case of MO with 40-60% metal character where correlation effects are negligibly small.

The electronic structure and the solid state properties of the one-dimensional tetraza porphin nickel (II ) system. A self-consistent-field Hartree-Fock crystal-orbital approach based on a semiempirical Hamiltonian

The electronic structure and the solid state properties of tetraza porphin nickel (II), 1, have been studied by means of self-consistent field (SCF) Hartree-Fock (HF) crystal-orbital (CO) calculations that are derived in the framework of a semiempirical INDO Hamiltonian. The iterative SCF procedure is based on an algorithm where Hartree damping of the bond-order matrices and a direct steepest-descent formalism have been combined in order to avoid SCF difficulties in the CO method as a result of the closely spaced occupied and virtual Fermi seas. The diatomic intercell energies are mainly determined by electrostatic contributions. The NiNi coupling is highly repulsive, large stabilising two-centre pairs are found for the interaction between the 3d centre of the reference cell and the heteroatoms (N) in the neighbouring fragments. A large number of ligand, pi , lone-pair and sigma bands are predicted to be on top of dispersion curves with substantial Ni3d character. Oxidation processes in 1 are ligand-centred leading to organic pi radical cations. The INDO CO results for 1 are compared with experimental data derived for nickel phthalocyanine, NiPc, and halogenated NiPc derivatives.

Comparison of the electronic spin-orbit splitting in CH3O using UHF and RHF wavefunctions

The electronic spin-orbit splitting λe of methoxy was calculated using RHF wavefunctions and a semiempirical spin-orbit hamiltonian. The result, λe = -158 cm-1, agrees well with a calculation that used a RHF wavefunction and the relativistic Breit hamiltonian (λe = -142 cm-1). However, this result does not agree with a calculation that used the same semiempirical spin-orbit hamiltonian and an UHF wavefunction (λe = -78 cm-1). The disagreement arises from the form of the UHF and RHF wavefunctions. The experimental evidence is not sufficiently conclusive for one to decide which wavefunction gives a better description of methoxy.

Electronic reorganization in the photoelectron spectra of transition metal compounds

The validity of Koopmans’ theorem in a series of 16 transition metal compounds with a large variety of 3d centers (Ti, Cr, Mn, Fe, Co, Ni, and Zn) is investigated. The reorganization energies are determined by means of the Green’s function method employed in a semiempirical INDO Hamiltonian. A self-energy approximation is used that allows a fragmentation of the calculated Koopmans’ defects into relaxation increments as well as into correlation parameters that take into account the loss of pair correlation in the electronic ground state and the modification of the pair correlation in the cationic hole state. The magnitude and the importance of these parameters are studied as a function of the 3d occupation pattern, the oxidation state of the transition metal center, the nature of the orbital wave functions and the one-particle energies. It is demonstrated that pair relaxation energies in the various hole states are by no means negligible in comparison to the relaxational corrections that lead to the most pronounced deviations from IKv,j (IKv,j=− εj). The limitations of purely relaxational models (e.g., ΔSCF approach) are analyzed in detail. The gradual modifications of the calculated Koopman’s defects within the 3d series are rationalized. The most pronounced reorganization energies are encountered in d6–d8 complexes. The magnitude of relaxation and correlation is reduced with a decreasing and an increasing number of 3d electrons. The physical background leading to the breakdown of Koopman’s theorem in 3d derivatives is compared with the results of recent studies in various molecular species (e.g., small molecules, organic lone-pair systems).

An INDO crystal orbital approach to the one-dimensional porphyrinatonickel(II) system

The band structure of the one-dimensional metallomacrocycle porphyrinatonickel(II), Ni(P), has been studied by means of the crystal orbital formalism based on a semi-empirical INDO Hamiltonian. The unoxidized Ni(P) polymer is an insulator, the highest occupied bands as well as the conduction band are localized in the ligand framework. Bands with significant Ni 3 d admixtures are predicted at lower energies. The dense manifold of ligand states in the vicinity of the Ni 3 d basis energies leads to a strong metal-ligand intermixing in Ni(P) bands in the outer valence region.