Showing papers in "Theoretical Chemistry Accounts in 1977"

Bonded-atom fragments for describing molecular charge densities

Abstract: For quantitative description of a molecular charge distribution it is convenient to dissect the molecule into well-defined atomic fragments. A general and natural choice is to share the charge density at each point among the several atoms in proportion to their free-atom densities at the corresponding distances from the nuclei. This prescription yields well-localized bonded-atom distributions each of which closely resembles the molecular density in its vicinity. Integration of the atomic deformation densities — bonded minus free atoms — defines net atomic charges and multipole moments which concisely summarize the molecular charge reorganization. They permit calculation of the external electrostatic potential and of the interaction energy between molecules or between parts of the same molecule. Sample results for several molecules indicate a high transferability of net atomic charges and moments.

On the calculation of multiplet energies by the hartree-fock-slater method

Abstract: It is shown that a consistent application of the p 1/3 approximation of the Hartree-Fock-Slater method requires the use of one specific procedure, the sum method, for the calculation of the energy E 1 of singlet excited states of closed shell molecules. Further, E 1 is found to be in reasonable agreement with experiment for a number of molecules, contrary to the energy E 2 obtained according to another method discussed in the literature. The calculation of other multiplet splittings than singlet-triplet in the Hartree-Fock-Slater method is also considered.

On the calculation of bonding energies by the Hartree Fock Slater method

Abstract: A transition state method has been proposed for the calculation of bonding energies and bond distances within the Hartree Fock Slater Method. Calculations on a number of diatomic molecules and a few transition metal complexes show better agreement with experiment than corresponding Hartree Fock results. The proposed transition state method gives a direct connection between bond orders and bonding energies.

Acyclic systems with extremal Hückel π-electron energy

Abstract: The main result of the present work is the proof that among acyclic polyenes CnHn+2, the linear isomer H2C=(CH)n−2=CH2 has maximal HMO π-electron energy. The 1,1-divinyl isomer (H2C=CH)2C(CH)n−6=CH2 has maximal π-energy among branched acyclic systems. Among trees withn vertices, the star has minimal energy. A number of additional inequalities for HMO total π-electron energy of acyclic conjugated systems are proved.

A semiempirical model for the two-center repulsion integrals in the NDDO approximation

Abstract: A self-consistent formalism is proposed for the two-center electron repulsion integrals in the NDDO approximation, based on their expansion in terms of multipole-multipole interactions and free from adjustable parameters.

Molecular orbital studies of hydrogen bonds

Abstract: The ground state, the lowest singlet and triplet n-π* states, and the lowest triplet π-π* state of the formic acid monomer and dimer are studied with the ab initio molecular orbital theory. The two-configuration electron-hole potential method is used for calculations of excited states of dimers. The potential energy curves for the symmetrical simultaneous movement of two bridging protons are studied for all of the states. The barrier of the proton transfer in the ground state is found to be the smallest of the states studied. The association energy is analyzed in terms of various components.

The convergence of the Rayleigh-Ritz Method in quantum chemistry

Abstract: The convergence of the Rayleigh-Ritz Method (RRM) or of CI calculations, respectively, for the non-relativistic electronic Hamiltonian of molecules is investigated using the conventional basis sets of Quantum Chemistry, such as systems of Slater, Gauss and two-electron functions. Conditions for the choice of orbitalexponents with respect to Slater and Gauss orbitals are especially given, such that the convergence is guaranteed. Inter alia, in Theorem 10 a proof of the convergence of the RRM for a Hylleraas basis in s,t,u-coordinates is presented, a question which is still being debated today.

Topological properties of benzenoid systems: An identity for the sextet polynomial

Abstract: The sextet polynomial of non-branched cata-condensed benzenoid molecules is proved to be related (Eq. (3)) to the characteristic polynomial of a tree.

Note on open shell restricted SCF calculations for rotation barriers about C-C double bonds: Ethylene and allene

Abstract: It is shown thatab initio open-shell SCF calculations yield acceptable results for rotation barriers about double bonds in contrast to more conventional closed-shell SCF calculations. Using basis sets of double zeta+polarization quality the SCF values for the rotation barriers of ethylene and allene are obtained to be 48 and 50 kcal/mole, respectively. An IEPA estimate of the influence of electron correlation leads to values of 64 and 52 kcal/mole, respectively, which are in reasonable agreement with the experimental values.

Cation binding to biomolecules

Abstract: SCF ab initio computations are carried out on the binding of alkali and alkaline-earth cations to the phosphate monoanion. The effect of the binding on the conformational properties of the phosphodiester linkage and of the polar head of phospholipids is investigated. The results indicate that following the nature of the cation and the site of its binding, the interaction may have a profound influence on the conformation of the ligand. The consequences of this situation on the use of lanthanide probes in NMR studies are considered.

Exchange polarization effects in the interaction of closed-shell systems

Abstract: Explicit formulae for the calculation of the exchange polarization energy in the interaction of closed-shell atoms or molecules have been derived by assuming neglect of the electron correlation within the noninteracting systems The dispersion part of the exchange polarization energy has been represented as a sum of contributions arising from the interaction of two, three or four orbitals at a time Each of these contributions is given by an integral involving the orbitals engaged in the interaction and the pair functions describing the dispersion interaction between these orbitals The numerical calculations for the interaction of two ground-state beryllium atoms show that the exchange dispersion energy is positive and quenches about 5 to 10 per cent of the dispersion term This results in a decrease of the interaction energy, computed as a sum of the SCF and dispersion components, by 6 to 30 per cent for interatomic distances ranging from 10 to 7 bohrs Simplified formulae for estimating the exchange dispersion energy in the interaction of larger systems are also proposed and their accuracy is discussed

On the direct calculation of localized HF orbitals in molecule clusters, layers and solids

Abstract: It is shown that the computational effort involved in HF calculations can be considerably reduced by applying the following concepts: 1) the use of a localization operator for the direct determination of localized non-orthogonal HF orbitals, 2) the approximation of the interaction potential between different localization centres by a Hartree-like ansatz, 3) the successive calculation of many-body corrections to molecular properties such as the total energy. A numerical application to LiH layers and solid LiH is described.

Ab initio Studies of long range interactions between ethylene molecules in the multipole expansion

Abstract: The multipole moments and multipole polarizabilities of ethylene and the long range coefficients for the interactions between two ethylene molecules have been calculated using LCAO-SCF wave functions. Subjecting different AO basis sets to a completeness test, we have shown that the inclusion of polarization functions slightly more diffuse than the valence orbitals is required for an appropriate description of the second order quantities. The (theoretical) Unsold procedure which is introduced to approximate the second order interaction energy, appears to be rather accurate and is preferable for small basis sets.

Generalized Brillouin Theorem Multiconfiguration Method for Excited States

Abstract: The Generalized Brillouin Theorem Multiconfiguration Method (GBT-MC) of Grein and Chang is extended and applied to the calculation of excited states. Orthogonality constraints to lower states as well as second-order interaction effects of states lying close together have been taken into account. In this way quadratic convergence can be guaranteed. Difficulties with coupling coefficients and Lagrangian multipliers of SCF methods can be circumvented. Test calculations have been performed on valence electron excited states of C, H2O, and CH2O, and on core excited states of Li.

An ab initio investigation into the SN2 reaction: Frontside attack versus backside attack in the reaction of F− with CH3F

Abstract: The energy hypersurface for the attack of fluoride ion on methyl fluoride has been explored with ab initio LCAO-SCF calculations at a split-valence basis set level. Transition states for frontside and backside attack have been located. In addition to transition states, two possible F−-CH3F clusters have been identified. The transition state for the substitution of fluoride with retention of configuration is found to be 56 kcal/mol higher than the transition state for inversion of configuration. The transition state for hydride displacement with inversion is 62 kcal/mol above the transition state for fluoride substitution with inversion.

Symmetry factoring of the characteristic equations of graphs corresponding to polyhedra

Abstract: A systematic procedure is described which uses two-and three-fold symmetry elements in graphs to reduce their adjacency matrices to lead to corresponding factorings of their characteristic polynomials. A graph splitting algorithm based on this matrix reduction procedure is described. Applications of these methods to the factoring of the characteristic polynomials of 28 polyhedra with nine or less vertices are given. General expressions for the eigenvalues of prisms, pyramids, and bipyramids in terms of the eigenvalues of their basal or equatorial regular polygons are calculated by closely related matrix methods.

An ab initio study of formamide

Abstract: Calculated energy and molecular properties of the ground and low-energy excited states of formamide are presented at the ground state geometry. Satisfactory results are obtained except for the 1ππ* energy which remains too high by 1 eV (which is nevertheless a large improvement over previous calculations). The predicted triplet energies lie at 5.4 eV (3nπ*) and 5.8 eV (3ππ*).

On basis set effects in SCF calculations of the interaction energy between closed-shell atoms

Abstract: The so-called “superposition error” is investigated for different Gaussian basis sets used in the SCF calculations of the interaction energy between neon atoms. The results show that unless the counterpoise method [1] is applied, a qualitatively wrong description of interaction can be obtained. This is observed even for the basis sets which give fairly accurate atomic energies. It is shown that, despite large super-position error, basis sets fitted to the exact density [2] can provide very reasonable results if the counterpoise method is applied.

Cation-binding to biomolecules: IV. An ab initio study on the interaction of Na+ with the purine and pyrimidine bases of the nucleic acids

Abstract: Ab initio SCF MO computations are performed on the binding of the Na+ ion to the purine and pyrimidine bases of the nucleic acids. The results are compared in particular with those of previous studies on proton affinities. The computations indicate two principal differences between these two types of interactions: 1) the increased significance in cation binding of the individual oxygen binding sites in bases containing both oxygen and nitrogen; 2) the appearance in cytosine and guanine of “bridged” positions between a nitrogen and a carbonyl oxygen as the preferred binding sites. The theoretical results are compared with the available experimental data. Their general significance for cation binding is discussed.

The computation of the representation matrices of the generators of the unitary group

Abstract: A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.

Calculation of molecular one-electron properties

Abstract: A comprehensive analysis of the reliability of computed first- and second-order properties is attempted. The best and most recent experimental and theoretical data available in the literature have been compiled and compared to those obtained using moderately sized and extensive basis sets in calculations at the coupled Hartree-Fock level. It is concluded that prediction of the properties dealt with in this paper is, in general, safe though there are certain problems concerning the description of charge density polarization phenomena.

The calculation of ground and excited state molecular polarizabilities: A simple perturbation treatment

Abstract: Second order perturbation theory has been coupled with the CNDO/S CI method of Del Bene and Jaffe to calculate the ground and excited state polarizabilities of various molecules. It is found that this treatment produces reasonably good polarizabilities with great computational ease.

Calculation of vertical ionization potentials of H2O and Ne by many-body Rayleigh-Schrödinger perturbation theory

Abstract: The vertical ionization potentials of H2O and Ne are calculated by many-body Rayleigh-Schrodinger perturbation theory up to third order. The comparison of the present method with the other approaches is done.

On the affinity of cytosine towards electrophiles

Abstract: Ab initio SCF computations on the intrinsic preferences of the H+, CH3+ and C2H5+ cations towards the two principal sites of protonation or alkylation on cytosine, N3 or O2, show that this preference undergoes a continuous modification with the increase in size and complexity of the cation. N3 is the preferred site of fixation of H+, O2 the preferred site of C2H5+, while CH3+ has no marked preference. The exchange repulsion term of the binding energy appears responsible for the preference of C2H5+ for O2.

Ab initio SCF and CI study of the electronic spectrum of pyridine N-oxide

Abstract: Configuration interaction (CI) studies of ground, n → π*, π * π* electronically excited states are reported for pyridine N-oxide. The transition energy to the lowest π → π* excited 1 B 2 state is calculated at 4.35 eV, compared to the experimental spectrum range of 3.67–4.0 eV. This state lies below the lowest n → π* excited 1 A 2 state calculated at 4.81 eV above the ground state. The only experimentally reported triplet state at 2.92 eV above the ground state is predicted to be the 3 A 1 (ππ*) state. The calculated energy lies at 3.27 eV. Numerous other high-lying singlet states as well as the triplet states have also been calculated. The intramolecular charge transfer character of the ground and the excited states have been studied in terms of the calculated dipole moment and other physical properties.

Selection of terms for a CI wavefunction to preserve potential surface features

Abstract: A cumulative selection procedure for choosing configuration functions for inclusion in CI calculations is described. The objective of the method is to obtain equal energy loss, relative to unselected calculations, for different states and different regions of the potential surface. Results obtained from calculations on the BH molecule indicate an overall advantage in comparison to the threshold selection procedure, particularly with regard to molecular geometry changes.

Theoretical investigation of structure and stability of oligomers of LiH, NaH, LiF, and NaF

Abstract: The molecules LinHn, NanHn, LinFn, n=1,..., 4, and NaF and Na2F2 are investigated by means of extended basis set SCF and CEPA-PNO computations. In analogy to the D 2h structure of dimers, it is found that trimers have a planar cyclic D 3h equilibrium geometry. For the tetramer of LiH and NaH, the D 4h structure has about the same energy as the 3-dimensional T d structure, whereas the latter is definitely favoured for Li4F4. Correlation effects are investigated for the oligomerization of LiH and the dimerization of LiF. The effect of electron correlation on corresponding ΔE turns out to be small (<4 kJ/mol), except for the case that the T d tetramer is involved which has a rather large correlation energy.

Efficient multipole expansion: Choice of order and density partitioning techniques

Abstract: Two approaches to improve the convergence of the multipole series were considered: 1) an increase in the order of the expansion; 2) decomposition of the molecular charge density into smaller distributions. New decompositions of the molecular electronic density and a computational procedure to generate high-order moments are presented. The accuracy and timing of test calculations on the H2O ... H2O system are given and suggestions are made for optimizing the choice of an expansion for more general systems.

A programmable spin-free method for configuration interaction

Abstract: In this note a method is presented for quick implementation of configuration interaction (CI) calculations in molecules. A spin-free Hamiltonian for anN electron system in a spin stateS, expressed in terms of the generators for the unitary group algebra, is diagonalized over orbital configurations forming a basis for the irreducible representation [21/2N-S 12S ] of the permutation group S N . It has been found that the basic algebraic expressions necessary for the CI calculation involve a limited category of permutations. These have been displayed explicitly.