Showing papers in "Theoretical Chemistry Accounts in 1978"
TL;DR: In this paper, the multiplicity and the full spin of the ground state of large alternate molecules with conjugated bonds are considered and it is strictly shown that if the numbers of starred and unstarred atoms (say, carbon) differ from each other, the full-spin of the molecule is more than zero.
Abstract: The multiplicity and the full spin of the ground state of large alternate molecules with conjugated bonds are considered. It is strictly shown that if the numbers of starred and unstarred atoms (say, carbon) differ from each other the full spin of the molecule is more than zero. Some possible planar and linear molecules having the full spin to be proportional to their sizes are presented. Particularly, they would be ferromagnets at infinite sizes.
675 citations
TL;DR: In this article, a spinless first-order density matrix was proposed as fundamental formula representing the spatial distribution of odd electrons in molecules, and the bonding properties of π electrons in some representative triatomic species have been examined in the light of D(r).
Abstract: A density function D(r) = 2γ(r, r) − tSγ(r, r′)γ(r′, r) dr′, where γ(r, r′) is a spinless first-order density matrix, has been proposed as fundamental formula representing the spatial distribution of odd electrons in molecules. The bonding properties of π electrons in some representative triatomic species have been examined in the light of D(r). The density function can also be used successfully to assess the diradical character of unstable singlet ground-state molecules.
285 citations
TL;DR: In this article, the roles of orbital, spin and permutation symmetries in the extended Hartree-Fock (EHF) wavefunction are investigated in relation to the applications of group theory to chemical reactions.
Abstract: The roles of orbital, spin and permutation symmetries in the extended Hartree-Fock (EHF) wavefunction are investigated in relation to the applications of group theory to chemical reactions. The utility of the magnetically ordered set for an extended HF calculation is pointed out. The relative stabilities among linear Huckel and Mobius three-center three-electron (3,3) systems are investigated by the generalized Hartree-Fock (GHF) and EHF methods in order to confirm the reliability of the valence-bond (VB) selection rule for free radical reactions.
194 citations
TL;DR: In this article, a detailed differential geometrical study of chemically reacting systems is presented, in particular the general solution of the intrinsic reaction coordinate (IRC) (henceforth referred to as meta-IRC), and extended definitions of the Hessian matrix and normal vibrations at any non-equilibrium point on the surface.
Abstract: This paper is a detailed differential geometrical study of chemically reacting systems. In particular the following coordinate-free properties of chemically reacting systems are obtained: 1) the general solution of the intrinsic reaction coordinate (IRC) (henceforth referred to as meta-IRC), 2) “extended” definitions of the Hessian matrix and normal vibrations at any non-equilibrium point on the surface, and 3) clarification of the close connection between the geometry of meta-IRC and the geography of the surface at a transition point. The theory is elucidated using a model potential surface.
138 citations
TL;DR: In this paper, it is shown that correlation effects can be adequately treated using the local spin density approximation using the computational effort of very small compared to CI calculations, and the method is applied to correlation energies and ionization potentials of the atoms Li to Ar and binding energies of the diatomic hydrides LiH to HCl.
Abstract: It is shown that dynamical correlation effects can be adequately treated using the local spin-density approximation. The computational effort is very small compared to CI calculations. The method is applied to correlation energies and ionization potentials of the atoms Li to Ar and binding energies of the diatomic hydrides LiH to HCl.
127 citations
TL;DR: A simple electrostatic analysis is given of the virtual charge (solvaton) model to represent the environment effect on the electronic wave function of a solute immersed in a polarizable surrounding as mentioned in this paper.
Abstract: A simple electrostatic analysis is given of the virtual charge (solvaton) model to represent the environment effect on the electronic wave function of a solute immersed in a polarizable surrounding. New features of this model are found. The classical aspects are discussed and secondly the quantal implications are considered. A correct Hartree-Fock-like operator is derived which represents an electron in a molecular orbital subjected to the average effect of the other electrons and to the reaction field produced by the virtual charges on the atomic centers. A general formalism based on the preceding model is presented in appendix. The final equations have a form similar to Newton's equation to represent a solvated electron. Unlike some other theories in this field, there is no cut-off involved in the evaluation of the molecular integrals.
96 citations
TL;DR: In this paper, a comparison of pure electrostatic approximation and complete supermolecule SCF ab initio computations on the hydration scheme of uracil and cytosine was performed.
Abstract: The comparison of a pure electrostatic approximation and complete supermolecule SCF ab initio computations on the hydration scheme of uracil and cytosine shows that the electrostatic procedure is capable to reproduce the general aspects of the results of the supermolecule treatment provided that different distances of shortest approach be adopted for the distances between the oxygen of water and the nitrogen of NH2 or NH groups or the oxygen of C-O groups on the one hand and the oxygen of water and pyridine-type nitrogens on the other hand.
94 citations
TL;DR: In this article, it is shown that spin polarization effects can lead to violations of Hund's multiplicity rule, particularly for singlet-triplet pairs, and quantitatively quantitatively spin polarization contributions to the correlation energies of open-shell singlet and triplet states.
Abstract: It is shown that spin polarization effects can lead to violations of Hund's multiplicity rule, particularly for singlet-triplet pairs. In systems with more than one unpaired electron we observe a dynamic spin polarization which depends on the relative spin orientation of the unpaired electrons and is different in open-shell singlet and triplet states. These effects are described by including singly substituted configurations in CI-type wavefunctions for the two states. In analyzing the contributions of the various singly substituted configurations a quantitative understanding of violations of Hund's rule is obtained; at the same time it is possible to calculate quantitatively spin polarization contributions to the correlation energies of open-shell singlet and triplet states. A series of model calculations is performed on systems like square planar H4 and C4H4, nπ* states of formaldehyde, rotated cumulenes, NH and O2, in order to investigate how strongly spin polarization influences singlet-triplet energy splittings and what are the properties of a molecule that lead to a violation of Hund's multiplicity rule.
92 citations
TL;DR: The Hartree-Fock instability of twelve polyatomic systems is studied at theab initio level in this article, where the existence of these instabilities is discussed with respect to the location of low-lying excited states and to the weight of ionic structure.
Abstract: The Hartree-Fock instability of twelve polyatomic systems is studied at theab initio level. It is found that all the systems with at least one double bond, exhibit a non-singlet instability. On the other hand instabilities of singlet type as well as instabilities of non-real type appear only in a small number of cases. The existence of these instabilities is discussed with respect to the location of low-lying excited states and to the weight of ionic structure.
81 citations
TL;DR: In this article, a CI method for calculating inner and valence shell vertical ionization potentials is presented based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest.
Abstract: A CI method for calculating inner and valence shell vertical ionization potentials is presented. It is based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for the ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest. The state energy is computed by performing a CI calculation for a set of selected configurations, and then adding the contributions of the remaining configurations as estimated by second order Brillouin-Wigner perturbation theory. The use of the same set of MO's for all states together with the CI perturbation method makes the method rather rapid. The numerical results are, in spite of the limited Gaussian basis sets used, in good agreement with experiment.
50 citations
TL;DR: In this paper, the binding properties of monoadducts of ZnII with various biologically significant ligands are characterized, using in particular energy decomposition scheme, population analysis and difference density curves.
Abstract: Zinc is one of the most important biological metals involved in the catalytic site of many enzymes. SCFab initio computations with good quality basis sets are reported for monoadducts of ZnII with various biologically significant ligands, and the fundamental features of the binding are characterized, using in particular energy decomposition scheme, population analysis and difference density curves. A test of the possibility of using pseudopotentials in this domain is also reported.
TL;DR: In this paper, the authors investigated the energy balances of the direct phosphate-Na+ binding, involving their prior dehydration, or their through-water binding, allowing them to conserve their hydration shells, indicating the competitivity of the two processes.
Abstract: SCFab initio computations in the supermolecule approach were carried out for the study of the hydration scheme of the dihydrogen phosphate anion, of the sodium cation and for the investigation of the direct and the through-water interaction of these two charged species. It is found that the energy balances of the direct phosphate-Na+ binding, involving their prior dehydration, or their through-water binding, allowing them to conserve their hydration shells, are of the same order of magnitude, indicating the competitivity of the two processes. This situation results in the existence of multiple possibilities for phosphate-Na+-water association. Appreciable energies of interaction exist between the different subunits of such systems. The Na+ cation and to a somewhat lesser extent the phosphate anion have a polarizing effect upon the charge distribution in the system over relatively appreciable distances. On the contrary, the charge transfers between the different components of the system are interpretable essentially in terms of displacements between adjacent units only.
TL;DR: In this paper, an energy partitioning scheme for the interpretation of AB initio SCF calculations is presented, which allows the deduction of well transferable, almost basis independent two-center terms which characterize bond strengths and non-bonded interactions.
Abstract: As a tool for the interpretation ofab initio SCF calculations, an energy partitioning scheme is presented. When performed within an orthogonalized basis, the scheme allows the deduction of well transferable, almost basis independent two-center terms which characterize bond strengths and non-bonded interactions. The results for a large number of molecules are given. The construction of an orthogonal minimal basis (OMBA) from arbitrary basis sets as a generalization of the symmetrical orthogonalization is described. The transferability of Fock matrix elements is discussed. The energy partitioning quantities are related to the corresponding terms obtained with the semiempirical schemes CNDO and MINDO/3.
TL;DR: In this article, the influence of an increase of the basis set, an increase in the number of neighbors and increase of density of k-points in the Brillouin zone on the calculated equilibrium geometries and band structures has been studied systematically.
Abstract: Ab initio calculations on the linear lithium chain, the linear lithium hydride chain and a beryllium hydride polymer have been performed using the crystal orbital method. The influence of an increase of the basis set, an increase in the number of neighbors and an increase of the density ofk-points in the Brillouin zone on the calculated equilibrium geometries and band structures has been studied systematically. A proper description of the unit cell and the interaction between neighboring cells turned out to be most important. Energy bands were found to be extremely sensitive to any variation in the basis set applied.
TL;DR: In this article, coupled Hartree-Fock (CHF) perturbation approach and its extension to multiconfiguration wavefunctions (MC CHF) were used to calculate the magnetic susceptibility of the BH molecule.
Abstract: The coupled Hartree-Fock (CHF) perturbation approach and its extension to multiconfiguration wavefunctions (MC CHF scheme) were used to calculate the magnetic susceptibility of the BH molecule. The results obtained for an SCF and two pair-excitation MC SCF functions confirm the paramagnetism of the BH molecule and indicate a rather weak dependence of the computed molecular susceptibility on the correlation effects.
TL;DR: In this paper, the electric field variant (EFV) Gaussian basis sets of double-zeta (2-ζ) quality were used for the calculation of the electric dipole polarizabilities of diatomic molecules.
Abstract: The electric field variant (EFV) Gaussian basis sets of double-zeta (2-ζ) quality are used for the calculation of the electric dipole polarizabilities of diatomic molecules in the Hartree-Fock approximation. The explicit external electric field dependence of the GTO basis set, introduced according to the method described in Part I of this series, is shown to account for the major portion of the electric field induced deformation of the wavefunction. The Polarizabilities obtained in the present calculations are quite close to the best Hartree-Fock results. The deviations from near-Hartree-Fock values amount to 3–8 per cent for the parallel component and to 10–15 per cent for the perpendicular one. It was also shown that the same method leads simultaneously to a considerable improvement of the dipole moments.
TL;DR: In this article, the acyclic polynomial has been analyzed for recursive evaluation in a series of graphs, and mathematical properties of derivatives of the derivatives have been given.
Abstract: Graphical methods are developed for recursive evaluation of the acyclic polynomial. Analytical formulas of the acyclic polynomials for several specific series of graphs are given. Mathematical properties of the derivatives of the acyclic polynomial are given.
TL;DR: The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited 1P and 3P terms of Be, B+ and C++ using wavefunctions at different levels of approximations published in the literature as discussed by the authors.
Abstract: The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited1P and3P terms of Be, B+ and C++ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.
TL;DR: In this paper, an energy decomposition scheme useful for the analysis of the coupled types of interactions in strongly interacting systems is developed within the Hartree-Fock approximation, which involves the interactions between vacant orbitals of component molecules, as can be justified from the third-order perturbation theory.
Abstract: An energy decomposition scheme useful for the analysis of the coupled types of interactions in strongly interacting systems is developed within the Hartree-Fock approximation. A dominant characteristic of the scheme is that it involves the interactions between vacant orbitals of component molecules, as can be justified from the third-order perturbation theory. On the basis ofab
initio molecular orbital calculations, the utility of the scheme is illustrated for the BH3-NH3 complexation and the SN2 reaction of CH4 with H−. It is found that the charge transfer from electron donor (i.e. NH3 or H−) to acceptor (i.e. BH3 or CH4) is strongly coupled with the polarization of the acceptor, to contribute appreciably to the stabilization of the entire system. A specific role of this coupling mode in the progress of reactions is discussed.
TL;DR: In this article, the adiabatic potential surface for icosahedral systems having three-, four-and fivefold degenerate orbital states interacting with five-fold degenerates vibrations (T-v, U-v and V-v problems) is investigated.
Abstract: The adiabatic potential surface for icosahedral systems having three-, four- and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v,U-v andV-v problems) is investigated. It is shown that for theT-v andV-v Jahn-Teller cases the potential surface possesses respectively a two- or three-dimensional equipotential continuum of minima. For theU-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on the adiabatic potential surfaces is elucidated. In the linear approximation to theV-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.
TL;DR: In this paper, the modifications of the electrostatic molecular potential brought about by hydrogen bonding both in the hydrogen-bond region itself and in the external regions of the proton acceptor and proton donor molecules were studied.
Abstract: A study is made of the modifications of the electrostatic molecular potential brought about by hydrogen bonding both in the hydrogen-bond region itself and in the external regions of the proton-acceptor and proton-donor molecules. Systems up to four successive units in a chain of donor-acceptors are considered. The possibility of obtaining a satisfactory picture of the global potential by a simple superposition of the potentials of the individual units is evaluated.
TL;DR: In this article, the variational solution to the non-linear Schrodinger equation is considered; a necessary and sufficient constraint to be added to the standard variational procedure is discussed.
Abstract: Some aspects concerning the self-consistent reaction field theory of solvent effects are discussed. In particular, the variational solution to the non-linear Schrodinger equation is considered; a necessary and sufficient constraint to be added to the standard variational procedure is discussed. The exact solution of the non-linear equation is presented within the molecular orbital approach; correlation defaults to the Hartree-Fock like solutions are stated. Some thermodynamical correspondences are established with the magnitudes calculated with the self-consistent reaction field theory. Finally, we have commented upon the proton potentials calculated within this theory. An INDO calculation of a water trimer has been used as an example to discuss different types of proton translocation potentials.
TL;DR: In this paper, the Hartree-Fock self-consistent field calculations, employing extended Gaussian basis sets, and configuration interaction studies are performed to calculate the energy hypersurface of the electronic ground state of the water molecule and to investigate the accuracy requirements in view of the determination of molecular spectroscopic constants.
Abstract: Large-scale Hartree-Fock self-consistent field calculations, employing extended Gaussian basis sets, and configuration interaction studies are performed to calculate the energy hypersurface of the electronic ground state of the water molecule and to investigate the accuracy requirements in view of the determination of molecular spectroscopic constants. From the calculated points on the hypersurface the theoretical equilibrium geometry, the force field through fourth order, the spectroscopic constants ωi, xij, αi as well as the Darling-Dennison and Fermi resonance constants are evaluated. The CI surface yields an equilibrium structure for H2O withr
e
= 0.9501 A and αe=105.33 ° (r
exp
= 0.9572 A and αexp = 104.52 °). The vibrational levels are obtained with a systematic error of about 2 percent and the rotational constants to about 1 percent compared to spectroscopic data. The relative energy maximum corresponding to the linear structure with α = π is calculated to be 11890cm−1, within the error limits of the values deduced from experimental measurements.
TL;DR: In this paper, the geometries of the 2-hydroxyethyl and isomeric oxiranium cations have been fully optimized using ab initio molecular orbital calculations employing the split valence shell 4-31G basis set.
Abstract: The geometries of the 2-hydroxyethyl and isomeric oxiranium cations have been fully optimized using ab initio molecular orbital calculations employing the split valence shell 4-31G basis set. These species are possible intermediates in both the electrophilic addition of OH⊕ to ethylene and in the acid catalysed ring opening of oxirane. The optimized structures were then used to compute more accurate wave functions using Dunning's double-zeta basis set, and with this large basis set the bridged oxiranium ion was found to be the more stable by 7.2 kcal/mole. The barrier to interconversion of these two C2H4OH⊕ ions was computed to be 25.0 kcal/mole above the oxiranium ion.
TL;DR: In this paper, the semi-empirical zero-differential-overlap molecular orbital model was extended to give a good account of the charge transfer and π-π* spectra of Fe(II) complexes with conjugated ligands such as 2,2′-bipyridyl and 1,10-phenanthroline.
Abstract: The semiempirical zero-differential-overlap molecular orbital model which was shown in earlier papers in this series to give a good account of the charge transfer and π-π* spectra of Fe(II) complexes with conjugated ligands such as 2,2′-bipyridyl and 1,10-phenanthroline is extended to complexes having openshell ground states, such as those of Fe(III), and to complexes of Ru(II) and Ru(III). The results are used to assign the observed charge transfer and intra-ligand absorption bands to specific orbital transitions. Observed and calculated intensities are in good agreement: reasons are advanced for the much lower intensity of the charge transfer bands in Ru(III) compared to Ru(II) complexes.
TL;DR: In this article, a method for direct calculation of localized non-orthogonal orbitals, which has been proposed by the authors recently, is extended to cases where the overlap between different subsystems is very large.
Abstract: A method for direct calculation of localized non-orthogonal orbitals, which has been proposed by the authors recently, is extended to cases where the overlap between different subsystems is very large. This is achieved by using a steepest-descent procedure. In addition, a computationally simple treatment of correlation effects is introduced into the method by means of the density functional formalism. Results of the method are given for e.g. LiH, CH4, Ne2, CO,(FH)2.
TL;DR: In this paper, the perturbations in the molecular electrostatic potentials of the bases of the nucleic acids, brought about by hydrogen-bonding into complementary pairs, are evaluated by a superposition procedure.
Abstract: The perturbations in the molecular electrostatic potentials of the bases of the nucleic acids, brought about by hydrogen-bonding into complementary pairs are evaluated by a superposition procedure.
TL;DR: In this article, the statistical correlation between electrons of like spin introduced by the antisymmetry requirement on the many-electron wavefunction is contrasted with the manner in which unlike-spin electron correlation is introduced through the inclusion of configuration interaction.
Abstract: Electron pair distribution functions are analyzed for a variety of SCF+CI wavefunctions, for a range of simple molecules. The statistical correlation between electrons of like spin introduced by the antisymmetry requirement on the many-electron wavefunction is contrasted with the manner in which unlike-spin electron correlation is introduced through the inclusion of configuration interaction.
TL;DR: In this article, the trans isomer is calculated to be more stable by 5.7 kcal/mole than the cis isomer, confirming the experimental estimate according to which the energy of isomerization is about 3 kcal/Mole.
Abstract: Ab initio SCF calculations of cis- and trans-stilbene at different conformations were performed using two program systems. Minimal energy is obtained for cis-stilbene when the phenyl rings are rotated by 52 ° out of the molecular plane. The deviation from planarity due to steric hindrance is smaller for the trans isomer yielding a rotational angle of 19 °. The trans isomer is calculated to be more stable by 5.7 kcal/mole than the cis isomer, confirming the experimental estimate according to which the energy of isomerization is about 3 kcal/mole. This is an improvement over semiempirical calculations which predict a lower energy for the trans configuration.
TL;DR: In this article, the minimum energy paths for the formation of HCO+, COH+, and HCOH2+ from CO by protonation were studied. And the energy barriers to the creation of the various species were given, where appropriate, and changes in geometry, ordering of molecular orbitals and orbital occupancy were discussed.
Abstract: Ab initio molecular orbital calculations employing a 4-31G basis set have been used to study the minimum energy paths for the formation of HCO+, COH+, and HCOH2+ from CO by protonation. The protonation of N2 to give NNH+ and HNNH2+ and of NO+ to form HNO2+ and NOH2+ have also been investigated. All species formed have linear equilibrium geometries and the minimum energy path for approach of the proton is along the line-of-centers of the heavy atoms. Energy barriers to the formation of the various species are given, where appropriate, and changes in geometry, ordering of molecular orbitals and orbital occupancy are discussed.