Showing papers in "Theoretical Chemistry Accounts in 1988"

Clifford algebra and unitary group formulations of the many-electron problem

Abstract: An essential role of Clifford algebras for quantum-chemical finite-dimensional orbital models of many-electron systems is pointed out The relationship between Clifford algebra matric units, the generators of the unitary group approach (UGA) and the higher order replacement or excitation operators, as well as between their first and second quantized realizations, is elucidated The usefulness of higher order replacement operators in the spin-adaptation of various many-body theories is briefly outlined and illustrated on the orthogonally spin-adapted coupled-pair approach A natural connection with the Clifford algebra UGA is explored and new possibilities for its exploitation in large scale configuration interaction calculations are suggested

Systematics of bonding in non-icosahedral carbon clusters

Abstract: General formulas are presented for the vertex numbers, ν, of pentagon+hexagon polyhedra of icosahedral, tetrahedral or dihedral symmetries. Criteria for uniqueness of representation, isomer counts and grouping of pentagons are established. All polyhedra with 256 vertices or less and belonging to T, D5, D6or their supergroups are listed. With the addition of C3ν to the dihedral and higher groups, at least one pentagon+hexagon cluster is found for all even ν≥20 except for ν = 22 which is unrealisable in any symmetry, and ν = 46 (for which a C3 polyhedron exists). Carbon clusters with closed electronic shells are shown to be generated by a geometrical leapfrog procedure: for all ν = 60+6k (where k is zero or greater than one) at least one closed shell structure is predicted. In dihedral symmetry closed shells also exist for some other values of ν. Separation of the 12 pentagonal faces is not sufficient to ensure a closed electronic shell but appears to be a necessary condition in dihedral or tetrahedral symmetry.

A gradient extremal walking algorithm

Abstract: Gradient extremals define stream beds connecting stationary points on molecular potential energy surfaces. Using this concept we have developed an algorithm to determine transition states. We initiate walks at equilibrium geometries and follow the gradient extremals until a stationary point is reached. As an illustration we have investigated the mechanism for exchange of protons on carbon in methylenimine (H2C=NH) using a multi-reference self-consistent-field wave function.

On the counterpoise correction for the basis set superposition error in large systems

Abstract: The appropriateness of the use of the counterpoise correction for the basis set superposition error in SCF calculations of the interaction energies for pairs of aliphatic amino acids is analyzed in this paper. Our results show that for this type of molecule where the magnitude of the basis set superposition error can become quite big, the use of the counterpoise method provides interaction energies in good agreement with near Hartree-Fock values. The inaccuracies associated with the counterpoise method are much less important compared with the basis set superposition error itself. It is shown that the use of a well-balanced minimal basis set together with the counterpoise method is a good compromise (quality versus computational cost) for calculating interaction energies in systems involving molecules of biological interest.

Origin and meaning of the Fermi contact interaction

Abstract: The Fermi-contact interaction (FCI) can easily be derived from 1st order perturbation theory applied to the non-relativistic wave equation for a spin-(1/2) particle of Levy-Leblond, with the nuclear spin described by the field of an “external” magnetic dipole, and it results from the fact that the “turn-over-rule” for the operator \(\vec \sigma \vec p\)is only valid if the derivatives implicit in \(\vec p\) are taken “in the distribution sense”. If one avoids to apply the turn-over-rule, the FCI is obtained without the need to introduce a “δ-function”. It is also shown that the formulation of a magnetic point dipole as the limit of an extended nucleus directly leads to the FCI. Traditional methods of the derivation of the FCI are analyzed in the light of this new interpretation. It is then explained why the perturbation expansions in powers of the magnetic moment of the nucleus necessarily diverges, but that the expression for the 1st order energy on which the concept of the FCI is based, can nevertheless be justified by means of the Hellmann-Feynman theorem with a correction term if singular wave functions are involved. Finally some comments on a theory beyond first order are made.

Model studies of the chemisorption of hydrogen and oxygen on nickel surfaces

Abstract: Atomic chemisorption of hydrogen and oxygen on the Ni(100) surface has been studied using an Effective Core Potential (ECP) approach described in a previous paper. Clusters of up to 50 nickel atoms have been used to model the surface. The computed chemisorption energies are 62 kcal/mol (exp. 63 kcal/mol) for hydrogen and 106 kcal/mol (exp. 115–130 kcal/mol) for oxygen. Correlating the adsorbate and the cluster-adsorbate bonds is extremely important for obtaining accceptable results, particularly for oxygen. Reasonable convergence of chemisorption energies is obtained with 40–50 cluster atoms for both hydrogen and oxygen. For hydrogen the addition of a third cluster layer stabilizes the results considerably. Both hydrogen and oxygen are adsorbed at (or close to) the four-fold hollow site. The calculated barriers for surface migration are also in good agreement with the experimental estimates. The calculated equilibrium heights above the surface are on the other hand too high compared with experiments. This disagreement is believed to be due to core-valence correlation effects, which are not incorporated in the present ECP. The cluster convergence for the height above the surface is much slower than for the chemisorption energy.

Broken orbital symmetry and the description of valence hole states in the tetrahedral [CrO4]2− anion

Abstract: The localization of ligand-based valence holes in the tetrahedral complex ion [CrO4]2− in a crystalline environment is studied by SCF calculations on the hole states, with progressively less restrictions on the spatial symmetry of the molecular orbitals. The final wavefunctions are obtained by constructing, from the symmetry broken SCF solutions, wavefunctions that exhibit again the proper transformation properties under the operations of T d . The crystal environment of the [CrO4]2− anion is represented by a point charge model. In contrast with the situation for core hole states, the projection afterwards into T d symmetry is important. The final ionization energies, which are obtained from projected C 3v adapted SCF solutions, are reduced considerably (≅3 eV) with respect to the T d ΔSCF results, but the ordering of the states has not changed essentially. The calculated ionization energies compare favourably with results of XPS experiments on Na2CrO4. The evaluation of the energies of projected symmetry broken SCF solutions requires the calculation of hamiltonian matrix elements between determinantal wavefunctions built from mutually non-orthogonal orbital sets. An efficient method for the calculation of such matrix elements is presented.

The atomic states of nickel

Abstract: The Ni 3d9 4s1(3D)−3d10(1S) and 3d9 4s1(3D)-3d84s2(3F) atomic excitation energies have been computed using large multireference CI wave functions in conjunction with a large ANO basis set Radial correlation effects in the 3d shell are found to be very important and are included using CASSCF wave functions having the 3d and correlating 3d′ orbitals in the active space The previous discrepancy (05 eV) with experiment for the 3D−1S excitation is reduced to 01 eV when the 3d→3d′ references are included in the CI For the 3F state, the 4s-4p near degeneracy gives rise to important 4s2→4p2 excitations in addition to the 3d→3d′ excitations which are important for the 3D and 1S states Inclusion of only 3d-3d′ correlation in the 3F and 3D CI reference spaces yields a 3F−3D separation which is in error by 012 eV Addition of the 4s2→4p2 excitations to the 3F reference space is estimated to increase the discrepancy with experiment by an additional 01 eV

On expectation value calculations of one-electron properties using the coupled cluster wave functions

Abstract: The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (〈O〉=〈φ¦exp (T+)O exp (T)¦φ〉c) was truncated so that T1T2, T3, and (1/2) T2T2 clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T1, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.

Overlap integrals of B functions. A numerical study of infinite series representations and integral representations

Abstract: Two different methods for the evaluation of overlap integrals of B functions with different scaling parameters are analyzed critically. The first method consists of an infinite series expansion in terms of overlap integrals with equal scaling parameters [14]. The second method consists of an integral representation for the overlap integral which has to be evaluated numerically. Bhattacharya and Dhabal [13] recommend the use of Gauss-Legendre quadrature for this purpose. However, we show that Gauss-Jacobi quadrature gives better results, in particular for larger quantum number. We also show that the convergence of the infinite series can be improved if suitable convergence accelerators are applied. Since an internal error analysis can be done quite easily in the case of an infinite series even if it is accelerated, whereas it is very costly in the case of Gauss quadratures, the infinite series is probably more efficient than the integral representation. Overlap integrals of all commonly occurring exponentially declining basis functions such as Slater-type functions, can be expressed by finite sums of overlap integrals of B functions, because these basis functions can be represented by linear combinations of B functions.

Symmetry and equivalence restrictions in electronic structure calculations

Abstract: A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.

An ab initio study of the molecular structure and vibration-rotation spectrum of the triplet radical HCCN

Abstract: The bent triplet cyanocarbene H-C-C≡N and the linear triplet allene H-C=C=N have been studied by the CASSCF and CI methods, using a DZP basis. Relaxation of all geometrical parameters for the CASSCF energy results in a bent molecule with CCH angle 133° and a barrier to linearity of 6.4 kcal/mol, which was lowered to 2.3 kcal/mol in a subsequent CI calculation. The Davidson correction lowered it further to 1.8 kcal/mol. A 26-term analytical potential energy surface (PES) was fitted to CASSCF, CI, and Davidson corrected CI energies in 94 different geometries. Using these three potentials, the semi-rigid bender model predicts a CCH bending frequency of 782, 505, and 503 cm−1, resp., which compares favourably with an experimentally observed IR transition line at 458 cm−1. For the deuterated species, the corresponding frequencies are 610, 407, and 402 cm−1, to be compared with two possible absorption lines at 405 and 317.5 cm−1. The PES was then parametrized by adding a variable CCH angle dependence, and a comprehensive vibration-rotation spectrum was calculated variationally, using the exact 4-atom vibration-rotation kinetic Hamiltonian, for a range of barrier heights. Comparison with experiment indicates a barrier in the range 1±0.5 kcal/mol.

Electronic structures of the S2O and S3 isomers: an ab initio CI study

Abstract: The electronic structures of the S2O and S3 isomers have been dealt with by the multireference double-excitation (MRD) configuration-interaction (CI) calculations, using contracted [5s3p1d] and [4s2p1d] basis functions for the S and O atoms, respectively. The ground-state geometries for the SOS (symmetric chain), S2O (symmetric ring) and SSO (unsymmetric chain) are optimized, and their vertical singlet excitation energies are calculated. It is found that SSO is the most stable of the three isomers and that the ground state (1A1) of the S2O (ring) is correlated with the excited states of SOS (21A1) and SSO (31A′). The chain and ring isomers of S3 have been treated in a similar manner. Energetics for the ring closure of the O3, SO2, SSO and S3 chain molecules are discussed on a unified ground.

Vibrational partition functions for H2O derived from perturbation-theory energy levels

Abstract: Purely vibrational energy levels and partition functions are calculated using three different potential energy surfaces for the H2O molecule. Results obtained with perturbation-theory, independent-normal-mode (INM), and harmonic approximations are compared with accurate values. For the cases considered here, the expected improvement that perturbation theory provides over the corresponding harmonic treatment is found to be substantial, while the INM approximation leads to results which are worse than the corresponding harmonic ones. In fact, we show that reliable partition functions for these potential surfaces can be obtained when resonance contributions are removed from the perturbation-theory treatment, and we propose a theoretical criterion for deciding when a particular interaction should be treated as resonant.

The structure and harmonic vibrational frequencies of the weakly bound complexes formed by HF with CO, CO2 and N2O

Abstract: The structure and harmonic vibrational frequencies of several weakly bound complexes formed by HF are reported. Theab initio MP2 approach is used with large basis sets for the optimisation of geometries and the determination of harmonic frequencies. CO⋯HF and OC⋯HF are examined; both are found to be minima, with the latter being the dominant structure. The linear OCO⋯HF andT shaped OCO⋯FH are studied, but only the linear structure is a minimum. N2O⋯HF has two minima on the surface corresponding to bent NNO⋯HF and linear ONN⋯HF structures.

Classical structures in modern valence bond theory

Abstract: The results of some recent ab initio valence bond calculations, in which both structure coefficients and orbital forms are optimized, are analysed. The origin of structures in which the optimum orbitals are no longer “atomic” in character but instead delocalized, is traced back to the presence of certain symmetries in the wavefunction. When such symmetries exist it is possible to choose alternative linear combinations of the delocalized orbitals and to rewrite the wavefunction in terms of VB structures of “classical” form. The advantages of the classical structures are discussed in the context of a simple example — a square planar conformation of four hydrogen atoms.

Molecules with holes

Abstract: The bual and laub operations are defined and shown to be a useful means of analysing and coordinating previous descriptions of polyhexes. Some implications of a polyhex having a hole are explored. The position of such molecules in the Dias periodic table is argued. Formulae for moments of the Huckel energy in terms of graphical invariants are derived. The change in π-electron energy when a hole is formed is calculated for some molecules.

Structure and properties of nonclassical polymers. IV: The effect of long-range Coulomb interaction on the elementary excitation spectrum

Abstract: Utilizing an extended Hubbard-type Hamiltonian which incorporates both nearest-neighbour Coulomb repulsion and exchange interactions, we have studied the energy dispersion of the lowest elementary excitation from the ferromagnetically aligned state of quasi one-dimensional alternant hydrocarbon networks. It was found that the main effect of the long range Coulomb interaction may be thought of as a renormalization (screening) of the on-site Hubbard integral. This implies an enhancement of the kinetic exchange term and impairs the stability of the ferromagnetic state towards single spin inversions. However, for physically relevant values of the parameters entering the model Hamiltonian, the collective spin excitation represents a magnon, whose energy band lies above the reference value pertaining to the magnetically saturated configuration.

Full configuration interaction benchmark calculations for transition moments

Abstract: Full configuration-interaction (FCI) calculations have been performed for the dlAI-f~IB1 and dIAI-(2)IA1 transitions in CH2 and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.

Electric properties of the chloride ion

Abstract: The dipole (α), quadrupole (C), and dipole-quadrupole (B) polarizabilities and the dipole hyperpolarizability (γ) of the chloride ion have been calculated by using the many-body perturbation theory approach and a series of large polarized GTO/CGTO basis sets. The complete fourth-order treatment of the electron correlation effects with a basis set comprising the s, p, d, f, and g functions gives: α=38.01 a.u., C=211.5 a.u., B=−5.14×103 a.u., and γ=128. 5×103 a.u. as compared to the corresponding SCF values (α=31.49 a.u., C=158.9 a.u., B=−2.92×103 a.u., γ=57.7×103 a.u.). The quenching of polarizabilities of the Cl− ion in solutions and ionic crystals is discussed.

A CASSCF study of the singlet-singlet and triplet-triplet spectroscopy of naphthalene

Abstract: Ab initio complete active space (CAS) SCF calculations have been carried out for the singlet and triplet excited states of naphthalene molecule. The CASSCF active space comprised 10π-type molecular orbitals. The basis set was of ANO type and included both diffuse functions and polarization functions. The calculated excitation energies and transition moment provide a sound theoretical basis for the assignment of the experimental singlet-singlet and triplet-triplet spectra of the naphthalene molecule.

Origin and information content of the compensation effect

Abstract: An attempt is made to assess: (i) The conditions under which a compensation effect should be observable, (ii) The associated physical properties affected by such compensation. (iii) The nature of the information which can be gleaned from studies of compensation. Specific attention is given to simple desorption processes and the main conclusion is that the compensation law in adsorption indicates a phenomenon involving many molecules. However the Meyer-Neldel rule in semiconductors is also embraced, as well as observations of the compensation effect in liquids.

Conjugated circuit theory for graphite

Abstract: Computations for the “conjugated circuits” model which has previously only been treated for finite and quasi-one-dimensional conjugatedπ-networks are here extended to the graphite lattice. Many-body techniques give the resultant resonance energy per site as a function of a physically relevant long-range order parameter.

Composition as a method for data reduction: application to carbon-13 NMR chemical shifts

Abstract: The concept of composition as the counterpart to partition is introduced and advocated for the discussion of molecular properties. In the partition approach an observable (experimental) quantity is fragmented into contributions which are non-observable but which hopefully maintain constancy for fragments (bonds) in similar environments and thus facilitate comparison of data. With the composition as an approach the role of “fragments” and “whole” are reversed: one starts with a collection of observable fragment properties (e.g., atomic chemical shifts of NMR spectra) and then constructs an abstract non-observable quantity representing the collection of fragments as a “whole”. If a so-derived quantity for different molecules shows some regularity, the initial loss of information in condensation of independent fragment data is compensated by insight into novel structural correlations. The approach is illustrated first by ordering isomers (e.g., nonanes C9H20) with respect to their content of special graph invariants p2 and p3 (numbers of paths of length two and length three, respectively) and then showing that the constructed global quantity derived from individual carbon-13 NMR chemical shifts shows a regular variation with p2 and p3, very similar to isomeric variations of numerous thermodynamic properties of nonanes. Subsequently it is outlined how the difference (p2p3) leads to a correlation for mean carbon-13 chemical shifts in octanes and nonanes, taken as an illustration for the approach. It is expected that the outlined approach opens new avenues for data reduction and the search for structure-property correlations.

Potential energy surface of the (H2)2 dimer: an MP2 study

Abstract: Fifteen structures of the (H2)2 dimer have been investigated at the MP2/[4s3p] level. The SCF and MP2 (2nd order Moller-Plesser treatment) interaction energies have been corrected for the basis set superposition error. Only the T-shaped structure has been established as a minimum on the potential energy surface. Two equivalent T-shaped structures are connected by a saddle point with a rhomboid structure.

A new method for the direct calculation of resonance parameters with application to the quasibound states of the H2X1? g + system

Abstract: A new method for the direct calculation of resonance parameters is presented. It is based upon searching for poles of the scattering matrix at complex energies. This search is expedited by the use of analytic derivatives of the scattering matrix with respect to the total energy. This procedure is applied initially to a single channel problem, but is generalizable to more complicated systems. Using the most accurate available potential energy data, we calculate resonance parameters for all of the physically important quasibound states of the ground electronic state of the hydrogen molecule. Corrections to the Born-Oppenheimer potential are included and assessed. The new method has no difficulty locating resonances with widths greater than about 1×10−7 cm−1. It is easier to find narrow resonances by monitoring the dependence of the imaginary part of the reactance matrix on the real part of a complex energy than to monitor the dependence of the eigenphase sum on energy at real energies.

Theoretical study of PO and PO

Abstract: The diatomic systems, PO and PO− are studied, using numerical Hartree-Fock (NHF) and coupled-cluster calculations The latter employs a hybrid NHF and Slater orbital basis set Highly accurate CCSD methods predict bond lengths accurate to <0004 A and frequencies to ∼60 cm−1 In addition the electron affinity of PO is computed to be 089 eV compared to an experimental value of 109±001 Comparisons are made with SCF and MBPT(2) results for PO+ using conventional basis sets

Topological hamiltonian spectra of polycyclic benzenoid hydrocarbons

Abstract: A general theory which points out the relations between Huckelπ-electron energy, the number of Kekule structures and the HOMO-LUMO separation is presented. Some normalized topological invariants are derived from the concept of the spectral density function. A reasonably simple (three parameters) model spectral density function leads to universal relations between topological invariants that, although valid for any alternant molecule, were tested numerically for polycyclic benzenoid hydrocarbons. Some general conclusions concerning a distribution of the adjacency matrix eigenvalues are drawn.

Application of a dynamic method of minimisation in the study of reaction surfaces

Abstract: This paper describes the application of Snyman's dynamic minimisation method to a fitted potential surface of H3. Comparisons are made with conventional algorithms. A method is described to extend Snyman's method so that it will find only a particular kind of stationary point. It is emphasized that this method enables saddle points to be found without having to resort to approaches based on trial and error.