Static electric properties of LiH: explicitly correlated coupled cluster calculations

Explicitly correlated MBPT-R12 and coupled cluster [up to CCSD(T)-R12] methods have been used in calculations of various (vibrationless) electrical properties for the LiH molecule, including the dipole and quadrupole moments, dipole and quadrupole polarizability tensors, dipole hyperpolarizability tensors, and the second dipole hyperpolarizability tensors. Generally, with extension of the basis set the R12 method did not lead to faster convergence for the calculated properties towards the basis limit. Nevertheless, R12 calculations serve as useful indicators to judge the reliability of the results, and substantially help in determining the accuracy. Results obtained with the 11s8p6d5f/9s8p6d5f basis and CCSD(T)-R12 calculated within this work should be close to the basis set limit. Received: 8 June 1998 / Accepted: 23 July 1998 / Published online: 7 October 1998     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Diagrammatic expansion of the long-range intermolecular potential and the total contribution of the first hyperpolarizability

The potential for pure dispersion forces can be defined in terms of a simple classical cluster expansion. The diagrams for the first hyperpolarizability contribution are summed for a one frequency model.     

CCSD(T) expectation value calculations of first-order properties

An expectation value approach to calculations of first-order properties using the non-iterative, triple-excitation amplitudes in the coupled cluster wave function is exploited. Three methods are suggested and analysed using the many body perturbation theory (MBPT) expansion arguments. The first method, in which non-iterative triple-excitation amplitudes are used in the expression for the expectation values, makes the wave function accurate through the second order of MBPT. In the second method, which is an extension of the first, effects of triple-excitation amplitudes are coupled with single- and double-excitation amplitudes. The correlated density matrix equivalent through the fourth order to that obtained when CCSDT-la amplitudes are used is employed in the third method. The suggested methods are tested on dipole moment and polarizability calculations for several diatomic closed-shell molecules and are compared to other related approaches. Received: 15 May 1997 / Accepted: 5 June 1997     

Calculation of macroscopic first- and third-order optical susceptibilities for the benzene crystal

Starting from a set of high-level ab initio frequency-dependent molecular first- and third-order polarizabilities, the macroscopic first-order (linear) and third-order (cubic) susceptibilities of the benzene crystal are calculated. Environmental effects are taken into account using a rigorous local-field theory and are compared with the anisotropic Lorentz field factor approach. The experimentally determined first-order susceptibility of crystalline benzene is accurately reproduced. Dispersion curves for the first-order susceptibility and results for electric-field-induced second-harmonic generation and third-harmonic generation experiments are predicted. Comparison with similar calculations conducted in the course of molecular simulations of liquid benzene shows that the theoretical results for the two phases are of comparable accuracy. Overall, the results show that for the fairly compact nonpolar benzene molecules, environmental effects on the effective molecular response are small. Received: 11 February 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

A Comparative Study of the Nonlinear Optical Properties of Cd<Subscript>n</Subscript>X<Subscript>n</Subscript> (X: S,Se and Te) Clusters

We report results of hyperpolarizability calculations on Cd_nX_n (X: S, Se and Te; n = 1–10) clusters. Our results show that the geometric configurations of different types of clusters under investigation are quite similar at specific values of n. Both static and frequency dependent components of first and second order hyperpolarizability tensors of Cd_nS_n, Cd_nSe_n and Cd_nTe_n are compared. It is observed that in general nonlinear optical coefficients show identical variation in all the cluster materials. The present investigation also manifests the improvement of these coefficients due to the introduction of asymptotically correct generalized gradient approximation functional over the local density functional and normal gradient corrected functional. Symmetrized fragment orbital analysis has been performed to provide explanation of the observed hyperpolarizability variation. We also analyse how geometries with closely lying energy values influence the hyperpolarizabilities of these cluster materials.     

Calculation of three-center electric and magnetic multipole moment integrals using translation formulas for Slater-type orbitals

 By the use of translation formulas for the expansion of Slater-type orbitals (STOs) in terms of STOs at a new origin, three-center electric and magnetic multipole moment integrals are expressed in terms of two-center multipole moment integrals for the evaluation of which closed analytical formulas are used. The convergence of the series is tested by calculating concrete cases. Computer results with an accuracy of 10⁻⁷ are obtained for 2^ν– pole electric and magnetic multipole moment integrals for 1≤ν≤5 and for arbitrary values of screening constants of atomic orbitals and internuclear distances. Received: 28 October 1999 / Accepted: 15 February 2000 / Published online: 5 June 2000     

Expansion coefficients and moments of electron momentum densities for singly charged ions

Numerical Hartree–Fock calculations of the first three coefficients of the MacLaurin expansion and the leading coefficient of the large-p asymptotic expansion of the electron momentum densities Π(p) are reported for 54 singly charged atomic cations from He⁺ (atomic number Z = 2) to Cs⁺ (Z = 55) and 43 anions from H⁻ (Z = 1) to I⁻ (Z = 53) in their experimental ground states. We also report all the finite moments <p ^k > (−2≤k≤+4) of the momentum densities Π(p) for the above-mentioned 97 ionic species. The results are compared with the previous ones for neutral atoms [Koga and Thakkar (1996) J Phys B 29: 2973], and the dependence of the expansion coefficients and moments on nuclear charge is discussed among isoelectronic species. Received: 20 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999     

Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω⁻¹ HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH⁺ and N₂ molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI. Received: 2 July 1998 / Accepted: 28 August 1998 / Published online: 11 November 1998     

Convergence of multipole expanded intermolecular interaction energies for Gaussian-type-function and Slater-type-function basis sets

 It is shown that the multipole expansion of each order of the polarization series converges for large enough intermolecular distances when finite basis sets of Gaussian or Slater-type functions are used to approximate molecular response properties. Convergence of the multipole expansion for each order of the polarization series does not imply convergence of the polarization series itself. A corresponding convergence condition is extracted from the general perturbation theory in a finite-dimensional space and is applied to the H + H⁺ problem. Received: 29 September 1999 / Accepted: 22 May 2000 / Published online: 18 August 2000     

The saddle point of the nucleophilic substitution reaction Cl− + CH3Cl: results of large-scale coupled cluster calculations

On the basis of large-scale coupled cluster calculations including connectedz triple substitutions in a perturbative way, the geometrical parameters of the D _{3 h} saddle point of the Walden inversion reaction Cl⁻ + CH₃Cl′→ ClCH₃ + Cl′⁻ are predicted to be R _s (C—Cl) = 2.301 ? and r _s (C—H) = 1.069 ?. The barrier height with respect to the reactants is recommended to be 11.5 ± 1.0 kJ mol⁻¹. Connected triple substitutions lower the barrier height by almost a factor of 2, but have very little influence on the geometric structure of the saddle point. Received: 26 June 1998 / Accepted: 15 July 1998 / Published online: 28 September 1998     

Anharmonic force field and spectroscopic constants of silene: an ab initio study

High-level ab initio calculations with large basis sets are reported for silene, H₂C=SiH₂. Correlated harmonic force fields are obtained from coupled cluster CCSD(T) calculations with the cc-pVQZ basis (cc-pVTZ for H) while the anharmonic force fields are computed at the MP2/TZ2Pf level. There is excellent agreement with the available experimental data, in particular the equilibrium geometry and the fundamental vibrational frequencies. Many other spectroscopic constants are predicted for the C _{2 v} isotopomers of silene. Received: 27 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

Convergence of the density functional one-centre expansion for the molecular continuum: N2 and (CH3)3N

A large-scale one-centre expansion with a radial B-spline basis set is implemented for bound and continuum states. A Kohn-Sham hamiltonian is employed with Hartree and exchange-correlation potentials calculated from the SCF electron density taken from a previous LCAO calculation. An inverse iteration method is used to obtain the continuum wavefunction, from which the cross section and asymmetry parameter are calculated. The convergence with respect to angular momentum and cut-off radius is analysed for N₂. The relevance of multipolar contributions even at large distances is shown and suggestions for further improvements are given. In order to show that the present method is suitable to treat systems of moderate size, the (CH₃)₃N molecule has also been calculated and the results are compared with experiment. Received: 19 May 1998 / Accepted: 20 August 1998 / Published online: 7 December 1998     

A reexamination of virial coefficients of the Lennard-Jones fluid

The fourth-order virial coefficients have been calculated exactly to five decimal places for pure fluids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more significance than was thought from previous studies, especially in the low-temperature range. This result was confirmed by direct evaluation of the diagrams which construct the virial coefficients, as given by Rowlinson, Barker, and coworkers. This calculation confirmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These differences, though minor at higher temperatures, can be seen to be more significant at the lower temperature ranges. Received: 31 July 2000 / Accepted: 18 September 2000 / Published online: 21 December 2000     

Stationary points on the H2CO potential energy surface: dependence on theoretical level

A total of 36 stationary points have been located on the H₂CO potential energy surface by means of gradient extremal following. These 36 points are believed to represent all the important stationary points on this surface. There is no indication that the structure of the surface becomes less complicated as the size of the basis set is enlarged at the Hartree-Fock level of theory, but many of the second- and third-order saddle points disappear when electron correlation is introduced. Of the ten first-order saddle points (transition structures) located, the majority have reaction paths entering the associated minima in a side-on approach, i.e. these cannot be located by uphill walking from the minimum. Received: 5 February 1998 / Accepted: 21 May 1998 / Published online: 29 July 1998     

Extensions and tests of “multimode”: a code to obtain accurate vibration/rotation energies of many-mode molecules

We describe extensions and tests of the code “multimode” which does vibrational self-consistent field method (VSCF) and two types of state-mixing (denoted VSCF-CI and V-CI) for rovibrational energies of many-mode systems. The extensions include an exact treatment of rotation, flexible approaches to perform the CI calculations, and the inclusion of a Davidson diagonalization routine to find low-lying eigenvalues of large matrices. The code is tested against previous exact variational calculations for non-rotating H₂CN, and J=0 and J=1 rovibrational states of H₂CS. The code represents the full potential by a hierarchical n-mode representation, where n is the number of normal coordinates that are coupled together. Tests are presented for the convergence and accuracy of this representation for n equal to 3 and 4, where 4 is the current maximum value. These tests are done at the VSCF and V-CI level, with very encouraging results. Received: 8 June 1998 / Accepted: 11 August 1998 / Published online: 19 October 1998     

A new dipole-free sum-over-states expression for the second hyperpolarizability

The generalized Thomas-Kuhn sum rules are used to eliminate the explicit dependence on dipolar terms in the traditional sum-over-states (SOS) expression for the second hyperpolarizability to derive a new, yet equivalent, SOS expression. This new dipole-free expression may be better suited to study the second hyperpolarizability of nondipolar systems such as quadrupolar, octupolar, and dodecapolar structures. The two expressions lead to the same fundamental limits of the off-resonance second hyperpolarizability; and when applied to a particle in a box and a clipped harmonic oscillator, have the same frequency dependence. We propose that the new dipole-free equation, when used in conjunction with the standard SOS expression, can be used to develop a three-state model of the dispersion of the third-order susceptibility that can be applied to molecules in cases where normally many more states would have been required. Furthermore, a comparison between the two expressions can be used as a convergence test of molecular orbital calculations when applied to the second hyperpolarizability.     

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998