L'Étude Théorique des Systèmes Périodiques. II. La Méthode LCAO?SCF?CO

The formalism of the LCAO ? SCF ? CO method is described. This method enables the theoretical study of conjugated periodic systems. In these systems some integrals of the SCF operator matrix elements are evaluated by a semi-empirical procedure.     

First-order properties and the Hellmann–Feynman theorem in the case of a limited CI wave function

Two distinct approaches to the calculation of first-order properties with a limited CI wave function are discussed. One is based on the Hellmann–Feynman theorem and the other on the direct evaluation of the total energy derivative at zero perturbation. Corrections to the Hellmann–Feynman expectation value are given for the CI wave function consisting of a single determinant reference state and all single and double replacements of this. These corrections are the extended Brillouin matrix elements and involve interactions between the zeroth-order wave function and triply substituted configurations. The usefulness of these matrix elements for the generation of MC SCF orbitals and for the calculation of cluster corrections to the wave function is briefly discussed. The formulas for the Brillouin matrix elements expressed in terms of one- and two-electron integrals have been automatically generated using the syntax of the algebraic program SCHOONSCHIP.     

大体系多电子相关研究中应用群对称定域轨道的构想

大体系多电子相关研究中应用群对称定域轨道的构想周泰锦，刘爱民（厦门大学化学系，厦门３６１００５）关键词：组态相关，多构型自治叠代，多中心积分，群对称定域轨道，对称约化有关原子簇化合物及化学吸附、过渡态、激发态、催化反应等大体系的量子化学研究，对于探讨...     

An efficient self-consistent field method for large systems of weakly interacting components

An efficient method for removing the self-consistent field (SCF) diagonalization bottleneck is proposed for systems of weakly interacting components. The method is based on the equations of the locally projected SCF for molecular interactions (SCF MI) which utilize absolutely localized nonorthogonal molecular orbitals expanded in local subsets of the atomic basis set. A generalization of direct inversion in the iterative subspace for nonorthogonal molecular orbitals is formulated to increase the rate of convergence of the SCF MI equations. Single Roothaan step perturbative corrections are developed to improve the accuracy of the SCF MI energies. The resulting energies closely reproduce the conventional SCF energy. Extensive test calculations are performed on water clusters up to several hundred molecules. Compared to conventional SCF, speedups of the order of (N/O)2 have been achieved for the diagonalization step, where N is the size of the atomic orbital basis, and O is the number of occupied molecular orbitals.     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

Hypervirial SCF treatment for vibrational energy levels of triatomic molecules

The SCF method for the calculation of energy levels of triatomic molecules is applied using the hypervirial perturbative procedure for solving the coupled equations. This treatment allows to obtain in a recursive way the energy corrections and the expectation values required in the SCF treatment, avoiding the explicit calculation of the wave functions. A numerical application is made to the SO₂ and O₃ molecules, comparing our results with those obtained by other methods.     

On the use of frozen orbitals in molecular orbital cluster calculations: Cl on Si(111)

By using the corresponding orbital transformation a quantitative criterion is found for the MOs that can be kept fixed during calculations using a perturbative SCF procedure. Results obtained keeping fixed a subset of molecular orbitals are quantitatively in agreement with those obtained by using the canonical SCF procedure but with a considerable saving of computer time in the SCF step.     

Adiabatic calculations of the 2Σ+g excited states of He+2

The first six ²Σ⁺_g adiabatic potential energy curves of He⁺₂ are calculated with the MRD CI method employing configuration selection (T = 10 μ hartree) and perturbative energy corrections and using two basis sets differing in the number of diffuse functions. The non-adiabatic matrix elements at the numerous avoided crossings are also calculated and approximate diabatic curves are constructed. Various aspects of the results are discussed.     

Electron spin-spin coupling from multireference configuration interaction wave functions

We present the implementation of two-electron spin-spin coupling as a quasidegenerate perturbative treatment of the Breit-Pauli spin-spin Hamiltonian. The evaluation is based on a multireference CI treatment and constitutes one of the first efforts in the calculation of this effect within a highly sophisticated consideration of both nondynamical and dynamical correlation. The extension of existing schemes for efficient calculation, in particular, of the spin-coupling elements necessitated some involved derivations, the outline of which is presented herein. Application of the program to calculations of diagonal as well as off-diagonal spin-coupling elements is illustrated with the test cases O(2) and NH.     

Efficient methods for configuration interaction calculations

Advanced techniques are developed to provide efficient economic treatment of the large scale eigenvalue problem posed when configuration interaction is carried out on SCF basis sets of moderate size. When the characteristic properties of the hamiltonian matrix are examined in light of the type of solution required, partitioning of the configuration space is shown to result in an expansion of the problem about a limited core of states, where the small but cumulative interactions of vast regions of the remaining space are reduced to the form of an effective potential. With proper selection of the core, the evaluation of this potential can be readily and accurately truncated to a level involving minimum expenditure in time and effort. In particular only diagonal elements and a strip of the full CI matrix are required to achieve an accuracy of 1 – 5 kcal/mole with complete treatment for configuration spaces of order tens of thousands. In addition, a close look at current theory on the generation of matrix elements between spin symmetry adapted configurations leads to simplified expressions where the matrix elements are derived in the form of a weighted sum of molecular integrals in which the weighting coefficients represent the integrated value of the wavefunctions over spin coordinates. For typical cases of low multiplicity and limited numbers of open shells the list of unique parameters needed to generate all weights are shown to be readily stored as a program library. Actual times for matrix element generation are believed to be an order of magnitude faster than current techniques. Practical demonstration of the accuracy and efficiency of the method is provided by calculations on formaldehyde, water, and ethylene.     

Ab initio calculation of the dipole moment function of hydrogen iodide

SCEP/CEPA and MC SCF potential energy and dipole moment functions for hydrogen iodide have been calculated. Spectroscopic constants and vibrational dipole matrix elements obtained from the CEPA functions are in good agreement with experimental data. In contrast to previous results for hydrogen fluoride, the MC SCF dipole moment function is less accurate than the CEPA function.     

Generalized brillouin theorem for multiconfigurational SCF theories

The matrix elements of the total Hamiltonian between a multiconfigurational SCF wave function and some well-defined linear combinations of excited Slater determinants are equal to zero. By means of this generalized Brillouin theorem it is possible to estimate the improvements to be expected from a subsequent configuration-interaction treatment. The expression of the effective potential for the orbitals can be also derived in the frame of a given multiconfigurational theory. As an example, the case of the CMC-SCF method recently suggested [9] is examined.     

Calculation of frequency-dependent polarizabilities by means of SCF perturbation theory

The SCF perturbative method developed for the calculation of static polarizabilities is extended to the frequency-dependent case. Calculations are reported for helium and methane. The helium results are compared with those of other workers.     

Convergence optimization of restricted open-shell self-consistent field calculations

Different self-consistent field (SCF) iteration schemes for open-shell systems are discussed. After a brief summary of the well-known level shifting and damping procedure, we describe the quadratically convergent SCF (QCSCF) approach based on the gradient and the Hessian matrix in a space of orbital rotation parameters. An analytical expression for the latter is derived for the general many-shell case. Starting from the expression for the energy change obtained by the QCSCF method, we then present a simplified direct procedure avoiding matrix diagonalization but also the difficulties of the QCSCF method in handling the Hessian matrix. Numerical calculations on some open-shell systems involving transition-metal complexes show that this method leads to rapid and reliable convergence of the iteration process in cases where the usual SCF procedure of iterative diagonalization tends to diverge. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 617–637, 1997     

Molekulares SSi(H)CI Matrix-IR-Untersuchungen und ab- initio SCF-Rechnungen

The Molecule S?Si(H)CI. Matrix IR Investigation and Initio SCF Calculation Molecular S?Si(H)CI is formed in an argon matrix after the Photochemically induced reaction of SiS with HCI. From the isotopic splittings (H/D and ³⁵,CI/³⁷CI) of the IR absorptions the C_s-structure of the species with silicon as the central atom can be deduced. By an normal coordinate analysis a value of 4.83 mdyn/Å is obtained for the SiS force constant. These experimental results are confirmed by ab initio SCF calculations of the IR spectrum.     

Direct minimization in mc scf theory. the quasi-newton method

The efficiency of the use of a diagonal approximation to the hessian matrix coupled with a quasi-Newton updating method in MC SCF calculations is examined. In general, satisfactory convergence is obtained provided the CI expansion corresponds to a full valence shell CI.     

Eigenvalue independent partitioning and direct minimization in self-consistent field theory

It is pointed out that the matrix elements of a partitioning operator, f, introduced previously for constructing effective hamiltonians, provide natural sets of unconstrained and non-redundant variables in which to formulate self-consistent field theory. The elements of f are complementary to corresponding elements of the density matrix, the relation being essentially that between covariant and contravariant vectors. Some consequences for direct minimization SCF techniques are considered.     

Core correlating basis functions for elements 31–118

Gaussian functions for correlation of all core shells of elements from Z = 31 to Z = 118 have been optimized in relativistic singles and doubles CI calculations, performed on the shell of highest angular momentum for each principal quantum number. The SCF functions were derived from the double-zeta, triple-zeta, and quadruple-zeta basis sets previously optimized by the author. Only those Gaussian functions that are not represented in the SCF basis sets were optimized. The functions are available from the Dirac program web site, .     

Ab-initio and pseudo-potential calculations on some first,second and third row molecules. A comparative study

Calculations using a pseudo-potential approach on test systems containing first, second and third row elements have been performed. Orbital energies and equilibrium geometries are compared with results obtained from full SCF calculations.