Modified one-electron hamiltonian method in the MC SCF theory

For orbital optimization within the MC SCF theory a modification of the OEH method is proposed with the direction of descent determined according to the Fletcher–Reeves gradient method. The combined method developed on this basis ensures the convergence of the iterative process when the Hessian singularities occur. The convergence properties of the method proposed are studied by performing the ab initio water molecule calculations using two types of multiconfigurational wave functions.     

Calculation in K space of integrals arising in the theory of Van Der Waals forces

Sources of occasional convergence problems in our recently proposed algorithm for orthonormality constrained orbital optimization in SCF calculation, as well as in the partly equivalent orthogonal gradient method, are traced and remedial measures are suggested. A simple scaling technique for accelerating convergence in the related orthogonal gradient method is tested.     

Convergence of the Rayleigh—Ritz method in self-consistent-field and multiconfiguration self-consistent-field calculations

We investigate the analytical convergence of SCF and MCSCF calculations, when the dimension of the subspaces to which the orbitals are restricted tends to infinity. We show that the completeness only inL ²(R ³;C ²) of the orbital bases does not ensure the convergence of the Ritz-energy, neither in SCF nor in MCSCF calculations, but that this convergence — as well as the convergence of the Ritz-orbitals in SCF calculations — is on the contrary guaranteed if the orbital bases are complete in the Sobolev spaceW ^1,2(R ³;C ²). Some consequences on the choice of the orbital exponents of Slater and Gauss functions are also discussed.     

Analytic energy derivatives for the equation-of-motion coupled-cluster method: Algebraic expressions,implementation and application to theS 1 state of HFCO

Summary The general theory of analytic derivatives for the equation-of-motion coupled cluster (EOM-CC) method is reviewed. Special attention is paid to the EOM-CC singles and doubles (EOM-CCSD) approximation, which has the same computational scaling properties as the coupled-cluster singles doubles (CCSD) ground state method and is therefore applicable to a wide range of molecular systems. The detailed spin orbital equations that must be solved in EOM-CCSD gradient calculations are presented for the first time, and some guidelines are discussed regarding their computational implementation. Finally, use of the EOM-CCSD gradient method is illustrated by determining the structure, dipole moment components, harmonic frequencies and infrared intensities of formyl fluoride (HFCO) in its singlet excited (n, *) state.     

Convergence problems in SCF calculations: Further applications of a new technique based on the use of inverse Fock operator

A recently proposed orbital optimization technique based on the use of the inverse of the level-shifted Fock operator is successfully applied to a large number of pathologically divergent cases. The possibility of eliminating convergence problems by adopting a similar modification in the operation of the orthogonal gradient method is also successfully tested.     

Study on the behavior of energy convergence in ab initio crystal orbital calculations

Summary This article studies the dependence on the cutoff scheme of ab initio crystal orbital calculations with no long-range correction. We have thoroughly studied the Namur cutoff and cell-wise cutoff schemes through calculations of polyethylene and LiH chains. The Namur cutoff gives the fastest energy convergence with respect to the number of neighbors (N ₀). The energy convergence behavior with respect to N ₀ depends on the basis set. The Namur cutoff shows the fastest convergence with the STO-3G basis set, intermediate convergence with the MINI basis set, and the slowest convergence with the (7s4p/3s) basis set. The cell-wise cutoff shows exactly the reverse order of the Namur cutoff. The Namur cutoff destroys the translational symmetry. Both the Namur cutoff and cell-wise cutoff schemes introduce slight asymmetry on the two equivalent C-C bonds of polyethylene when calculating with a C₂H₄ unit cell. The asymmetry with the Namur cutoff can be made to disappear by increasing N ₀ a little. The calculations on two different unit-cell structures of trans-polyacetylene show the effect of the cutoff scheme on the total energy. Only the symmetric cutoff energies are the same. Disagreement related to the Namur cutoff disappears at N ₀ = 20, however, that related to the cell-wise and modified symmetric cutoff schemes remains at N ₀ 20. The optimized geometry and vibrational frequency are not as sensitive to the cutoff method except with the symmetric cutoff. A compilation of all results shows that the Namur cutoff is the superior cutoff scheme when calculating the insulator using the minimal basis set, especially the STO-3G basis set.     

Pseudodiagonalization-based wavefunction optimization with contracted planewave basis functions

Electronic structure calculations representing the molecular orbitals (MOs) with contracted planewave basis functions (CPWBFs) have been reported recently. CPWBFs are Fourier-series representations of atom-centered basis functions. The mathematical features of CPWBFs permit the construction of matrix–vector products, FC _o , involving the application of the Fock matrix, F , to the set of occupied MOs, C _o , without the explicit evaluation of F . This approach offers a theoretical speed-up of M/n over F -based methods, where M and n are the number of basis functions and occupied MOs, respectively. The present study reports methodological advances that permit FC _o -based optimization of wavefunction formed from CPWBFs. In particular, a technique is reported for optimizing wavefunctions by combining pseudodiagonalization techniques based on an exact representation of FC _o , approximate information regarding the virtual orbital energies, and direct inversion of the iterative subspace optimization schemes to guide the wavefunction to a converged solution. This method is found to speed-up wavefunction optimizations by factors of up to ~6 − 8 over F -based optimization methods while providing identical results. Further, the computational cost of this technique is relatively insensitive to basis set size, thus providing further benefits in calculations using large CPWBF basis sets. The results of density functional theory calculations show that this method permits the use of hybrid exchange-correlation (XC) functionals with a small increase in effort over analogous calculations using generalized gradient approximation XC functionals. © 2019 Wiley Periodicals, Inc.     

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.     

Convergence problem in ab initio crystal orbital calculations

The various computational procedures for treating the problem of lattice summations in ab initio crystal orbital calculations are briefly reviewed and the cutoff problem is discussed. Several numerical examples are presented for demonstrating the fast convergence of the total energy per unit cell with respect to the inclusion of further neighbors' interactions, in case reasonable cutoff procedures are applied. The importance of electrostatic considerations for the interpretation of long range effects is stressed.     

A charge-conserving approximation method for ab initio calculations

A new method is presented for approximate ab initio calculations in quantum chemistry. It is called CCAM (charge conserving approximation method). The calculation method does not include the use of empirical parameters. We use Slater type orbitals as basis set, replacing STO's by STO-2G functions to evaluate three- and four-center integrals and making the STO-2G two-orbital charge distributions have the same total charge as STO. The results are presented for test calculations on five molecules. In view of these results, CCAM is better than ab initio calculations over STO-6G in the results on total energies, kinetic energies and occupied orbital energies. In atomic populations, dipole moments and unoccupied orbital energies, CCAM is also satisfactory. We estimate that CCAM would be as fast as ab initio calculations over STO-2G in evaluating molecular integrals.     

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     

Molecular enthalpies: 2. ground-state thermodynamic and computed enthalpies of bicyclo[2.2.2]octa-2,5,7-triene and its hydrogenation products

This article is a continuation of our investigation of enthalpies of formation and strain-compensated enthalpies of hydrogenation of medium-sized hydrocarbons. We have carried out calculations of H _f by MM2, MM3, and by the MNDO, AM1, and PM3 semi-empirical molecular orbital methods. Results are given for the bicyclo[2.2]octa-2,5,7-triene series ([2.2.2]barrelenes) Two of these compounds are potentially homoantiaromatic. Comparisons with ab initio calculations are made. A novel method of estimating strain relaxation during the stepwise hydrogenation of [2.2.2]barrelene is given.     

TheRate: Program for ab initio direct dynamics calculations of thermal and vibrational-state-selected rate constants

We introduce TheRate (THEoretical RATEs), a complete application program with a graphical user interface (GUI) for calculating rate constants from first principles. It is based on canonical variational transition-state theory (CVT) augmented by multidimensional semiclassical zero and small curvature tunneling approximations. Conventional transition-state theory (TST) with one-dimensional Wigner or Eckart tunneling corrections is also available. Potential energy information needed for the rate calculations are obtained from ab initio molecular orbital and/or density functional electronic structure theory. Vibrational-state-selected rate constants may be calculated using a diabetic model. TheRate also introduces several technical advancements, namely the focusing technique and energy interpolation procedure. The focusing technique minimizes the number of Hessian calculations required by distributing more Hessian grid points in regions that are critical to the CVT and tunneling calculations and fewer Hessian grid points elsewhere. The energy interpolation procedure allows the use of a computationally less demanding electronic structure theory such as DFT to calculate the Hessians and geometries, while the energetics can be improved by performing a small number of single-point energy calculations along the MEP at a more accurate level of theory. The CH₄+H↔CH₃+H₂ reaction is used as a model to demonstrate usage of the program, and the convergence of the rate constants with respect to the number of electronic structure calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1039–1052, 1998     

Molecular geometries from spin Hamiltonian calculations through simultaneous optimization of geometry and wave function

The recently developed spin Hamiltonian approach to conjugated-electron molecules is reexamined. A simultaneous optimization of the geometry and wave functions, achieved by the use of the conjugate gradient method, facilitates calculations of the molecular geometries in the ground and excited electronic states. The computation time increases approximately linearly with the number of basis functions, making calculations for molecules having up to 18 carbon atoms (48 620 basis functions) readily available. Geometries of several benzenoid hydrocarbons are optimized and the results are discussed.     

A theoretical study of the electromagnetic properties of ferrocene and the ferrocenium ion

An iterative extended Hückel molecular orbital calculation was used to obtain wave functions for the ground state of ferrocene and several low lying states of the ferrocenium ion. Photoemission spectra in terms of relative ionization potentials and the electric field gradient at the iron nucleus were calculated for ferrocene andg values and the electric field gradient were calculated for the ferrocenium ion. These values are in good agreement with experiment. The nature of the molecular orbitals was compared with results of previous semi-empirical andab initio calculations.     

Ab initio studies of the electronic structure of Be93, Be105, Be111, and Be123 clusters

Ab initio self-consistent-field calculations are reported for electronic states of beryllium clusters comprised of 93, 105, 111, and 123 atoms. The respective clusters correspond to coordination shells 12-15 of a central Be atom with internuclear separations derived from the lattice constants of the bulk metal. Ab initio effective core potentials have been employed to replace the 1 s electrons, thereby reducing the complexity of the calculations. In addition, use of the full D_3h point group symmetry of the clusters results in a substantial reduction of the numbers of two-electron integrals that must be computed and processed. Binding energies, orbital energies, electric field gradient, nuclear-electrostatic potential, diamagnetic shielding constant, second moments, and Mulliken populations are calculated for selected electronic states. Calculated binding energies when compared among the different clusters as well as to smaller and larger fragments from earlier studies provide evidence for the onset of convergence to the Hartree–Fock limit of the bulk. Lowest-state ionization potentials are consistently above and agree to within 14% of the experimental workfunction. The net charge on the central beryllium atom decreases toward zero. The variability of observed bulklike behavior for the different properties indicates that the transition between cluster and bulklike behavior is not sharp and depends on the quantity of interest. © 1995 John Wiley & Sons, Inc.     

Multiconfigurational SCF approach for high-symmetry molecules and its applications to fullerene trianion

A symmetry-adapted multiconfiguration self-consistent field (MC SCF) approach aimed at calculations of high-symmetry molecules is proposed. The self-consistency procedure applicable to the molecular terms of any symmetry and multiplicity is developed. It holds the symmetry transformation properties of varied molecular orbitals, thus taking advantage of the relationships within the set of two-electron integrals through molecular invariants. For orbital optimization, a unified coupling operator is constructed on the basis of the pseudosecular method providing for efficient convergence to energy minimum. Based on the group-theory technique, computer codes have been developed for straightforward determination of the invariant expansions for two-electron integrals and configuration interaction (CI) matrix elements. Calculated in this way, the expansion coefficients are presented for the three-electron states that originate from joint t_1u and t_1g shells of an icosahedral fullerene C₆₀, the case important for the calculations of anion C₆₀³⁻ representing the charge state of the fullerene molecule in the superconducting ionic solids K₃C₆₀ or Rb₃C₆₀. The results of MC SCF calculations for lowest quasi-π-electronic states of C₆₀³⁻ are discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 293–304, 1998     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.     

MO-Berechnungen an Heterocyclen, 19. Mitt.: Zum Einfluß unterschiedlicher Orbitalexponenten für 2 s-und 2 p-STO auf die Sequenz der Orbitalenergien in CNDO-Typ-Rechnungen

CNDO-typ calculations based on a different choice of orbital exponents for 2s- and 2p-STO are able to reproduce almost exactly the order ofHartree-Fock orbital energies from high-accuracyab initio calculations. A uniform symmetry consideration for monocyclic molecules represents a useful method to correlate and compare the results. Some comments are given concerning the interpretation of UPS by means ofKoopmans theorem.

18. Mitt.:G. Kluge, undM. Scholz, Z. Chem., im Druck.     

Effects of global orbital cutoff value and numerical basis set size on accuracies of theoretical atomization energies

Numerical basis sets are known for their rapid convergence in density functional theory calculations. The selections of global orbital cutoff values and numerical basis set sizes are important to the computational accuracies and efficiencies. In this study, the effects of global orbital cutoff values and numerical basis set sizes on the theoretical atomization energies (D ₀) were investigated using density functional theory with the generalized gradient approximation. Our results on the total energies of seven atoms and D ₀ of a set of 44 molecules demonstrate that the numerical orbital cutoff value should be larger than 6.5 Å to get the converged energetic properties. Through comparing the D ₀ of these 44 molecules obtained by using four kinds of different numerical basis sets, DN, DND, DNP, and TNP, it demonstrates that the DNP basis set is good enough to predict accurate D ₀ with affordable computational cost.