Configuration Expansion Research Articles

Analytical gradients for the coupled-cluster method

A nondiagrammatic formulation of the analytical first derivative of the coupled-cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree-Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first-order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non-perturbation-dependent set of equations can be solved instead. This and the first-order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

The mean static dipole polarisability of scandium

The mean static dipole polarisability of scandium is calculated. Perturbation theory was used so that the polarisability is expressed in terms of the second-order energy correction. The ground-state and necessary first-order correction to the wavefunction were determined variationally as a superposition of configurations. The importance of the various polarising orbitals and the length of the configuration expansion are examined.

Configuration interaction in the L 2,3—MM Auger spectrum of HCl and Ar

The L 2,3—MM Auger spectra of HCl and Ar have been calculated. Strong interaction between the Auger diagram state 4σ −2 and correlation states explains the absence of the L 2,3—M 1 2 peak in the HCl spectrum. For argon semi-internal CI reproduces the high-kinetic-energy region, while a fairly large expansion of configurations is necessary to reproduce the low-kinetic-energy part of the spectrum.

Spectral distribution calculations of the level density and spin-cutoff parameters ofSi28

Spectral distribution calculations of the separate positive and negative parity level densities and spin cutoff parameters for $^{28}\mathrm{Si}$ have been made in an $\mathrm{sdf}$ basis. A configuration expansion utilizing higher moments of the Hamiltonian is found to be important in improving agreement between calculation and experiment at low excitation energies. The Hamiltonian moments were corrected for the effects of spurious c.m. motion. The present results suggest that spectral distribution calculations can yield level densities which agree with experimental information on the number of levels, spin cutoff factors, and parity ratios over an energy range of over 20 MeV.NUCLEAR STRUCTURE $^{28}\mathrm{Si}$; calculated level density and spin cutoff parameter 0-25 MeV.

Multiple excitations and charge transfer in the ESCA N1s (NO2) spectrum of paranitroaniline. A theoretical and experimental study

The N1s (NO2) ESCA spectrum of paranitroaniline (PNA) is analyzed theoretically and experimentally. New monochromatized high-resolution spectra in the vapor (gas) and condensed phases are presented. In the condensed phase spectrum two distinct peaks are discerned, whereas the gas phase spectrum shows a drastically different feature in which the two peaks are reduced to an asymmetric band. The gas phase spectrum has been interpreted based on large-scale MCSCF wave functions calculated using a complete configuration expansion in the π valence orbital space. Emphasis is placed on the identification of features due to ’’shake’’ effects. Multiple excitations in the charge transfer excited states, as well as configuration near-degeneracy effects in the NO2 group, are found to be crucial for this identification. Our results are different from an earlier many-body, Green’s function, treatment of PNA. We find that the charge transfer shake states lie higher in energy (shakeup) and not lower (negative shakeup).

An electron pair operator approach to coupled cluster wave functions. Application to He2, Be2, and Mg2 and comparison with CEPA methods

A method for obtaining coupled cluster expansions with double substitutions (CCD) utilizing the electron pair operator approach of self-consistent electron pair (SCEP) theory is presented. A fairly simple operator is developed in this method and its calculation increases the expense over a typical variational configuration expansion only moderately. With this method, large basis set calculations have been performed on the weakly interacting dimers He2, Be2, and Mg2. Comparison calculations have been performed with various types of coupled electron pair approximations (CEPA), which may be viewed as approximations to coupled cluster theory, and with modification of the internal orbitals in the CCD treatment.

A quadratically convergent multiconfiguration–self-consistent field method with simultaneous optimization of orbitals and CI coefficients

A quadratically convergent MC–SCF procedure is described which is based on the direct minimization of the energy. In comparison to the Newton–Raphson technique, which has previously been applied by several authors for orbital optimization, the convergence radius is much improved by taking into account in the energy expansion those parts of third and higher order terms which account exactly for the orthonormality constraints imposed on the orbitals. The nonlinear equations which define the improved orbitals are solved iteratively by a simple adaption of the Gauss–Seidel method. The coefficients of the configuration expansion can be optimized simultaneously with the orbitals, a necessary requirement for over-all quadratic convergence. The removal of redundant variables as well as useful approximations for the optimization of core orbitals are discussed. The convergence of the method is demonstrated to be much superior to classical Fock operator techniques and MC–SCF methods which are based on the generalized Brillouin theorem. The formalism is carried down to matrix operations and shows a simple structure.

Ab initio theory of the polarizability and polarizability derivatives in H 2S

Ab initio finite-perturbation self-consistent-field (SCF) and configuration interaction (CI) calculations utilizing an extensive basis of cartesian gaussian orbitals are reported for the electric dipole polarizability tensor, α, and the polarizability derivative tensor, α′, of H 2S. Particular attention was devoted to the selection of an appropriate molecular orbital basis and configuration expansion for determining electron correlation contributions to the polarizability. The common practice of truncating configuration expansions based on a perturbation theory correction to the energy is shown to be inadequate for this property. Contrary to the predictions of such an approach, we conclude that electron correlation has little effect on α and α′ in H 2S. Our calculation yielded a nearly isotropic polarizability tensor, whose trace, α , is ca. 5% below the experimental result. The magnitude of the derivative ( α ′) along the symmetric stretch is also in good agreementwith experiment. It is positive and roughly an order of magnitude larger than the components along the other two modes. The derivative anisotropy parameter is found to be positive for all three normal modes. Theoretical dipole moment derivatives have also been evaluated and are compared to those determined from the infrared spectrum. Recent data from Rayleigh and Raman scattering experiments on H 2O are discussed in light of our results for H 2S.

Comments on "Self-generated magnetic fields in laser-produced plasmas for metallic targets"

It is shown that the measurements of Edwards et al. do not demonstrate the existence of two independent self-generated magnetic fields in the laser-target interaction region. On the contrary, these results illustrate, once more, the two-phase expansion of the magnetic fields spatial configuration: diffusion within the photoionized background followed by convection with the laser plasma.

The H3+ potential surface

An accurate potential surface of 68 grid points for the H3+ system is given. The surface was calculated at the level of a full configuration expansion using a large basis set of 63 contracted Gaussian functions. This surface should be suitable for extremely accurate predictions of the vibration–rotation spectrum of H3+.

Excitation energies of the n → π* 3A″ and π → π* 3A′ states of acrolein

The vertical and adiabatic excitation energies between the ground and lowest two triplet states of acrolein were studied using ab initio correlated wavefunctions. A double zeta basis set was used in the configuration interaction calculations and each configuration expansion included about 6000 determinants selected from the list of singly and doubly substituted determinants, relative to the SCF reference wavefunction. The calculated vertical and adiabatic excitation energies are respectively, 27 200 cm −1 and 21 700 cm −1 for the n → π* 3A″ state, and 32 000 cm −1 and 23 100 cm −1 for the π → π* 3A′ state. For the 3A″ state, an upward correction of ≈ 1000 cm −1 for the effects of unlinked clusters yields reasonable agreement with the experimental T e = 24 300 cm −1.

The direct configuration interaction method with a contracted configuration expansion

A variant of the configuration interaction method is outlined. There are four characteristic features of the method. First, the freezing, contraction of coefficients in the configuration expansion. In the present approach Rayleigh-Schrödinger perturbation theory has been used for this purpose. Second, the use of the direct CI-method to construct hamiltonian matrix elements between functions with contracted coefficients, in only one sequential read of the molecular integrals. Third, a diagonalization of the resulting small matrix. Fourth, an important computational advantage in that only one CI-vector is needed in core storage instead of two as in the usual direct CI-method. The method has been programmed for the case of all single and double replacements from a spin-unrestricted Hartree-Fock determinant. Test calculations indicate that usually less than 2% of the correlation energy is lost because of the contraction of the CI-expansion. A possibility to avoid the major part of the integral transformation and work directly with atomic basis functions is also discussed.

Configuration of unsheared nucleohistone. Effects of ionic strength and of histone F1 removal.

Nucleohistone solubilized from rabbit thymus nuclei by an endogenous nuclease has in 0.15 M salt an exceptionally low intrinsic viscosity and very high sedimentation velocity. A fully reversible expansion of configuration occurs on lowering ionic strength. When [eta] is plotted against I-1/2 and extrapolated to high I, [eta] = 0 is reached at I = 0.4-1 M and [eta] at I = infinity is negative, contrary to the behavior of DNA and of the great majority of polyelectrolytes, which extrapolate to a positive [eta] at I = infinity. This behavior demands that the configuration of nucleohistone depends not only on electrostatic expansive forces but also on contracting forces which are not electrostatic and do not go to zero in any accessible configuration. Intramolecular hydrophobic bonds might provide such contracting forces. Increasing I above 0.15 M leads to precipitation near 0.3 M and redissolution with dissociation of F1 and expansion in 0.6 M. The expansion is largely but not completely reversed on return to 0.15 M. Much further expansion occurs in I = 1.2 M. Nucleohistone exposed to 1.2 M could not be redissolved in the original medium. Nucleohistone depleted of F1 exhibits a similar expansion as ionic strength is reduced, at higher viscosities throughout. On extrapolation to I = infinity both positive and negative viscosities were observed, on different lots, perhaps reflecting variable extraction of other histones. Circular dichroism spectra are very little affected by ionic strength (0.6 M and lower) or F1 removal, despite tenfold changes in viscosity.

Orbital correlation effects: The independent pair-potential approximation with application to the ground state and first ionized state of boron hydride

A new method is proposed for calculating correlation effects in atomic and molecular systems. The basis of the method is the formulation of a set of partial configuration expansions which yield directly variational orbital correlation corrections which are appropriately summed in order to obtain an estimate of the total correlation energy. This method is applied to the ground state of boron hydride and its cation at the equilibrium distance of BH. The results of the method are compared in detail with independent electron pair results and second order CI results. It is further shown that multiple substitutions are approximately accounted for in this method and the extent to which they are included is compared with other approximations. Finally, three methods of increasing accuracy, aimed at reducing the necessary computational effort, are given for determining the vertical ionization potential. The most economical method yields an IP of 9.70 eV or 0.03 eV less than the experimental IP. Completion of the basis is estimated to improve this value to 9.77 eV.

A variational procedure for the optimisation of multi-configuration self-consistent field (MC SCF) orbitals

A variational procedure has been developed for the optimisation of multi-configuration self-consistent field (MC SCF) orbitals for a special type of configuration expansion. Applicability of the method and the computational procedure are discussed.

PNO–CI Studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane

It is shown that the convergence of the configuration expansion of a many-electron wavefunction may be drastically improved without significantly complicating the energy matrix elements by using partially non-orthogonal orbitals. The wavefunction thus obtained is the many-electron analog to the natural orbital expansion of a two-electron wavefunction. The orbitals involved may be approximated by pseudonatural orbitals (``PNO–CI''), and an efficient way of calculating these orbitals is presented. An approximate treatment of multiple substitutions is discussed yielding a coupled electron pair theory formulated within the CI scheme. These methods are applied to the ground state and three ionized states of methane. Including only double substitutions, the computed upper bound to the energy of the ground state is −40.4584 hartree, i.e. 0.057 above the experimental nonrelativistic energy. About 83% of the total correlation energy is accounted for variationally, whereas the coupled-pair approximation yields 89%. The ratio between intraorbital and interorbital valence shell correlation energy is calculated as 1.56 in the case of localized electrons. The equilibrium distance in CH4 is found to be shifted from 2.046 bohr to 2.061 bohr due to correlation, and the harmonic frequency ν1 is reduced from 3149 cm−1 to 3037 cm−1. These results indicate that the anharmonicity corrections to the observed values have probably been over estimated. The correlation contributions to the ionization potentials are analyzed. The theoretical potentials differ from the observed values by 1%–2%. The energy surface of CH4+ is investigated and is used to discuss the photoelectron spectrum of CH4. Contrary to previous work, the lowest minimum of CH4+ is found to have C2v symmetry. In all applications the variational results are compared with those of the independent-pair and coupled-pair approaches, and it is concluded that the latter represents a definite improvement over the first two.

Atomic Multiconfiguration Self-Consistent-Field Wavefunctions

The ground-state 1S wavefunctions of the atomic isoelectronic series with two and four electrons (Z = 1 – 8, and 3–8, respectively), were calculated using the MC–SCF method restricted to pair replacements. These calculations were to test and demonstrate how rapidly the configuration expansions of the MC–SCF wavefunctions converge. In the two-electron series, nine configurations were required to yield 97% of the correlation energy, while ten configurations accounted for 86% of the correlation energy in the four-electron series. The quality of the reported wavefunctions has been tested by computing the expectation values of several one- and two-electron operators. The results obtained agree in general satisfactorily (deviations of ∼1%) with values computed from more complex wavefunctions, indicating that the compact MC–SCF functions reported are indeed of high quality.