Geometry optimizations with explicit inclusion of electron correlation

Automatic techniques for geometry optimization are applied in conjunction with configuration interaction and perturbation treatments of electron correlation. The computational effort and numerical accuracy of the optimizations are discussed, as well as problems with approximate correlation methods concerning the continuity of the potential surface. The optimized geometries of fourteen molecules obtained with different correlation treatments (MNDO SCF MOs) are compared. The configuration interaction results are reproduced satisfactorily by simple perturbation approaches. The largest change of the optimized SCF geometry is found for hydrogen peroxide.     

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.     

The modified Hartree–Fock self-consistent field equation

A one-electron correlation operator is introduced into the Hartree–Fock self-consistent field equation. The correlation operator is derived from the second-order perturbation theory. Energies of atomic and molecular systems calculated from this modified Hartree–Fock equation are equal to that from second-order perturbation of Hartree–Fock equation. The modified equation can also be solved self-consistently by the LCAO approximation. We also presented the modified expressions for other operators.     

The viscosity and temperature dependence of X-band ESR lineshapes of Gd(III) aqueous complex

X-band ESR spectra of Gd-aqua complex in various weight concentration of glycerol have been recorded at four temperatures. The interpretation of the ESR linewidth is preformed using both the stochastic Liouville approach (SLA) and a perturbation theory. The SLA uses a one dynamic model of the zero-field splitting whereas the perturbation approach uses a two dynamic model. Both models can reproduce the variation of the linewidth with respect to viscosity. In the SLA model, both the zero-field splitting (ZFS) interaction and the correlation time vary with the glycerol content. In the two dynamic perturbation model, only the correlation times are viscosity dependent. The two models give different NMRD profiles.     

Correlation effects in externally perturbed many-electron systems

Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self-consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many-electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many-body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree–Fock solution for the one-electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.     

Bond alternation in infinite polyene: Peierls distortion reduced by electron correlation

The formation of the bond-alternating structure in polyene is investigated both within the one-particle (Hartree-Fock) picture and including electron correlation effects by perturbation theory. An off-diagonal charge-density wave of the equi-distant structure is identified at the Hartree-Fock level as precursor of the bond-alternate state which is found by subsequent lattice optimization. The valence-shell correlation energy is calculated by using second-order Møller-Plesset perturbation theory. It is found to be finite also in the metallic one-dimensional chain and a comparison with results obtained for the acetylene unit shows that this method recovers ~-70–75% of the total valence-shell correlation. Correlation effects are shown to reduce the Peierls distortion and the corresponding energy barrier but the bond alternation persists also if the results are extrapolated to the case of full correlation.     

Vibrational quasi-degenerate perturbation theory: applications to fermi resonance in CO2, H2CO, and C6H6

A quasi-degenerate perturbation method with vibrational self-consistent field (VSCF) reference wavefunction is developed. It simultaneously accounts for strong anharmonic mode-mode coupling among a few states (static correlation) by a configuration interaction theory and for weak coupling with a vast number of the other states (dynamic correlation) by a perturbation theory. A general formula is derived based on the van Vleck perturbation theory. An algorithm that selects a compact set of the most important VSCF configurations which contribute to the static correlation is proposed and a scheme to limit the number of configurations considered for dynamic correlation is also implemented. This method reproduces the vibrational frequencies of CO2 and H2CO that are subject to the strongest anharmonic mode-mode coupling within 10 cm(-1) of vibrational configuration interaction results in a computational expense reduced by a factor of one to two orders of magnitude. The method also reproduces the infrared absorption of C6H6 in the CH stretching (nu12) frequency region, in which combination tones nu13nu16 and nu2nu13nu18 appear on account of an intensity borrowing from nu12via the anharmonic coupling.     

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

A recently proposed perturbational approach to the electron correlation cusp problem 1 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Many-body calculation of the electric field gradient in the hydrogen molecule

The electric field gradient in the hydrogen molecule has been calculated by diagrammatic many-body perturbation theory (MBPT ) in Gaussian basis sets. The procedure through third order in electron correlation gives a value for the field gradient of 0.34041 a.u., which is 0.8% greater than the accurate value. The result is discussed in terms of the completeness of the basis sets and the convergence of the perturbation expansion.     

g-Hartree ab-initio calculations of the total energies of the four-electron isoelectronic series

The atomic total energies of the four-electron isoelectronic series are calculated by theg-Hartree 2nd order perturbation theory and the Dirac-Hartree-Fock-Rayleigh-Schrödinger 2nd order perturbation theory. The Coulomb correlation energy is calculated by these theories. The Breit interaction, vacuum polarization, self-energy and Q.E.D. corrections are calculated by the lowest order approximation. The results show that theg-Hartree approach overestimates the Coulomb correlation energy. However, with an increase of the nuclear charge, it overestimates much less. In the case of the Hartree-Fock 2nd order calculation, it underestimates the Coulomb correlation energy. With an increase of the nuclear charge, it underestimates much more.     

Variational second-order Møller-Plesset theory based on the Luttinger-Ward functional

In recent years there have been some rather successful applications of a new variational technique for calculating the total energies of electronic systems. The new method is based on many-body perturbation theory and uses the one-electron Green function as the basic "variable" rather than the wave function of traditional variational calculations. It is the purpose of the present work to promote the new methods within the realm of traditional theoretical chemistry by demonstrating their utility for calculating the correlation energies of a number of atoms at a level corresponding to second-order M?ller-Plesset perturbation theory. The generalization to any desired order of perturbation theory is not hard to accomplish.     

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational M?ller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.     

The perturbation theory of the extended Hartree–Fock approximation for two-electron atoms

The first-order 1/Z perturbation theory of the extended Hartree–Fock approximation for two-electron atoms is described. A number of unexpected features emerge: (a) it is proved that the orbitals must be expanded in powers of Z^?1/2, rather than in Z^?1 as expected; (b) it is shown that the restricted Hartree–Fock and correlation parts of the orbitals can be uncoupled to first order, so that second-order energies are additive; (c) the equation describing the first-order correlation orbital has an infinite number of solutions of all angular symmetries in general, rather than only one of a single symmetry as expected; (d) the first-order correlation equation is a homogeneous linear eigenvalue-type equation with a non-local potential. It involves a parameter μ and an eigenvalue ω(μ) which may be interpreted as the probability amplitude and energy of a virtual correlation state. The second-order correlation energy is 2μ²ω. Numerical solutions for the first-order correlation orbitals, obtained variationally, are presented. The approximate second-order correlation energy is nearly 90% of the exact value. The first-order 1/Z perturbation theory of the natural-orbital expansion is described, and the coupled first-order integro-differential perturbation equations are obtained. The close relationship between the first-order extended Hartree–Fock correlation orbitals and the first-order natural correlation orbitals is discussed. A comparison of the numerical results with those of Kutzelnigg confirms the similarity.     

Two-dimensional correlation analysis useful for spectroscopy, chromatography, and other analytical measurements.

Application of generalized two-dimensional (2D) correlation in various analytical fields is explored. 2D correlation is a powerful and versatile technique applicable to spectroscopy, chromatography, and other measurements. Construction of 2D spectra is relatively straightforward, requiring only a series of systematically varying analytical signals, like spectra or chromatograms, induced by an external perturbation applied to the system of interest. Perturbation can take many different forms, like change in temperature, pressure or concentration, chemical reactions, electrical or mechanical stimuli, and so on. A set of analytical signals collected under a perturbation are then converted to 2D correlation spectra, which provide rich and useful information about the presence of coordinated or independent changes among signals, as well as relative directions and sequential order of signal intensity variations. The signal resolution is also enhanced by spreading overlapped bands along the second dimension. Illustrative examples of 2D correlation are given for spectroscopic and chromatographic applications.     

Problems in electron propagator calculations of the correlation energy

Approximations to the one-electron propagator, G(ω), are discussed asa basis for correlation energy calculations. The random-phase approximation (RPA) and second-order perturbation theory estimates of the self-energy are used to determine G(ω). Correlation energy expressions, resulting from contour integration, are compared with the standard perturbation expansion. We suggest that some of the simpler approximations to the electron propagator may be unsuited to calculations of the correlation energy.     

红外光谱法研究温度变化对卵粘蛋白构象的影响

采用傅里叶变换红外(FTIR)光谱法和二维相关分析(2D Correlation analysis)技术研究了卵粘蛋白(Ovomucin)的构象转变与温度之间的关系. 结果表明, 当温度为55~65℃时, 卵粘蛋白的红外谱峰的位置和强度发生较大改变. 二维相关分析表明, 在升温过程中, 与肽链相比卵粘蛋白分子中的糖链对温度变化更为敏感, 且优先发生构象改变, 糖链分子的存在利于维持卵粘蛋白构象的热稳定性. 在25~95℃升温过程中, 卵粘蛋白分子二级结构的变化次序依次为α-螺旋、 β-折叠、 β-转角和无规卷曲. 由温度变化引起的卵粘蛋白分子结构动态变化的微观信息, 为揭示变温微扰引起的蛋白构象变化机理提供了初步的理论依据.     

An alternative approach for the calculation of correlation energy in periodic systems: a hybrid MP2(B3LYP) study of the He-MgO(100) interaction

A practical and efficient method for exploiting second order Rayleigh-Schr?dinger perturbation theory to approximate the correlation energy contribution to the London dispersion interaction is presented. The correlation energy is estimated as the M?ller-Plesset contribution computed using single particle orbitals from hybrid exchange density functional theory as the reference state.     

A kinetic energy fitting metric for resolution of the identity second-order Møller-Plesset perturbation theory

A kinetic-energy-based fitting metric for application in the context of resolution of the identity second-order M?ller-Plesset perturbation theory is presented, which is derived from the Poisson equation. Preliminary tests of the applicability include the evaluation of the error in the correlation energy, compared to standard M?ller-Plesset perturbation theory, with respect to the auxiliary basis set employed. We comment on the potential merits of this fitting metric, compared to standard resolution of the identity second-order M?ller-Plesset perturbation theory, and discuss its scaling behavior in the limit of large molecules.