Higher-order Correlation Effects Research Articles

Calculation of the hyperfine fields in the noble-metal atoms

The hyperfine fields in the noble-metal atoms Cu, Ag, and Au have been calculated by means of a relativistic many-body perturbation-theory technique. The resulting hyperfine fields for these atoms were 256\ifmmode\pm\else\textpm\fi{}11, 531\ifmmode\pm\else\textpm\fi{}22, and 1997\ifmmode\pm\else\textpm\fi{}92 T, respectively, in good agreement with the experimental results of 259.95, 499.12, and 2085.1781 T. The reasons for the error bars in the theoretical results are discussed and are associated with the substantial sizes of the third- and higher-order correlation effects, which are found to be of great importance in these atoms. We will discuss the contributions to the total field from various one- and two-body interaction mechanisms and compare these contributions to those in related systems. Our results for the Cu and Au systems will also be compared with those available from other calculations reported in the literature.

The silicon–carbon symmetric stretching fundamental ν1 of Si2C: Nonintuitive theoretical behavior

There are two experimental values for ν1(Si2C), namely 658 and 839 cm−1. Previous theoretical studies suggest a third value slightly below 800 cm−1. Here, elaborate theoretical studies using very large basis sets confirm that the ν1=839 cm−1 experiment of Presilla-Marquez and Graham is correct. The contributions of both higher order correlation effects (as gauged by coupled cluster methods) and f functions are contrary to previous experience.

Spectroscopic properties of 34 electronic states of zirconium dimer (Zr2)

State-averaged complete active space multiconfiguration self-consistent field followed by multireference singles + doubles configuration interaction calculations are carried out on low-lying electronic states of zirconium dimer (Zr2). In addition relativistic configuration interaction calculations are carried out including spin–orbit effects. Thirty-four bound electronic states are found for Zr2. Three very low-lying states of 7∑+u, 3∑+u, and 1∑+g symmetries are found as candidates for the ground state. Higher-order correlation effects and extension of basis sets tend to favor the 1∑+g state as the ground state of Zr2 exhibiting approximately a quadruple bond (bond order =3.6). Complete potential energy curves of seven states of Zr2 are presented. The nature of low-lying electronic states is analyzed through Mulliken populations, natural orbitals and their occupations, spin–orbit effects and weights of various configurations.

Higher-order correlation effects on thermodynamic properties of liquid Hg-Na alloys determined by EMF measurements

The electromotive force (EMF) of liquid Hg-Na alloys was measured in detail below 15 at.% Na as functions of Na concentration and of temperature. On the basis of observed EMF values, thermodynamic functions of mixing were obtained at 398 K and 448 K. At 2-8 at.% Na anomalous changes were observed in the concentration dependence curve of the excess partial molar entropy, SPi,E (i=Na or Hg), and on that of the partial molar enthalpy of Na, HPNa,E. These anomalies indicate higher-order correlation effects arising from the characteristic changes in the concentration derivatives of n-body (n>or=2) correlation function galpha beta gamma (n). ( delta galpha beta gamma (n)./ delta ci)V,T,cj( not=i), which could be derived explicitly to be the function of the higher-order (n+1)-body correlation function galpha beta gamma (n) (n+1). . /sub /.

Spectroscopic properties and potential energy curves of Sb2

Complete active space MCSCF followed by first-order and relativistic configuration interaction calculations are carried out on 33 electronic states of Sb2. In addition, multireference singles + doubles CI (MRSDCI)RCI calculations are carried out on seven low-lying electronic states with the objective of estimating the higher-order correlation effects not included in the FOCI. Potential energy surfaces of the calculated electronic states are reported. Our calculations enable confirmation of earlier assignments of the observed B-X bands. The observed A-X bands are reassigned to the 3Δu(1u)-1Σg+(0g+) transition. In addition, tentative assignments of four more observed bands are suggested. Our calculations predict many allowed electronic transitions for Sb2 which are yet to be observed. The spin-orbit effects are found to be significant for Sb2. The contribution of the 3Πg state to the 1Σg+ ground state is only 2%. The singlet-triplet mixing in the excited Δ and Π states is significant. Mulliken population analyses are also carried out for all the electronic states.

An application of the full CCSDT coupled-cluster method to potential energy curves: The CH 4→CH 3+H dissociation

The potential energy surface for the dissociation of methane CH 4→CH 3 •+H • is investigated using many-body perturbation theory (MBPT) and coupled-cluster (CC) methods including full CCSDT. Full fourth-order MBPT(4) based upon an unrestricted Hartree-Fock reference function shows the characteristic rise in the 1.5–3.0 Å region due to spin contamination. The full CCSDT and its approximations based on a restricted Hartree-Fock sum higher-order correlation effects even in the 3.0–5.0 Å range, where degeneracy effects are quite large, essentially recovering all the MR-CI correlation energy.

Expected value analysis: Experimental considerations and convergence properties

In a companion paper, we developed a method, EVA (expected value analysis), to analyze the effect of the uncertainty of parameters in multiparameter systems described by ordinary differential equations. In this paper, we first interpret the output mean of EVA from an experimental point of view. Secondly, we discuss the convergence properties of EVA. The only approximation is the truncation of higher order correlation effects. A quantitative analysis of the approximations is presented, justifying the methodology.

Estimation of higher-order correlation effects on the potential energy surface for the F+H2 reaction in the saddle point vicinity

Estimation of higher-order correlation effects on the potential energy surface for the F+H2 reaction in the saddle point vicinity

The Concentration and Temperature Dependence of the Magnetic Susceptibility of Liquid Mercury Alloys

The molar magnetic susceptibility, χ M of liquid Hg–Na and Hg–In alloys was measured from room temperature to 723 K using the Faraday method. The concentration dependence curve (CDC) of χ M for liquid Hg–In alloys shows positive deviations from the linear law. The results of liquid Hg–Na alloys have a positively enhanced tendency in the intermediate concentration range, though the overall concentration dependence remains to be slightly negative (“W shape”); this type of CDC of χ M is similar to that of liquid Hg-Cs alloys. Such a tendency of deviations has been discussed in terms of the nearly free electron theory for χ M of liquid alloys. Maxima at a few at.% solute (In or Na) found in the CDC of the temperature coefficient of χ M , dχ M /d T , appear to indicate an evidence of higher order correlation effects, as observed in many liquid Hg alloys.

The volume and thermal expansion coefficients of liquid Hg-In and Hg-Sn alloys-evidence for higher-order correlation effects in liquid Hg alloys

The molar volumes VM and the thermal expansion coefficients alpha p of liquid Hg-In and Hg-Sn alloys were measured as detailed functions of composition in the range of dilute solute (In or Sn) concentration (below 15 at.% In and 10 at.% Sn). The excess molar volume Delta VM for each kind of alloy decreases monotonically with increasing concentration of solute (In or Sn) atoms. On the other hand, the concentration dependences of alpha p differ; a slight hump exists at a few at.% In for liquid Hg-In alloys, while no anomalous behaviour of alpha p is found for liquid Hg-Sn alloys. These results are closely related to the fact that there is a minimum in the curve of the thermoelectric power Q plotted against concentration for Hg-In but not for Hg-Sn, and appear to show the importance of higher-order correlation effects in liquid Hg-In alloys. It is also pointed out that similar anomalies can be found in the literature values of the partial molar excess entropy of solute component in liquid Hg-In and Hg-Tl systems.

The potential energy surface for the F+H2 reaction as a function of bond angle in the saddle point vicinity

We report large-basis-set CASSCF/MR-CISD/SEC (complete active space self-consistent-field orbitals used for multireference configuration interaction with all single and double excitations and scaled external correlation) and MP4 (Mo/ller–Plesset fourth order perturbation theory) calculations of the FH2 potential energy surface for collinear and bent geometries in the vicinity of the F---H--H saddle point. These calculations indicate that higher order correlation effects become much more important as the generalized transition states are bent, and that the unrestricted saddle point for this reaction is noncollinear. This means that the sterically allowed cone of reactive configurations is much broader than either previously available ab initio calculations or the present lower-order ones would predict.

A linear response, coupled-cluster theory for excitation energy

Expressions for static and dynamic properties in coupled-cluster (CC) theory are derived. In the static case, using diagrammatic techniques, it is shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects. For the dynamic case, excitation energy expressions are obtained without consideration of orbital relaxation effects and shown to be equivalent to an equation of motion (EOM) approach subject to a coupled-cluster ground-state wave function and an excitation operator consisting of single and double excitations. Illustrative applications for excited states of ethylene are reported.

Higher-order correlation effects on thermodynamic and electronic properties of liquid alloys

The higher-order atom-atom correlation function effect, which has been recently revealed to be related to the origin of the minimum in the thermoelectric power Q of liquid Hg alloys, is discussed in some detail. New experimental results of the electrical resistivity ϱ and Q of liquid HgLi alloys are included in this discussion. The relation between the higher order correlation function effects and the thermodynamic function of liquid Hg alloys (the heat of mixing ΔH M) is stressed. The charge transfer effect, which can been clarified by the modified Miedema's plot, seems to produce the local structural change which can be seen as the higher order correlation effect.

The Specific Mass Shift of the Ionisation Energy in Ne Calculated by Many-Body Perturbation Theory

The specific mass shift of the ionisation energy between 20Ne and 22Ne has been calculated using many-body perturbation theory. The first-order expectation value, neglecting relaxation effects is -41.0 GHz. Allowing for relaxation effects changes the result to -16.3 GHz, which, together with a lowest-order correlation effect of 9.3 GHz, gives a total result of -7.0 GHz. The experimental value is (-11 ± 3) GHz and the discrepancy is ascribed to higher-order correlation effects, which have not been evaluated.

Evidence of higher order correlation effects on properties of liquid mercury alloys

In order to study the origin of the minimum at a few at.% solute concentration in the isotherm of the thermoelectric power Q versus composition of liquid mercury alloys (the 'minimum in Q'), the electrical resistivity rho of liquid Hg-In alloys and Hg-Sn alloys has been measured precisely as a detailed function of composition. The present measurements indicate that the temperature dependence of rho , delta rho / delta T, shows a hump at about 5 at.% In for liquid Hg-In alloys in contrast to a smooth decrease observed for liquid Hg-Sn alloys; the former system shows the 'minimum in Q' and the latter does not. These experimental facts suggest that the higher order correlation effect stressed already by the present authors is important in understanding the origin of the 'minimum in Q'.

Specific mass shifts in Li and K calculated using many-body perturbation theory

Recently, experimental isotope shifts have become available for individual levels of Li and K. The authors have used many-body perturbation theory to calculate all first- and second-order contributions to the specific mass shifts. The correlation effects were obtained by numerical solution of inhomogeneous radial 'pair equations'. For the lowest s, p and d states of Li the authors results were 962, -3273 and -2 MHz compared with the experimental results of 1111(6), -3608(11) and 0(6) MHz, respectively. As in the authors earlier hyperfine structure calculations, the need to include higher-order effects is more pronounced for K, especially for the strongly perturbed d states. Adding the lowest-order correlation effects to the results obtained with a self-consistent treatment of the change in the core orbitals due to the valence electron gave satisfactory agreement for the 4s and 4p states in K, -53 and -30 MHz, respectively, compared with the experimental data, -61(2) and -28(2) MHz. The 5d state shows a larger discrepancy, the theoretical shift being -22 MHz compared with the experimental result-53(8)MHz, emphasising the need to include higher-order correlation effects.

A full coupled-cluster singles and doubles model: The inclusion of disconnected triples

The coupled-cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher-order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth-order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low-order models provide estimates of the effect of the higher-order terms T1T2, T21T2, T31, and T41 on the correlation energy.

Higher-order electron correlation effects in triatomic potential energy surfaces. Stretching vibrations of HCN and HNC

An assessment of the importance of higher-order electron correlation effects on harmonic vibrational frequencies, anharmonicities, and equilibrium structures is made for the simple triatomics HCN and HNC. Potential energy surfaces for bond stretching were generated with a large, polarized basis set of contracted Gaussian functions and using self-consistent field (SCF), correlated self-consistent electron pair (SCEP), and approximate double substitution coupled cluster (ACCD) wave functions. SCEP includes correlating configurations that mix directly with the reference wave function, while ACCD includes these configurations and also indirectly mixing configurations that arise from a cluster model of the wave function. The surfaces are compared in the prediction of spectroscopic parameters by using a low-order perturbational treatment of the vibrational wave functions in a basis of normal mode functions and with several polynomial surface fits. The neglect of correlation effects at the SCF level leads to overestimates of the vibrational frequencies. Higher-order correlation effects correct for roughly one third of this overestimation. For all parameters, the ACCD treatment yields the best predictions.

Application of an approximate double substitution coupled cluster (ACCD) method to the potential curves of CO and NeHe: Higher order correlation effects in chemically and weakly bonded molecules

The recently introduced approximate double substitution coupled cluster (ACCD) method has been applied to two diatomics: CO and NeHe. The ACCD method, using an electron pair matrix operator approach, is computationally efficient, has the orbital invariance properties of the complete CCD treatment, and goes to the proper pair description in the limit of separated electron pairs. ACCD and CCD results for the He2 potential curve are virtually identical. The calculations on CO and NeHe are among the first tests of ACCD for more than a four-electron system. Application to these two diatomics provides an opportunity to compare higher order correlation effects in chemically bonded and weakly attractive species. It is found that ACCD agrees quite well with CCD for both systems. However, the higher order correlation effects seem much less important in NeHe than in CO, where CCD reduces the error in the prediction of the vibrational frequency by a factor of 3 over a variational treatment that accounted only for singly and doubly substituted correlating configurations.

Double photoionization of helium

Many-body perturbation theory is applied to calculate double-electron photoionization for helium. While lowest-order results show reasonable agreement with experiment, it is found that certain higher-order correlation effects are significant. Techniques are presented for approximating these effects in a calculation which is first order in electron correlations.