Correlation Energy Contributions Research Articles

A theoretic study of halomethanes hydrogen atom transfer reactions by methyl radicals

The kinetics of hydrogen atom transfer reactions from chloro–fluoro methanes (CFH 3, CF 2H 2, CF 3H, CClH 3, CCl 2H 2 and CCl 3H) by methyl radical (CH 3 ) was studied using ab initio calculations. The transition states were determined at the HF level of theory with the 3-21G ∗ and 6-31G ∗∗ basis sets. The activation energies calculated for the hydrogen abstraction reactions were in reasonably good agreement with the experimental values when they were corrected taking into account the correlation energy contribution on reactants and transition states. Therefore, single point MP2 calculations were carried out on the geometries previously optimized at the UHF-RHF/6-31G ∗∗//3-21G ∗ level. For a better description of the contributing factors to the activation entropy, the internal rotation contributions were calculated following the procedure introduced by Benson. The influence of the quantum tunneling effect on the rate constants values showed a direct correlation with the potential barriers for the reactions studied.

A Theoretical Investigation of the Torsional Potential in 3,3‘-Dimethyl-2,2‘-bithiophene and 3,4‘-Dimethyl-2,2‘-bithiophene: A Comparison between HF, MP2, and DFT Theory

The torsional potential curve of 3,3‘-dimethyl-2,2‘-bithiophene has been investigated at the MP2 and DFT (B3LYP and BLYP) levels with the 6-31G* basis. The DFT (B3LYP) method has also been used to compute the torsional curve for 3,4‘-dimethyl-2,2‘-bithiophene. In contrast with previous HF computations, our results indicate for both isomers the existence of a syn-gauche and an anti-gauche conformational minimum. This finding is in agreement with X-ray structural investigations and UV data. Our computations point out the importance of including the correlation energy contributions to study the conformational properties of oligo and polythiophenes and indicate that the DFT approach (in particular the hybrid B3LYP functional) provides a description of these systems which is in satisfactory agreement with the experimental evidence.

Simple Approximation of Core-Correlation Effects on Binding Energies

The majority of the ab initio electronic structure calculations that are performed today include the correlation energy of only the valence electrons. This is sometimes called the frozen-core (FC) approximation. Even when correlated calculations are carried out without the FC approximation, one cannot make a realistic estimate of core correlation energy unless one adds extra basis functions in the core region, and standard basis sets 1 do not include these. The idea that only the valence electrons contribute to binding has a long and venerable history, dating to the early days of quantum chemistry, and it is essentially correct, rightfully constituting one of the key elements for understanding why the periodic table explains so much of chemistry. 2 However recent years have seen great progress in the calculation of molecular binding energies, 3 and in some cases errors due to neglecting the contribution of core correlation energy may exceed all other errors combined. In fact, over the past few years a number of researchers 4-17 have shown that the change in correlation energy of core electrons must be accounted for quantitatively to predict accurate molecular structures or energetics. Accounting for the correlation energy of core electrons by explicitly including them in correlated electronic structure calculations increases the computational cost by a very significant amount, due both to the need for larger one-electron basis sets and also to the larger number of manyelectron configurations that need be considered. This is prohibitively expensive for larger molecules. The purpose of the present paper is to point out that one can formulate a useful approximation to core correlation effects on binding energies by counting the heavy-atom bonds in a molecule.

Molecular fragment approach to the study of pyrrole oligomers and polypyrrole

A molecular fragment approach is used to compute ionization potentials, transition energies and electron affinities of pyrrole oligomers. The calculations of these quantities include correlation energy contributions evaluated by integrating a functional of the two-particle Hartree-Fock density matrix. Pyrrole oligomers with chains of up to 16 rings are explicitly treated and the calculated quantities extrapolated to the limit of an infinitely long chain, to predict polymer properties. The theoretical results compare favorably with data on gas-phase ionization potentials deduced from experimental oxidation potentials, and with optical absorption peaks recorded in solution or on solid films. The large discrepancy between electron affinities obtained from the eigenvalues of an independent-particle frozen-orbital calculation and those obtained from separate, correlated calculations on the neutral system and the negative ion in shown.

Correlation energy contributions from low-lying states to density functionals based on an electron gas with a gap

Correlation energy contributions from low-lying states to density functionals based on an electron gas with a gap

Correlation energy contributions from low-lying states to density functionals based on an electron gas with a gap

Correlation energy contributions from low-lying states to density functionals based on an electron gas with a gap

Bond Functions and Core Correlation Energy Contributions To HeBe Potential

An empirical scheme for implementation of bond functions in heteronuclear diatomics is suggested and applied to HeBe using universal even-tempered functions. The effects of bond functions and core-correlation energy on the interaction potential of HeBe calculated at the uncorrelated (SCF) and correlated (MBPT and CC) levels are examined. The results confirm that an accuracy of sub μ Hartree level can be obtained using even-tempered functions with s-, p-, and d- symmetry and that bond functions of size {4s2p} for He and {6s3p} for Be recovers 100% of energy lowering obtained from the addition of 10d atom-centered functions to He and 13d atom centred functions to Be. The various treatments of the electron correlation, conclude that the system is interacting weakly with a well depth from 14.5–24.7 μE h at a separation near 9.1a0 compared with 20.7–25.5 μE h previously reported with a rather limited basis set. The most reliable well depth corrected for BSSE (19.0 μE h ) was obtained at the CC-SD(T)level at separation of 8.71a0 taking into account the effects of bond functions and core correlation energy. Potential energy curves at the CC-SD(T) valence and CC-SD(T) valence + core correlation levels are analyzed in analytical forms in terms of exchange repulsion, induction and dispersion components.

Stability Order of Basic Peptide Conformations Reflected by Density Functional Theory

Ab initio density functional methods at the B3LYP/6-311+G(d, p) and 6-31G(d) levels were performed on several basic peptide conformations representing typical elements of secondary structure (β-sheets, β- and γ-turns). The results are compared with those from Hartree-Fock and MP2 correlation energy calculations. Whereas the geometries of the structures are well described at all approximation levels, there are considerable discrepancies of the stability orders. Contrary to the Hartree-Fock calculations, the correlation energy methods provide the more compact structures with intramolecular hydrogen bonds distinctly favoured over extended conformations when comparing the energy differences. However, due to considerable compensation of correlation energy and entropy contributions, the stability order at the Gibbs free energy level closely corresponds to that at the Hartree-Fock level.

Correlation Energy, Thermal Energy, and Entropy Effects in Stabilizing Different Secondary Structures of Peptides

Quantum chemical calculations on some typical elements of secondary structure in peptides and proteins (β sheets, β and γ turns) at the Hartree−Fock and MP2 correlation energy levels show considerable differences in the stability orders of alternative structures. The correlation energy data indicate an overestimation of hydrogen-bonded structures. Thus, correlation energy data may be misleading when comparing peptide structures of different type, as for instance, conformations with and without hydrogen bonds or with a different number of hydrogen bonds. This effect is corrected at the Gibbs free energy level when including thermal energy and entropy contributions. Considerable compensation of correlation energy and entropy contributions is mainly responsible for the relatively good correspondence of Hartree−Fock energy differences obtained with more extended basis sets and the free enthalpy data at the correlation energy level.

Green's-function approach to atomic many-body calculations with application to the ground state in alkali-metal atoms

In this paper we apply the single-particle Green's-function method to the atomic many-body perturbation theory. We present an all-order evaluation scheme for the proper self-energy operator based on the systematic use of Dyson's integral equations. The method is complete to third order in perturbation theory and, in addition, large classes of higher-order effects are included by solving the Dyson equations. Certain classes of many-body correlation effects beyond the pair-correlation approximation are included. The proposed method is tested by calculating the ground-state valence-electron binding energy for the alkali-metal atoms Li, Na, and K. Agreement with experimental results corresponds to an error in the correlation energy contribution of 3--4%. If certain three-particle effects, not evaluated in this work, are added, the agreement with experiments is, for sodium and potassium, approximately within 1% of the correlation energy.

MP2 and CCSD(T) study on hydrogen bonding, aromatic stacking and nonaromatic stacking

Three groups of molecular clusters were studied using the coupled cluster method with non-iterative triple excitations (CCSD(T)) and the second-order Møller-Plesset perturbational method (MP2): H-bonded DNA base pairs ((cytosine) 2, (isocytosine) 2 and (uracil) 2), aromatic stacked complexes ((pyrrol) 2, (pyrimidine) 2, (triazine) 2, (aminotriazine) 2, (4-aminopyrimidine) 2 and (1-aminopyrimidine) 2) and cyclic H-bonded and stacked (formamide) 2 and (formamidine) 2 dimers. The higher-order correlation energy contributions are repulsive in all aromatic stacked clusters, while for all other systems the CCSD(T) and MP2 methods provide nearly identical results. The interaction energies of stacked complexes converge with the size of basis set much faster than the interaction energies of H-bonded clusters. It follows from the present data that the stacking energies of nucleic acid base pairs, evaluated at the MP2 level with diffuse-polarized medium-sized basis sets should be close to the actual values. The stabilization of H-bonded base pairs evaluated at the same level of theory is expected to be underestimated.

Ground state correlations of jellium metal clusters in local spin-density approximation

The role of S = 1 excitations on the ground state of jellium clusters is analyzed within the randomphase approximation (RPA). The importance of the correlation-energy contribution to the residual interaction in this channel, in order to obtain a consistent description of the cluster electronic states, is stressed. The modification of the single-particle occupation numbers in the RPA ground state is obtained. This modification is found too large when considering only Coulomb exchange contributions to the functional, which clearly points the inadequacy of RPA for this approximate functional and the necessity to include correlation-energy contributions.

Calculation of relative free energy differences for the covalent hydration of organic compounds: A combined quantum mechanical and free energy perturbation study

AbstractThe relative free energy difference (ΔΔGhyd) for the reversible addition of water to two unsaturated molecules is accurately computed using a combination of ab initio quantum mechanical calculations and free energy perturbation methods. Initial attempts to calculate the absolute hydration free energy difference (ΔGhyd) for formaldehyde and trichloroacetaldehyde gave values that differed substantially from experimental results even after inclusion of electron correlation energy contributions using third‐order (MP3) and fourth‐order (MP4) Møller‐Plesset perturbation theory and QCISD(T) correlation methods at the 6‐31G** basis set level. Inaccuracies in ΔGhyd were attributed to errors in the calculation of both ΔGgas and ΔΔGsol. Gas phase quantum mechanical free energies (ΔGgas) varied significantly (2–3 kcal/mol) depending on the level of theory. Errors in ΔΔGsol were attributed to slow convergence of the calculations using the thermodynamic cycle perturbation (TCP) method with explicit solvent. These errors were minimized or canceled, however, when relative hydration free energy differences (ΔΔGhyd) were calculated using a combination of ab initio quantum mechanical calculations and free energy perturbation methods. Calculated values for a variety of aldehydes and ketones were consistent with experimental data. © 1995 John Wiley & Sons, Inc.

An ab initio study of hydrogen abstraction by fluorine, chlorine and bromine atoms from ethane and propane

The H-abstraction reaction by F, Cl and Br radicals from ethane and propane is studied using ab initio UHF, UHF/ MP2 and UHF/MP4 computational methods with the 6–31G ∗ basis set. It is found that in all the cases examined the reaction proceeds through a transition state where the halogen atom, the abstracted H atom and the C atom are almost collinear. The geometries of the various transition states are not significantly modified by the dynamic correlation corrections included with the MP2 treatment. However the correlation energy contributions on reactants and transition states are essential to obtain values of activation energy in reasonable agreement with experimental results. Also the trend of reactivity, which decreases in the direction F → Cl → Br, and the selectivity toward primary and secondary hydrogens are in good agreement with experiment. Another interesting point concerns the performance of the effective potential basis set LAN1DZ, which is found to yield reliable geometries for the transition states. So, more accurate activation energies can be obtained cheaply by single-point computations with the 6–31G ∗ basis set on LANL1DZ optimized geometries. A simple diabatic model is used to rationalize the trend of reactivity along the series F → Cl → Br and the greater reactivity of secondary versus primary hydrogens.

Isomerization of cyanoborane anion

A previous study of the potential energy surface of borazirene revealed prohibitively large barriers on the reaction pathway from cyanoborane to borazirene. An alternative mechanism for its synthesis, based on a base-catalyzed reaction is proposed. It includes the deprotonation of cyanoborane and subsequent isomerization of the HBCN − chain to the HBCN − ring. Calculations of the X − + H 2BCN = HBCN − + HX equilibria (X = OH, H) show that proton transfer to the hydroxyl anion is thermodynamically feasible. The geometries of the stationary points on the potential energy surface corresponding to ring closure or ring opening to HBCN − and/or HBNC − chain-ions are obtained at the MBPT(2) level. Single-point calculations of the activation barriers and reaction enthalpies are performed at the CCSD + T(CCSD) level. The barriers are significantly lower compared to the isomerization of the neutral species and are in the range 100–130 kJ/mol. The reaction enthalpies are substantially lower and slightly favor the ring formation from the isocyanoborne anion. Trends in correlation energy contributions for the individual steps of the mechanism are analyzed.

Application of many‐body perturbation theory in the localized representation for the all‐trans conjugated polyenes

AbstractAb initio self‐consistent field (SCF) calculations are performed with the standard 6‐31G* basis set for all‐trans conjugated oligomers C2n+2H2n+4. The canonical occupied and virtual molecular orbitals (MOs) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two‐particle and into single‐particle terms; the MBPT is, therefore, a double‐perturbation expansion in this case. By using the localized representation of the MBPT, the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.

Correlation energies in the interaction energy of molecules. The water dimer

The interaction energy of two H 2O molecules was computed via the ‘localized’ supermolecule method. The essence of the approach applied lies in using a specific localization of the canonical orbitals of the dimer molecule both in the occupied and in the virtual spaces, respectively. This localization scheme, combined with our method elaborated and named the localized many-body perturbation theory, LMBPT, makes it possible to investigate the correlation energy contributions to the interaction energy at several levels of the MBPT in a straightforward manner.

Stability of charged aluminum clusters.

An all-electron study on neutral, singly, and doubly charged ${\mathrm{Al}}_{\mathit{n}}$ clusters (n=2--6) has been carried out within the Kohn-Sham formalism incorporating gradient corrections to the exchange and correlation energy contributions self-consistently. We present results on their equilibrium geometries, adiabatic and vertical ionization potentials, electron affinities, atomization energies, global hardness, and possible fragmentation channels. It is shown that global hardness decreases with cluster size and that it is useful in selecting the energetically more feasible fragmentation route.

Decomposition of the interaction correlation energy in terms of localized orbital contributions

The interaction energy between two He atoms was computed via a specific supermolecule method. The essence of the approach lies in using a localized representation both in occupied and in virtual space. This method, localized many-body perturbation theory, makes it possible to investigate the correlation energy contributions in a straightforward manner.

Ab initio study of the stability of [n]paracyclophanes and their Dewar benzene-type isomers

Ab initio calculations are carried out for [n]paracyclophanes and their Dewar benzene isomers forn=5, 6, and 7 as well as for the benzene and Dewar benzene itself. The benzene isomers are studied by employing various AO basis sets ranging from 6–31G type to such of triple-zeta type including twod and onef function on the carbons and twop and oned on the hydrogens. The correlation energy contribution is computed by employing MP2, CAS-SCF, MRD-CI and MCPF procedures. Potential curves for the low-energy states in the isomerization from benzene to its Dewar form are also computed under certain geometrical assumptions. The energy difference between the two potential minima is calculated to be 3.35 eV; neglect of electron correlation increases the value by about 0.3 eV, deficiencies in the polarization description (6-31G basis) overestimates it by another 0.65 eV. The calculations suggest that the experimental Dewar benzene geometry determination needs refinement and that the isomerization energy of hexamethylbenzene is considerably smaller than that of benzene itself.