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Correlation Energy (correlation + energy)
Selected AbstractsTwo Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A2 Type MoleculesCHINESE JOURNAL OF CHEMISTRY, Issue 4 2004Shu-Ping Zhuo Abstract Based on the calculation results of pair correlation energy contributions of the various electron pairs in Naz and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of mr, however, in this way, more than 90% of computational work can be. saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A, to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules. [source] Soft Coulomb hole method applied to moleculesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2007J. Ortega-Castro Abstract The soft Coulomb hole method introduces a perturbation operator, defined by ,e/r12 to take into account electron correlation effects, where , represents the width of the Coulomb hole. A new parametrization for the soft Coulomb hole operator is presented with the purpose of obtaining better molecular geometries than those resulting from Hartree,Fock calculations, as well as correlation energies. The 12 parameters included in , were determined for a reference set of 12 molecules and applied to a large set of molecules (38 homo- and heteronuclear diatomic molecules, and 37 small and medium-size molecules). For these systems, the optimized geometries were compared with experimental values; correlation energies were compared with results of the MP2, B3LYP, and Gaussian 3 approach. On average, molecular geometries are better than the Hartree,Fock values, and correlation energies yield results halfway between MP2 and B3LYP. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Left,right and dynamic correlationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2002Kian Molawi Within density functional theory, it is natural to separate the correlation energy into two parts: left,right correlation and dynamic correlation. Left,right correlation arises from the exchange part of functionals, and dynamic correlation arises from the correlation part of functionals. We examine the nature of these correlation energies as molecules are distorted. We observe that such a natural separation is not possible using the methods of quantum chemistry. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Two Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A2 Type MoleculesCHINESE JOURNAL OF CHEMISTRY, Issue 4 2004Shu-Ping Zhuo Abstract Based on the calculation results of pair correlation energy contributions of the various electron pairs in Naz and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of mr, however, in this way, more than 90% of computational work can be. saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A, to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules. [source] Nonlinear wave function expansions: A progress reportINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2007Ron Shepard Abstract Some recent progress is reported for a novel nonlinear expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions using the Graphical Unitary Group Approach and the wave function is expanded in a basis of product functions, allowing application to closed and open shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational expansion that depends on a relatively small number of nonlinear parameters called arc factors. Efficient recursive procedures for the computation of reduced one- and two-particle density matrices, overlap matrix elements, and Hamiltonian matrix elements result in a very efficient computational procedure that is applicable to very large configuration state function (CSF) expansions. A new energy-based optimization approach is presented based on product function splitting and variational recombination. Convergence of both valence correlation energy and dynamical correlation energy with respect to the product function basis dimension is examined. A wave function analysis approach suitable for very large CSF expansions is presented based on Shavitt graph node density and arc density. Some new closed-form expressions for various Shavitt Graph and Auxiliary Pair Graph statistics are presented. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Hierarchy of equations in the generalized density functional theoryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2006Á. NagyArticle first published online: 28 NOV 200 Abstract Functional relations and equations of hierarchy in the generalized density functional theory (DFT) are derived from coordinate scaling and adiabatic connection. Local and nonlocal solutions for the noninteracting kinetic energy, exchange energy, correlation energy, and the kinetic energy correction functionals are presented. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] One-particle density matrix functional for correlation in molecular systemsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003Mario Piris Abstract Based on the analysis of the general properties for the one- and two-particle reduced density matrices, a new natural orbital functional is obtained. It is shown that by partitioning the two-particle reduced density matrix in an antisymmeterized product of one-particle reduced density matrices and a correction ,c we can derive a corrected Hartree,Fock theory. The spin structure of the correction term from the improved Bardeen,Cooper,Schrieffer theory is considered to take into account the correlation between pairs of electrons with antiparallel spins. The analysis affords a nonidempotent condition for the one-particle reduced density matrix. Test calculations of the correlation energy and the dipole moment of several molecules in the ground state demonstrate the reliability of the formalism. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 317,323, 2003 [source] HF,CC model for atoms and molecules,INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002E. Clementi Abstract The Hartree,Fock,Clementi,Corongiu method (HF,CC) is revisited, aiming at an unified formulation for post-HF energy computations in atomic and molecular systems. For atomic systems new parameterizations of the HF,CC functional are proposed for the computation of atoms. The previous HF,CC molecular functional (Clementi, E.; Corongiu, G. Theochem 2001, 543, 39), revisited and recalibrated with a new optimization of the parameters, is tested with a sample of 131 molecules, including radicals, H-bond, and van der Waals systems. The atomization energy is decomposed into "HF classic" energy (the sum of the HF nuclear electron, HF kinetic, and HF Coulomb energies), "HF exchange" energy, and correlation energy; the latter is computed with a scaling functional with atomic, covalent, ionic, and van der Waals contributions. For the sample of 131 molecules, the computed HF,CC atomization energies have an average standard deviation of 1.89 kcal/mol. The atomic and molecular components of the correlation energy are decomposed into nuclear electron, kinetic, Coulomb, and exchange contributions; these decompositions characterize the HF,CC model and are used to explain the origin of the chemical bond. Computations on van der Waals systems show the validity of the HF,CC method also for long-range weak interactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Explicitly correlated SCF study of anharmonic vibrations in (H2O)2INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002Donald D. Shillady Abstract Modeling solvation in high-pressure liquid chromatography (HPLC) requires calculation of anharmonic vibrational frequencies of solvent clusters for a statistical partition function. An efficient computational method that includes electron correlation is highly desirable for large clusters. A modified version of the "soft Coulomb hole" method of Chakravorty and Clementi has recently been implemented in a Gaussian-lobe-orbital (GLO) program (PCLOBE) to include explicit electron,electron correlation in molecules. The soft Coulomb hole is based on a modified form of Coulomb's law: An algorithm has been developed to obtain the parameter "w" from a polynomial in the effective scaling of each primitive Gaussian orbital relative to the best single Gaussian of the H1s orbital. This method yields over 90% of the correlation energy for molecules of low symmetry for which the original formula of Chakravorty and Clementi does not apply. In this work, all the vibrations of the water dimer are treated anharmonically. A quartic perturbation of the harmonic vibrational modes is constrained to be equal to the exact Morse potential eigenvalue based on a three-point fit. This work evaluates the usefulness of fitting a Morse potential to a hydrogen bond vibrational mode and finds it to be slightly better than using MP2 vibrational analysis for this important dimer. A three-point estimate of the depth, De, of a Morse potential leads to a correction formula for anharmonicity in terms of the perturbed harmonic frequency: When scaled by 0.9141, the harmonic Morse method leads to essentially the same results as scaling the BPW91 local density method by 0.9827. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Left,right and dynamic correlationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2002Kian Molawi Within density functional theory, it is natural to separate the correlation energy into two parts: left,right correlation and dynamic correlation. Left,right correlation arises from the exchange part of functionals, and dynamic correlation arises from the correlation part of functionals. We examine the nature of these correlation energies as molecules are distorted. We observe that such a natural separation is not possible using the methods of quantum chemistry. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] How resonance assists hydrogen bonding interactions: An energy decomposition analysisJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2007John Frederick Beck Abstract Block-localized wave function (BLW) method, which is a variant of the ab initio valence bond (VB) theory, was employed to explore the nature of resonance-assisted hydrogen bonds (RAHBs) and to investigate the mechanism of synergistic interplay between , delocalization and hydrogen-bonding interactions. We examined the dimers of formic acid, formamide, 4-pyrimidinone, 2-pyridinone, 2-hydroxpyridine, and 2-hydroxycyclopenta-2,4-dien-1-one. In addition, we studied the interactions in ,-diketone enols with a simplified model, namely the hydrogen bonds of 3-hydroxypropenal with both ethenol and formaldehyde. The intermolecular interaction energies, either with or without the involvement of , resonance, were decomposed into the Hitler-London energy (,EHL), polarization energy (,Epol), charge transfer energy (,ECT), and electron correlation energy (,Ecor) terms. This allows for the examination of the character of hydrogen bonds and the impact of , conjugation on hydrogen bonding interactions. Although it has been proposed that resonance-assisted hydrogen bonds are accompanied with an increasing of covalency character, our analyses showed that the enhanced interactions mostly originate from the classical dipole,dipole (i.e., electrostatic) attraction, as resonance redistributes the electron density and increases the dipole moments in monomers. The covalency of hydrogen bonds, however, changes very little. This disputes the belief that RAHB is primarily covalent in nature. Accordingly, we recommend the term "resonance-assisted binding (RAB)" instead of "resonance-assisted hydrogen bonding (RHAB)" to highlight the electrostatic, which is a long-range effect, rather than the electron transfer nature of the enhanced stabilization in RAHBs. © 2006 Wiley Periodicals, Inc. J Comput Chem 28: 455,466, 2007 [source] Improved third-order Møller,Plesset perturbation theoryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2003Stefan Grimme Abstract Based on a partitioning of the total correlation energy into contributions from parallel- and antiparallel-spin pairs of electrons, a modified third-order Møller,Plesset (MP) perturbation theory is developed. The method, termed SCS,MP3 (SCS for spin-component-scaled) continues previous work on an improved version of MP2 (S. Grimme, J Chem Phys 2003, 118, 9095). A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third-order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C20 isomers, transition states) demonstrate that the SCS,MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1529,1537, 2003 [source] Electronic and structural properties of strontium chalcogenides SrS, SrSe and SrTePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 11 2004D. Rached Abstract We present the results of a first-principles study of the electronic and structural properties of strontium chalcogenides, SrS, SrSe and SrTe. The computational method is based on the full-potential linear muffin-tin orbitals method (FP-LMTO) augmented by a plane-wave basis (PLW). The exchange and correlation energy is described in the local density approximation (LDA) using the Perdew,Wang parameterization including a generalized gradient approximation (GGA). The calculated results of the structural properties are given for the NaCl (B1) and CsCl (B2) structures. We have also carried out band-structure calculations for the three considered compound, but only for the NaCl (B1) structure. A reasonable agreement is found from the comparison of our results with other theoretical calculations and experimental data. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Exact Fixed-node Quantum Monte Carlo: Differential ApproachCHINESE JOURNAL OF CHEMISTRY, Issue 11 2005Hong-Xin Huang Abstract A differential approach for exact fixed-node quantum Monte Carlo calculation was proposed in this paper. This new algorithm can be used to directly compute the energy differential between two systems in exact fixed-node quantum Monte Carlo process, making the statistical error of calculation reduce to order of 10,2 kJ/mol and recover about more than 90% of the correlation energy. The approach was employed to set up a potential energy surface of a molecule, through a model of rigid move, and Jacobi transformation utilized to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality depicted. This novel algorithm was used to study the potential energy curve of the ground state of BH and the potential energy surface of H3, and could be also applied to study other related fields such as molecular spectroscopy and the energy variation of chemical reactions. [source] Two Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A2 Type MoleculesCHINESE JOURNAL OF CHEMISTRY, Issue 4 2004Shu-Ping Zhuo Abstract Based on the calculation results of pair correlation energy contributions of the various electron pairs in Naz and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of mr, however, in this way, more than 90% of computational work can be. saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A, to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules. [source] A Novel Method for Fixed-node Quantum Monte CarloCHINESE JOURNAL OF CHEMISTRY, Issue 10 2001Hong-Xin Huang Abstract In this paper, a novel method for fixed-node quantum Monte Carlo is given. By comparing this method with the traditional fixed-node one, this novel method can be applied to calculate molecular energy more exactly. An expansion of the eigenvalue of the energy for a system has been derived. It is proved that the value of the energy calculated using the traditional fixed-node method is only the zeroth order approximation of the eigenvalue of the energy. But when using this novel method, in the case of only increasing less computing amounts ( < 1%), the first order approximation, the second order approximation, and so on can be obtained conveniently with the detailed equations and steps in the practical calculation to calculate the values of the zeroth, first and second approximation of the energies of 1 1A, state of CH2, 1A2(C4h, acet) state of C8 and the ground-states of H2, LiH, Li2, and H2O The results indicate that for these states it needs only the second order approximation to obtain over 97% of electronic correlation energy, which demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required. [source] | ||||||||||