Divide-and-conquer local correlation approach to the correlation energy of large molecules

A divide-and-conquer local correlation approach for correlation energy calculations on large molecules is proposed for any post-Hartree-Fock correlation method. The main idea of this approach is to decompose a large system into various fragments capped by their local environments. The total correlation energy of the whole system can be approximately obtained as the summation of correlation energies from all capped fragments, from which correlation energies from all adjacent caps are removed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations for a wide range of molecules using the 6-31G or 6-31G( * *) basis set demonstrate that this simple approach recovers more than 99.0% of the conventional second-order Moller-Plesset perturbation theory and coupled cluster with single and double excitations correlation energies.     

A group contribution method applied to electronic correlation energies of molecules

A scheme for assigning molecular correlation energies to bonds within the molecule is proposed and applied to a variety of molecules for which nonempirical electronic energies and heats of formation are available. The bond correlation energies are employed to predict the molecular correlation energies of some molecules and good agreement was found between the predicted and “experimental” values.     

Assessing the efficacy of nonsteroidal anti-inflammatory drugs through the quantum computation of molecular ionization energies

The clinical efficacy of nonsteroidal anti-inflammatory drugs has been related to ionization energies [Mehler and Gerhards, Int. J. Quantum Chem. 1989, 25, 205]. In this paper we employ modern quantum-chemical calculations to re-examine the statistical correlation between clinical efficacy and ionization energies. Ionization energies are computed by density functional theory, with and without Koopman's theorem, for a series of salicylic acids and phenols whose activities, or efficacy, are known. Using a regression analysis, we show that improving the treatment of electron correlation beyond previous studies enhances the statistical correlation between clinical activities and ionization energies.     

Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine

The method of extrapolation by intrinsic scaling, recently introduced to obtain correlation energies, is generalized to multiconfigurational reference functions and used to calculate the binding energies of the diatomic molecules C2, N2, O2, and F2. First, accurate approximations to the full configuration interaction energies of the individual molecules and their constituent atoms are determined, employing Dunning's correlation consistent double-, triple- and quadruple zeta basis sets. Then, these energies are extrapolated to their full basis set limits. Chemical accuracy is attained for the binding energies of all molecules.     

On the accuracy of second-order Møller-Plesset correlation energies

Accurate second-order Møller-Plesset correlation energies are computed and compared with several semi-empirical estimates of the total correlation energies including those provided by Clementi, Anno and Teruya, and the recent results of Davidson, Froese and co-workers, for atoms with ten, twelve and eighteen electrons. Somewhat surprisingly, the MP2 correlation energies present what is considered to be in good agreement with the newest estimates, especially when the behaviour with the nuclear charge is examined.     

Inclusion of correlations in He, Be, and Ne by the configuration interaction method

The influence of various approximations used to include correlations in He, Be, and Ne atoms on correlation energies and on the structure of correlation functions is analyzed. The effects of three-and four-electron correlations are evaluated. For He, Be, and Ne atoms, the correlation energies were found to equal 99.99, 100.11, and 97.9% of the experimental value, respectively. A method of obtaining a one-electron function basis is proposed to ensure the best convergence of correlation energies as the number of included configurations increases. Translated fromZhurnal Struktumoi Khimii, Vol. 39, No. 6, pp. 1001–1012, November–December, 1998.     

HF,Ne等电子体系对内对间电子相关能的比较研究

采用MELD程序ROHF－OPT1方法在MP2/6-311++G(d)水平上,计算了HF分子基态1^∑和Ne原子基态1^S的对内对间电子相关能,并对两等电子体系的对相关能进行了分析和比较,深入研究两等电子体系对内对间相关能所具有的共同规律和存在的差异性,通过比较说明分子内的化学键是影响电子相关能的重要因素之一。HF分子和Ne原子两体系三重激发和四重激发对体系电子相关能的贡献的计算结果表明高激发项对电子相关能的贡献在精确量子化学计算中是不可以忽略的。     

Dyson-corrected orbital energies for the perturbative treatment of electron correlation

The effect of replacing the Hartree–Fock one-particle energies with ionization potentials obtained from inverse Dyson equation when calculating electron correlation energies perturbatively is investigated. Though the energy shifts vary from system to system, the slight decrease of the resulting excitation energies at around equilibrium geometries leads to a slight increase of the correlation energies in most cases. In the dissociation limit the inverse Dyson equation opens the gap, thus nondiverging potential curves emerge even at the restricted Hartree–Fock (RHF)+RS2 level. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 713–719, 1998     

Basis set and correlation effects on computed positive ion hydrogen bond energies of the complexes AHn · AHn + 1+1: AHn = NH3, OH2, and FH

Basis set expansion and correlation effects on computed hydrogen bond energies of the positive ion complexes AH_n · AH_{n + 1}⁺¹, for AH_n = NH₃, OH₂ and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms is the single most important enhancement of split-valence plus polarization basis sets for computing hydrogen bond energies. Basis set enhancement effects appear to be additive in these systems. The correlation energy contribution to the stabilization energies of these complexes is significant, with the second order term being the largest term and having a stabilizing effect. The third order term is smaller and of opposite sign, while the fourth order term is smaller yet and stabilizing. As a result, computed MP4 stabilization energies are bracketed by the MP2 and MP3 energies. The overall effect of basis set enhancement is to decrease hydrogen bond energies, whereas the addition of electron correlation increases stabilization energies.     

HX体系电子对内、对间相关研究

在6-311+G^*基组水平上用CISD（configurationinteractionwithsinglyanddoublyexcitedconfigurations)方法研究HX(X=Li-F,HBe)体系电子对内、对间的相关能。计算结果表明不同元素形成的HX(X=Li-F,HBe^+,HBe)体系,其价层电子对内、对间相关能的变化较大,它们之间存在着轨道差别,不宜将其相关贡献归为简单的常数。在使用相同理论方法和相同质量基组的前提下,电子数将直接影响到电子对间相关能的大小。对于多电子体系,电子对间相关在总相关中占有优势,若将其忽略会引起较大误差。     

On the nature of DNA-duplex stability

The unwinding free energy of 128 DNA octamers was correlated with the sum of interaction energies among DNA bases and their solvation energies. The former energies were determined by using the recently developed density functional theory procedure augmented by London dispersion energy (RI-DFT-D) that provides accurate hydrogen-bonding and stacking energies highly comparable with CCSD(T)/complete basis set limit benchmark data. Efficient tight-binding DFT covering dispersion energy was also used and yielded satisfactory results. The latter method can be used for extended systems. The solvation energy was determined by using a C-PCM continuum solvent at HF level calculations. Various models were adopted to correlate theoretical energies with experimental unwinding free energies. Unless all energy components (hydrogen-bonding, intra- and interstrand-stacking, and solvation energies) were included and weighted individually, no satisfactory correlation resulted. The most advanced model yielded very close correlation (RMSE=0.32 kcal mol(-1)) fully comparable with the entirely empirical correlation introduced in the original paper. Analysis of the theoretical results shows the importance of inter- and intramolecular stacking energies, and especially the latter term plays a key role in determining DNA-duplex stabilization.     

Estimation of the ground state correlation energy for isoelectronic series of 2 to 20 electrons

Correlation energies for all isoelectronic sequences of 2 to 20 electrons andZ=2 to 25 are obtained by taking differences between theoretical total energies of Dirac-Fock calculations and experimental total energies. These are pure relativistic correlation energies because relativistic and QED effects are already taken care of. The theoretical as well as the experimental values are analysed critically in order to get values as accurate as possible. The correlation energies obtained show an essentially consistent behaviour fromZ=2 to 17. ForZ>17 inconsistencies occur indicating errors in the experimental values which become very large forZ>25.     

Universal density functional approach to the calculation of correlation energies of atoms

A new local density functional approach for the calculation of correlation energies of many-electron atomic systems is proposed by using the exact results for the correlation energy of a two-electron system bound by a harmonic oscillator external potential. This is motivated by the fact that the correlation energy is a universal functional of the electron density, and the form of this functional is independent of the external potential. The calculated numerical results for the correlation energies show very good agreement with the standard values reported in the literature. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 461–465, 1997     

A family of intracules, a conjecture and the electron correlation problem

We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the two-electron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.     

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.     

Application of Wigner and Husimi intracule based electron correlation models to excited states

A new approach to the electron correlation problem based on phase space intracules derived from the Wigner distribution is applied to excited states. The computed electron correlation energy reduces the mean absolute error in the prediction of the excitation energies of 55 atomic excited states from 0.65 eV for unrestricted Hartree-Fock to 0.32 eV. This compares favorably to a mean absolute deviation of 0.52 eV for second order Moller-Plesset perturbation theory and 0.35 eV for the Lee-Yang-Parr functional. An analogous correlation model based on the Husimi distribution is developed. Predicted correlation energies and excitation energies from this model are significantly worse than for the Wigner intracule based model. Alternative correlation kernels may be more suitable for the Husimi intracule based approach.     

Empirical correlation methods for temporary anions

A temporary anion is a short-lived radical anion that decays through electron autodetachment into a neutral molecule and a free electron. The energies of these metastable species are often predicted using empirical correlation methods because ab initio predictions are computationally very expensive. Empirical correlation methods can be justified in the framework of Weisskopf-Fano-Feshbach theory but tend to work well only within closely related families of molecules or within a restricted energy range. The reason for this behavior can be understood using an alternative theoretical justification in the framework of the Hazi-Taylor stabilization method, which suggests that the empirical parameters do not so much correct for the coupling of the computed state to the continuum but for electron correlation effects and that therefore empirical correlation methods can be improved by using more accurate electronic structure methods to compute the energy of the confined electron. This idea is tested by choosing a heterogeneous reference set of temporary states and comparing empirical correlation schemes based on Hartree-Fock orbital energies, Kohn-Sham orbital energies, and attachment energies computed with the equation-of-motion coupled-cluster method. The results show that using more reliable energies for the confined electron indeed enhances the predictive power of empirical correlation schemes and that useful correlations can be established beyond closely related families of molecules. Certain types of σ* states are still problematic, and the reasons for this behavior are analyzed. On the other hand, preliminary results suggest that the new scheme can even be useful for predicting energies of bound anions at a fraction of the computational cost of reliable ab initio calculations. It is then used to make predictions for bound and temporary states of the furantrione and croconic acid radical anions.     

Multiple bonds and excited states from the Hartree-Fock-Heitler-London method

The recently proposed Hartree-Fock-Heitler-London, HF-HL, method (Corongiu, G. J. Phys. Chem. A 2006, 110, 11584) previously tested for single bond molecules is validated by potential energy computations for open and closed shells, single and multiple bonds, in ground and excited states of homopolar diatomic molecules of the first and second period. The simple HF-HL function, including the configurations for 2s/2p near degeneracy and avoiding state crossing, yields correct dissociation products, qualitatively correct binding, and accounts for non-dynamical correlation. Addition of ionic structures improves the ab initio HF-HL function and yields about 95% of the experimental binding energies on average. Computed excitation energies are also in agreement with laboratory values as verified for the 3 Pi u and 3 Zeta g- excited states of the C2 molecule. Computation of the remaining dynamical correlation using a semiempirical functional yields binding energies with an average deviation of 1.5 kcal/mol from laboratory values, and total energies with an average deviation of 0.7 kcal/mol from exact nonrelativistic dissociation energies.