Correlation Energy Of Molecules Research Articles

Possibilities of Distributive Gaussian sp-Functions for Calculating the Correlation Energy of Molecules in the Ground and Excited States

The possibilities of distributive bases from Gaussian sp-functions for calculating the correlation energy of molecules in the second order (Е(2)) of the Moller–Plesset perturbation theory (MPPT) have been investigated. The effectiveness of such bases has been demonstrated by comparing the Е(2) values obtained in distributive and standard atom-centered bases. Calculations have been performed for both the ground and excited states with ground symmetry. For this purpose, an analog of Moller–Plesset perturbation theory for excited states that preserves its advantages for the ground state has been developed. It has been shown that distributive sp-functions provide the accuracy of calculating Е(2) that is comparable to that of atom-centered bases including s-, p-, and d-functions.

Quantum Chemistry in Dataflow: Density-Fitting MP2.

We demonstrate the use of dataflow technology in the computation of the correlation energy in molecules at the Møller-Plesset perturbation theory (MP2) level. Specifically, we benchmark density fitting (DF)-MP2 for as many as 168 atoms (in valinomycin) and show that speed-ups between 3 and 3.8 times can be achieved when compared to the MOLPRO package run on a single CPU. Acceleration is achieved by offloading the matrix multiplications steps in DF-MP2 to Dataflow Engines (DFEs). We project that the acceleration factor could be as much as 24 with the next generation of DFEs.

Parallel Calculation of the Electron Correlation Energy

Calculation of electron correlation energy in molecules involves a very important computational effort, even in the simplest cases. Nowadays, using the new parallel libraries (PETSc and SLEPc) and MPI, we can resolve this calculation faster and with very big molecules. This result is a very important advance in chemical computation.

Estimation of atomic correlation energies from the electron density at the nucleus and atomic additivity of the correlation energy in molecules

A new method based on electron density at the nucleus is presented to determine electron correlation energy in atomic species. Using the nuclear-electron coalescence cusp condition, we have shown that the atomic correlation energy can be well represented by different power of atomic number for different isoelectronic series. The computed correlation energies have been achieved chemical accuracy with average absolute deviation in the order of 1 kcal/mol for 17 isoelectronic series. Also it is shown that the correlation energy for a molecule can be expressed in terms of the correlation energies of its constituent atoms and its number of electrons. The proposed formula confirms that in a molecule the electron correlation is larger than the sum over electron correlations of its corresponding constituent atoms.

Scaling Dynamical Correlation Energy from Density Functional Theory Correlation Functionals

The scaling of dynamical correlation energy in molecules obtained by the correlation functionals of density functional theory (DFT) is examined. The approach taken is very similar to the scaled external correlation method of Brown and Truhlar but is based on the observation that DFT correlation functionals, especially the LYP, appear to represent the dynamical portion of the correlation energy in molecules. We examine whether higher accuracy in atomization energies can be gained by scaling without significant deterioration of the structural and spectroscopic properties of the molecules using four DFT functionals (BLYP, OLYP, B3LYP, and O3LYP) on 19 molecules including the six molecule AE6 database, the latter being representative of a much larger, 109 molecule training set. We show that, with molecule specific scale factors, nearly perfect agreement with experiment can be achieved in atomization energies without increasing the average errors in other molecular properties relative to the DFT calculation. We further show that it is possible to find optimal scale factors which reduce the mean unsigned error per bond to levels comparable to those of some multilevel multicoefficient methods.

Atomic Additivity of the Correlation Energy in Molecules by the DFT-B3LYP Scheme

The problem of the electron correlation in the DFT-B3LYP method is considered. It is suggested that the effective correlation energy can be retrieved by a difference = E(B3LYP) − E(HF). Subsequently, it is shown that exhibits remarkable atomic additivity, similar to that found earlier for ab initio MP2, MP3, MP4, and G3 methods. Performance of the additivity formula in reproducing the B3LYP correlation energies of Lewis' systems described by a single dominant resonance structure is astonishing as evidenced by AAD = 1.3 kcal/mol and R2 = 0.99999. The effective correlation energies span a very large range of values extending from 199 to 1963 for the cc-pVDZ basis sets and from 204 to 1980 (in kcal/mol) if the G3Large basis set is employed. The calculations can be performed on the back of an envelope by elementary arithmetic operations. Importantly, it is shown that there is a close relation between and the correlation energy calculated by the G3 computational scheme. Moreover, it turns out that their differ...

Atomic additivity of the correlation energy in molecules—an ab initio MP4 and G3 study

It is shown that the closed shell valence electron molecular correlation energy of organic molecules in their ground states is a homogeneous multilinear function of the numbers of neutral atoms in their canonical hybridization state. The additivity is a robust feature, which holds for MP2(fc), MP3(fc) and MP4(fc) model calculations. The latter results obtained on a test set of 91 widely different organic molecules, exhibiting a whole gamut of electronic structure patterns, are excellent as evidenced by the absolute average deviation from the additivity values (AAD) of only 1.4 kcal mol−1 and R 2 = 0.999 93. The maximum absolute deviation (MAD) is 5.3 kcal mol−1. The additivity formula for the total molecular electron correlation retrieved from G3 calculations also has an excellent performance (AAD = 1.2 kcal mol−1, R 2 = 0.999 98 and MAD = 7.2 kcal mol−1). If it is taken into account that the additivity formulae require only back of the envelope calculations, these results are remarkable indeed, in particular since the G3 correlation energies span a very large range from 180.7 (methane) to 1642.8 (hexafluorocyclopropane) kcal mol−1. Comparison of the exact electron correlation energies in free atoms with the corresponding average correlation energies in molecules reveals that a substantial increase in the latter provides an important contribution in overcoming a very strong Coulomb repulsion between the nuclei. It is shown that the additivity formulae are useful in detecting some special molecular features such as strong resonance and anti-aromaticity.

Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides

The effective core potential and model potential methods were used in post-SCF calculations on HC1, HBr, Cl2, and Br2 in order to gain insight into the effect of insufficient representation of inner nodes in the valence orbitals of the approximate methods. The results show that while the correlation energy may be slightly overestimated (by 1–7%), both the electric moment functions and the quantities depending on energy differences are consistently similar for the methods studied and close to the results from all-electron calculations.

A simple method to calculate the correlation energy in molecules based on the bond orbital approximation

It is the main scope of this work to present a transparent numerical approach for the determination of interatomic correlation energies in molecules. The analysis is of model character, i.e. the presentation of quantitative numerical data is not intended. Our simple analytical method to calculate the correlation energy is based on the bond orbital approximation (BOA) for the mean-field ground state and on the local approach (LA) to electron correlation. The interatomic correlation energy is obtained as a sum of various intrabond and interbond contributions, for which simple analytic formulae are derived. In this way, the dependence of electron correlation on bond polarities, two-electron integrals and kinetic hopping elements becomes transparent. The remaining intra-atomic part of the correlation energy is described by analytic expressions which depend only on the total charge and the number of p and s electrons on a given atom. Therefore, the total correlation energy may be estimated by using the information available from the self-consistent field calculation. As an example, an application of the method to a number of molecules of the general topology X-Y≡Y-Z is presented. The correlation energies obtained in an analytic way agree rather well with those given by a direct numerical evaluation within the LA.

A general method for approximating the electronic correlation energy in molecules and solids

A detailed analysis of a method proposed earlier for calculating a good approximation to the electronic correlation energy is presented here. The principal advantages of this method compared to the usual CI techniques are discussed.

Pade approximants and many-body perturbation theory: an application to the CH+ion

Pade approximants to the diagrammatic many-body perturbation expansion for electron correlation energies in molecules are discussed. The numerical convergence properties of the perturbation expansion and the Pade approximants which can be formed from it are compared. Calculations of the ground-state potential energy curve for the CH+ ion are reported. Systems, such as CH+, which contain low-lying excited states, can be handled by forming (2/1) Pade approximants from third-order calculations using 'shifted' denominators.

The effect of disconnected wavefunction clusters of double excitations on the correlation energy of molecules

The effect of quadruply excited configurations through the fourth order of MB RSPT on the correlation energy of molecules is studied. The correlation energy of the BH. H 2O and N 2 molecules is calculated in such a way that the second plus third order of MB RSPT are included fully, and from the fourth order of MB RSPT only those diagrams are included which correspond to quadruply excited configurations. This correlation energy is compared with that obtained by CI calculations including quadruply excited configurations. Two effects can be studied by these calculations, namely, the size inconsistency terms in CI, as well as the net quadruple excitation effect, i.e. the further lowering of the correlation energy by quadruply excited configurations.

Extension of the Local Approach to excited states of molecules

The Local Approach for the calculation of electronic correlation energies in molecules is generalized to excited states. Within the Local Approach correlated states are obtained by applying a local projection operator on the Hartree-Fock ground state or simple reference states, which are used as zeroth order approximations for the excited states, respectively. In the case of excited states one has in addition to require the correlated states to be orthogonal on the states lower in energy. This is done by using Schmidt's orthogonalization. The method is applied to a simple model of the H6-ring for which an exact solution is available. The results obtained are of comparable quality as for the ground state.

Description of intraatomic correlations by the Local Approach

The Local Approach for calculating correlation energies of molecules is formulated for intraatomic correlations. This is an extension of earlier work in which it was successfully applied to interatomic correlations. In order to treat intraatomic correlations the atomic volume is divided into subspaces. The Hartree-Fock ground state is modified by decreasing electronic double occupancies of those subspaces. This leads to a generation of a correlation hole. A detailed description is given for the construction of the required subspaces. The theory is applied for the purpose of demonstration to the He and Be atoms, to the H2-molecule and to a system of two He atoms. A comparison with CI-calculations shows that only few percents of the correlation energy are missing when similar basis sets are used. The advantage of the Local Approach is its intrinsic simplicity and that it operates in a much smaller configuration space than the CI-method. This makes it an appropriate method for the treatment of larger systems.

A group contribution method applied to electronic correlation energies of molecules

Abstract 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.

Semi-empirical effective pair correlation parameters and correlation energies of BH, CH, NH, OH, HF, N2, and CH4

A set of approximations (“EPCE-F2σ”) is given for estimating the correlation energies of molecules. The approximations start from Sinanoglu's pair correlations and his many-electron theory for ground states (MET). For application of this method, “effective pair correlation energies” must be known. In the present paper three sets of one-center effective pair correlation energies are obtained from the atomic pair correlation energies. A weighted average method is introduced for handling the non-transferable atomic correlation energies. For the corresponding two-center effective pair correlation energies several empirical expressions are given. Then using three sets of one-center effective pair correlation energies and for the two-center ones, the correlation energies of some diatomic hydrides, N2 and CH4 molecules are estimated. The results agree quite well with each other, with experimental values, and with those obtained by other methods.