Pair Functional Method Research Articles

Spin-Free [2]R12 Basis Set Incompleteness Correction to the Local Multireference Configuration Interaction and the Local Multireference Average Coupled Pair Functional Methods.

The local multireference configuration interaction (LMRCI) and local multireference averaged coupled pair functional (LMRACPF) methods are extended to include explicit correlation via the universal spin-free [2]R12 basis set incompleteness correction. Four test cases are examined to measure the performance of the LMRCI+[2]R12 (without and with the Davidson + Q correction for size-extensivity) and LMRACPF+[2]R12 methods. These tests examine bond dissociation energies (BDEs) for ethene, perfluoroethene, propene, and 2-butene. As has been demonstrated for other methods, the LMRCI+[2]R12/LMRCI+Q+[2]R12/LMRACPF+[2]R12 BDEs are as accurate as the conventional LMRCI/LMRACPF BDEs that are computed with the basis set one cardinal number higher. It is shown that LMRCI+[2]R12/LMRCI+Q+[2]R12/LMRACPF+[2]R12 BDEs computed with the June calendar basis sets preserve the accuracy of the corresponding BDEs computed with the conventional aug-cc-pVXZ basis sets (where X = D, T, Q).

Bond dissociation energies of C10 and C18 methyl esters from local multireference averaged-coupled pair functional theory.

We previously developed a fast, local, reduced scaling Cholesky-decomposed multireference averaged-coupled pair functional (CD-LMRACPF2) method, which takes advantage of the locality of dynamic correlation and numerical approximations such as Cholesky decomposition and integral screening. Motivated by the desire to study large biodiesel methyl ester molecules, here we validate CD-LMRACPF2 for the computation of bond dissociation energies (BDEs) in a suite of oxygenated molecules, and show that the low-cost method is very accurate compared to the conventional variant. We then demonstrate the power of CD-LMRACPF2 for fast and accurate computation of energies of molecules containing up to 13 second-row atoms within a polarized triple-ζ (cc-pVTZ) basis set. We use biodiesel methyl esters as a chemically interesting model system and furnish BDEs of C10 and C18 methyl esters, with the latter performed within a cc-pVDZ basis set. We describe trends in the BDEs and explain how structural (isomeric) differences affect BDEs, as well as discuss implications of BDE trends for biodiesel physical and chemical properties.

On the structure of Si(100) surface: Importance of higher order correlations for buckled dimer

We revisit a dangling theoretical question of whether the surface reconstruction of the Si(100) surface would energetically favor the symmetric or buckled dimers on the intrinsic potential energy surfaces at 0 K. This seemingly simple question is still unanswered definitively since all existing density functional based calculations predict the dimers to be buckled, while most wavefunction based correlated treatments prefer the symmetric configurations. Here, we use the doubly hybrid density functional (DHDF) geometry optimizations, in particular, XYGJ-OS, complete active space self-consistent field theory, multi-reference perturbation theory, multi-reference configuration interaction (MRCI), MRCI with the Davidson correction (MRCI + Q), multi-reference average quadratic CC (MRAQCC), and multi-reference average coupled pair functional (MRACPF) methods to address this question. The symmetric dimers are still shown to be lower in energy than the buckled dimers when using the CASPT2 method on the DHDF optimized geometries, consistent with the previous results using B3LYP geometries [Y. Jung, Y. Shao, M. S. Gordon, D. J. Doren, and M. Head-Gordon, J. Chem. Phys. 119, 10917 (2003)]. Interestingly, however, the MRCI + Q, MRAQCC, and MRACPF results (which give a more refined description of electron correlation effects) suggest that the buckled dimer is marginally more stable than its symmetric counterpart. The present study underlines the significance of having an accurate description of the electron-electron correlation as well as proper multi-reference wave functions when exploring the extremely delicate potential energy surfaces of the reconstructed Si(100) surface.

Explicitly correlated multireference configuration interaction: MRCI-F12

An internally contracted multireference configuration interaction is developed which employs wave functions that explicitly depend on the electron-electron distance (MRCI-F12). This MRCI-F12 method has the same applicability as the MRCI method, while having much improved basis-set convergence with little extra computational cost. The F12b approximation is used to arrive at a computationally efficient implementation. The MRCI-F12 method is applied to the singlet-triplet separation of methylene, the dissociation energy of ozone, properties of diatomic molecules, and the reaction barrier and exothermicity of the F + H(2) reaction. These examples demonstrate that already with basis sets of moderate size the method provides near complete basis set MRCI accuracy, and hence quantitative agreement with the experimental data. As a side product, we have also implemented the explicitly correlated multireference averaged coupled pair functional method (MRACPF-F12).

Hg + Br → Hg Br recombination and collision-induced dissociation dynamics

A global potential energy surface has been constructed for the system HgBr+Ar-->Hg+Br+Ar to determine temperature dependent rate constants for the collision-induced dissociation (CID) and recombination of Hg and Br atoms. The surface was decomposed using a many-body expansion. Accurate two-body potentials for HgBr, HgAr, and ArBr were calculated using coupled cluster theory with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)], as well as the multireference averaged coupled pair functional method. Correlation consistent basis sets were used to extrapolate to the complete basis set limit and corrections were included to account for scalar and spin-orbit relativistic effects, core-valence correlation, and the Lamb shift. The three-body potential was computed with the CCSD(T) method and triple-zeta quality basis sets. Quasiclassical trajectories using the final analytical potential surface were directly carried out on the CID of HgBr by Ar for a large sampling of initial rotational, vibrational, and collision energies. The recombination rate of Hg and Br atoms is a likely first step in mercury depletion events that have been observed in the Arctic troposphere during polar sunrise. The effective second order rate constant for this process was determined in this work from the calculated CID rate as a function of temperature using the principle of detailed balance, which resulted in k(T) = 1.2 x 10(-12) cm(3) molecule(-1) s(-1) at 260 K and 1 bar pressure.

Basis set limit electronic excitation energies, ionization potentials, and electron affinities for the 3d transition metal atoms: Coupled cluster and multireference methods

Recently developed correlation consistent basis sets for the first row transition metal elements Sc-Zn have been utilized to determine complete basis set (CBS) scalar relativistic electron affinities, ionization potentials, and 4s(2)3d(n-2)-4s(1)d(n-1) electronic excitation energies with single reference coupled cluster methods [CCSD(T), CCSDT, and CCSDTQ] and multireference configuration interaction with three reference spaces: 3d4s, 3d4s4p, and 3d4s4p3d'. The theoretical values calculated with the highest order coupled cluster techniques at the CBS limit, including extrapolations to full configuration interaction, are well within 1 kcal/mol of the corresponding experimental data. For the early transition metal elements (Sc-Mn) the internally contracted multireference averaged coupled pair functional method yielded excellent agreement with experiment; however, the atomic properties for the late transition metals (Mn-Zn) proved to be much more difficult to describe with this level of theory, even with the largest reference function of the present work.

Size extensive modification of local multireference configuration interaction.

We recently developed a reduced scaling multireference configuration interaction (MRCI) method based on local correlation in the internal (occupied) and external (virtual) orbital spaces. This technique can be used, e.g., to predict bond dissociation energies in large molecules with reasonable accuracy. However, the inherent lack of size extensivity of truncated CI is a disadvantage that in principle worsens as the system size grows. Here we implement an a priori size-extensive modification of local MRCI known as the averaged coupled pair functional (ACPF) method. We demonstrate that local MR-ACPF recovers more correlation energy than local MRCI, in keeping with trends observed previously for nonlocal ACPF. We test the size extensivity of local ACPF on noninteracting He atoms and a series of hydrocarbons. Basis set and core correlation effects are explored, as well as bond breaking in a variety of organic molecules. The local MR-ACPF method proves to be a useful tool for investigating large molecules and represents a further improvement in predictive accuracy over local MRCI.

Size-consistent multireference configuration interaction method through the dressing of the norm of determinants

A new determinant-specific, effective change (‘dressing’) of the norm of the multireference configuration interaction (MRCI) wavefunction is proposed in order to achieve the size-consistency of the MRCI method. The new approach provides a unifying framework for analysis of size-consistent extensions of the MRCI method that are based on the coupled pair functional (CPF) strategy and lead to simplified computations of the analytical gradients. Using the new framework, a generalized multireference full coupled pair functional (MR-FCPF) method is introduced. The MR-FCPF method may be viewed as a functional counterpart of the recently proposed generalized (‘full’) coupled electron pair approximation (CEPA), referred to as the size-consistent self-consistent CI ((SC)2CI) method. A straightforward extension of the MR-FCPF method leads to a pseudo-functional form of the coupled cluster (CC) type formalisms. Therefore, the new approach may be used to introduce a simple alternative to existing CC-type gradient techniques. The new procedure is formally derived and compared with similar methods from the literature. Model systems calculations (H2O, LiF, CH+ 2) are further used to demonstrate the effect of various approximations and to elucidate the hierarchy of functional MR-CEPA schemes.

Alternative configuration interaction expansions for transition metal ions with intermediate oxidation states in crystals: The structure and absorption spectrum of Cs2GeF6:Mn4+

The vertical absorption spectrum of the MnF62− cluster embedded in the Cs2GeF6 host crystal was recently calculated using the averaged coupled pair functional method leading to very large discrepancies with accurate one- and two-photon spectra. The same multiconfigurational expansions had previously been successful in similar systems which involved transition metal impurities in lower oxidation states. In this paper we show that the ligand-to-metal charge transfer configurations become so important in this intermediate oxidation state impurity (and, possibly, non-negligible ligand–ligand weak bonding interactions) that none of the 18 molecular orbitals of F 2p character should be left inactive in the correlation treatment. This requirement can be satisfied in MnF62− because of the higher oxidation state of manganese, which enhances the ligand field splittings in the Mn 3d3 configuration manifold so much that one dominant Mn 3d3 configuration rather than the full Mn 3d3 active space can be used as a single reference for single and double excitations from all occupied ligand 2p orbitals. The results of this work, together with those of previous studies, outline two different alternative truncation schemes of the valence electron correlation which produce the same, necessary, high accuracy in structural and spectroscopic properties of transition metal ions doped in ionic crystals. Whether one or the other should be used depends, basically, on the formal oxidation state of the transition metal impurity.

The pair-functional method for direct solution of molecular structures. I. Statistical principles.

The pair-functional principle shows how to construct a unique statistical ensemble of strongly interacting atoms that corresponds to any feasible measured set of X-ray intensities. The ensemble and all its distribution functions are strictly periodic in the crystal lattice, so that each unit cell has exactly the same arrangement of atoms at all times. The mean particle density in the cell is uniform because the ensemble has undefined phases and the origin is not fixed. The atoms in this maximum-entropy ensemble interact through pairwise additive periodic statistical forces within the unit cell. The ensemble average pair-correlation function is matched to the observed originless Patterson function of the crystal. The derived pairing force then becomes approximately proportional to the Ornstein-Zernicke direct correlation function of the ensemble. The atoms have a many-body Boltzmann distribution and the logarithm of the likelihood of any particular conformation is related to its total pairing potential. The pairing potential of a group of atoms acts like a local field in the cell. This property is used in the pair-functional method. Molecular structures can be solved by a direct search in real space for clusters of atoms with high pair potentials. During a successful search, the atoms move from their original random positions to form larger and larger clusters of correctly formed fragments. Finally, every atom belongs to a single cluster, which is the correct solution.

Direct structure solution by a pair-functional method with self-consistent fields

Direct structure solution by a pair-functional method with self-consistent fields

Molecular adsorption of methane and methyl onto MgO(100) An embedded-cluster study

Embedded cluster models have been used to model the molecular adsorption of methane and methyl at the perfect (100) surface of MgO. Energies are computed using the modified coupled pair functional method, with corrections for basis set superposition errors applied both during geometry optimization and to adsorption energies. In the case of methane, interadsorbate interactions are taken into account through ab initio pair-interaction energies, facilitating adsorption energies at monolayer coverage. Methane is found to adsorb preferentially at magnesium sites, in a dipod configuration, i.e. with two hydrogen atoms pointed down and towards oxide anions. At monolayer coverage, neighboring methane molecules are rotated 90° relative to each other, keeping the dipod orientation. An adsorption energy of 8.5 kJ mol −1 is obtained for methane, which is somewhat low compared to experimental estimates. Methyl adsorbs preferably over Mg 2+ sites, with a binding energy only slightly higher than for methane. No elements of covalency was detected in the bond between the radical and the MgO(100) surface.

Structures and potential energy surface of faujasitic zeolite/water

The structures and the potential energy surface of the system faujasitic zeolite/water have been investigated by Hartree-Fock, second-order Moller-Plesset (MP2) and by the density functional theory (DFT) calculations, using five basis sets 6-31G(d), 6-31G(d,p), 6-311G(d), 6-311G(d,p) and 6-311 + G(d,p). The DFT calculations employ the Becke-3-Lee-Yang-Parr (B3LYP) and Becke-Lee-Yang-Parr (BLYP) density functional, and, for comparisons, the local density approximation with the Vosko-Wilk-Nusair (VWN) functional. The B3LYP approach is found to yield better agreement with the corresponding experimental results than the VWM and BLYP functionals. The B3LYP amd MP2 levels of theory yield basically the same results. Results of B3LYP with a 6-311 + G(3df,2p) basis set are also very close to those of the very accurate coupled pair functional (CPF) method. Also proton affinities (PA) computed by B3LYP reproduce the corresponding CPF and G1 results very well. The predicted PA of faujasitic catalyst is estimated to be 294 ± 3 kcal/mol, which is in the range of the experimentally determined value of 291–300 kcal/mol. The interaction of faujasite catalyst with water has revealed that the structures can be stabilized by the formation of two hydrogen bonds with water molecules adsorbed at the bridging hydroxyl groups which can act either as a proton acceptor or as a proton donor. Comparison of the faujasite complexes with silanol and hydrogen halides has demonstrated that the faujasitic zeolite is a strong acid. The potential energy surfaces of faujasite zeolite/water has been investigated and analytical interaction potentials have been derived.

First row benchmark tests of the parametrized configuration interaction with parameter X (PCI-X) scheme

A recently suggested scheme termed parametrized configuration interaction with parameter X (PCI-X) for scaling the correlation energy has been applied on a benchmark test consisting of 32 first row molecules. Several different methods like Mo/ller–Plesset second-order perturbation theory (MP2), modified coupled pair functional method (MCPF), averaged coupled pair functional method (ACPF), coupled cluster singles and doubles (CCSD), and CCSD with a perturbational estimate of triple excitations [CCSD(T)] have been tested using systematically chosen basis sets ranging from double zeta (DZ) to very large atomic natural orbital (ANO) sets containing several sets of d and f functions. For each method and basis set the scaling parameter is optimized. The scaling does in all cases lead to large, sometimes dramatic, improvements of the results. Typically, using a single reference state method like MCPF the average absolute deviation compared to experiments for the benchmark goes from an unscaled value of about 20 kcal/mol down to about 2 kcal/mol. For MCPF and similar methods no improvement of the results is obtained going beyond the DZ+polarization (DZP) level. Significant improvements due to scaling occurs even at the highest level using the CCSD(T) method and the largest basis set. For medium size basis sets the present scaling is far superior to the extrapolation schemes used in the Gaussian-1 and -2 (G1 and G2) theories.

Quantum chemical predictions of the electron affinities of carbon-hydrogen clusters C2nH·, the CH binding energies and the gas phase acidities of polyacetylenes C2nH2forn= 1–3

Accurate data for the adiabatic electron affinities of the radicals C2n H·, the CH bond dissociation energies and the gas phase acidities of the polyacetylenes C2n H2 for n = 1–3 have been obtained using the complete active space SCF approach to optimize the geometries and coupled cluster, and for some cases multi-reference configuration interaction and averaged coupled pair functional methods to refine the energies in connection with the polarized basis sets due to Sadlej and the generally contracted atomic natural orbitals basis sets, respectively. Harmonic frequencies have been computed for all species using a density functional theory/Hartree-Fock hybrid approach employing the Becke3LYP functional and the 6-311G** basis set. Our final theoretical predictions for the electron affinities are 2·96 ± 0·04, 3·46 ± 0·07 and 3·69 ± 0·07 eV for C2H·, C4H· and C6H·, respectively. For the CH binding energies and gas phase acidities we predict D 0 = 131·7 ± 1·2, 130·2 ± 2·0, and 127·5 ± 2·0 kcal mol-1 and ΔG acid,298 = 369·5 ± 2·1, 356·3 ± 3·6 and 348·7 ± 3·6 kcal mol-1 for C2H2, C4H2 and C6H2, respectively. Where available, these data compare very well with experimental results. In addition, the question of the ground state of the C4H· radical has been settled. It is of 2Π symmetry, with the 2Σ+ state lying only some 3 kcal mol-1 higher in energy. Hence there is no ‘alternation rule’ for the ground state of the species C n H· as all of them except C2H· assume a 2Π ground state.

Binding energies, molecular structures, and vibrational frequencies of transition metal carbonyls using density functional theory with gradient corrections

The performance of the density functional theory (DFT) methods with different gradient corrections as an approach for the computation of transition metal complexes has been evaluated. As a test, the structures, binding energies, and vibrational frequencies of a series of binary transition metal carbonyl complexes were calculated. Comparison with previous studies shows that the gradient correction significantly improves the performance of the DFT schemes, and that the results obtained generally match the quality of the data obtained from coupled cluster and pair functional methods.

Ab initio Study of the Potential Curves for CO (X1Σ+), CH (X2Π) and OH (X2Π)

Calculations on spectroscopic properties of the diatomic systems CO, CH, and OH have been carried out by the multiconfiguration SCF, single reference and multireference single and double excitation CI, and average coupled pair functional methods. An evaluation of the different theoretical approaches is performed in order to get better insight into the selection of appropriate procedures for the calculation of the potential energy surface of the H + CO system.

The spectroscopy and dynamics of the n=3,4 Rydberg states in O+2

An experimental and theoretical study is presented on the (4s) 2Σ+g, (3p) 2Σ+u, 2Πu, and (3d) 2Σ+g, 2Πg, 2Δg Rydberg states in O+2. Their spectroscopic properties (T0,ωe,ωexe) have been determined using translational spectroscopy. The Rydberg molecules are formed in collisions of fast O2+2 ions with atomic Cs, K, and Na. The potential energy curves of the Rydberg states have been calculated using a self-consistent field/averaged coupled pair functional (SCF/ACPF) method and agree well with the experimental results. The (3p) 2Σ+u state is strongly perturbed by the lowest valence state of the same symmetry. The Rydberg-valence interactions leading to the predissociative decay are discussed.

Tungsten hexahydride (WH6). An equilibrium geometry far from octahedral

Ab initio all-electron quantum mechanical methods were applied to the tungsten hexahydride (WH6) molecule using very large basis sets. Seven distinct structures were investigated with full geometry optimizations at the self-consistent field (SCF) level of theory. The effects of electron correlation were estimated with second-order Mo/ller–Plesset perturbation theory (MP2), modified coupled pair functional (MCPF) method, and the coupled cluster with single and double excitations (CCSD) method, and relativistic effects estimated using the Cowan–Griffin (mass–velocity and Darwin) corrections. Our results suggest that the ground state of the tungsten hexahydride (WH6) molecule is a closed-shell triangular prism belonging to the C3v point group, with a set of three hydrogens stacked on top of another set of three hydrogens. From the perspective of inorganic chemistry, it is truly remarkable that the octahedral structure lies 130 kcal/mol above the C3v ground state. Furthermore, these results imply major qualitative differences between WH6 and the well-known W(CH3)6 molecule. Another C3v structure, with one set of three hydrogens staggered with respect to the other set, is energetically nearby. With MCPF and relativistic corrections at the SCF optimized geometry, a third low-lying structure belonging to the C5v point group is virtually degenerate with the triangular prism C3v structure.

Hydrogen bonded complexes of HCl with CO, C2H2, C2H4, PH3, H2S, HCN, H2O and NH3

The results of ab initio quantum chemical calculations carried out using the MP2 perturbation and averaged coupled pair functional (ACPF) methods are reported on hydrogen bonded binary complexes of HCl with CO, C2H2, C2H4, PH3, H2S, HCN, H2O and NH3. The geometries, vibrational frequencies and related quantities such as zero point vibrational energies, librational amplitudes, infrared intensities, etc., have been computed at the MP2 level, while the ACPF method has been used to obtain electric field gradients, dipole moments and also dissociation energies. The theoretical predictions of geometries, intermolecular stretching frequencies, librational amplitudes and 35Cl nuclear quadrupole coupling constants are in good agreement with the corresponding experimental data. The effects of basis set superposition have been found to be significant in the case of the dissociation energies. Exploratory calculations on the NH3 … HCl complex, using atomic natural orbital (ANO) bases, demonstrate, however, that a significant reduction in the superposition error can be achieved with ANO's. The results of coupled cluster calculations, performed also on NH3 … HCl, indicate that triple excitations can make a substantial contribution to the dispersion energy.