Systematically convergent correlation consistent basis sets for molecular core-valence correlation effects: the third-row atoms gallium through krypton

The family of correlation consistent polarized valence basis sets has been extended in order to account for core-core and core-valence correlation effects within the third-row, main group atoms gallium through krypton. Construction of the basis sets is similar to that of the atoms boron through argon, where either the difference between core-correlated and valence-only correlation energies were calculated via configuration interaction (CISD) computations on the ground electronic states of the atoms (named cc-pCVnZ) or the sets were optimized with respect to the core-valence correlation energy and a small weight of core-core correlation energy (cc-pwCVnZ). Due to the correlation of 3d orbitals, added shells of higher angular momentum exponents compared to the valence sets are necessary to describe the core region. The pattern of added core-correlating functions is (1s1p1d1f) for double-zeta, (2s2p2d2f1g) for triple-zeta, (3s3p3d3f2g1h) for quadruple-zeta, and (4s4p4d4f3g2h1i) for quintuple-zeta. Atomic and molecular results show good convergence to the CBS limit, with the cc-pwCVnZ sets showing improved convergence compared to the cc-pCVnZ ones for molecular core-valence correlation effects. After testing the basis sets on the homonuclear diatomics Ga2-Kr2 with coupled cluster wave functions, it is concluded that a treatment of core-valence correlation effects is essential for high-accuracy ab initio investigations of third-row-containing molecules. Though the basis sets are optimal for 3s3p3d correlation, preliminary atomic and molecular results show the basis sets to be efficient with respect to 3d-only correlation, and these potentially could be used with 3d-only correlation for more qualitative studies on larger species.     

van der Waals interactions and dipole polarizabilities of lanthanides: Tm(2F)-He and Yb(1S)-He potentials

Anisotropic dipole polarizabilities of Tm(2F), Tm+2(2F), and Yb(1S) are calculated using the finite-field multireference averaged quadratic coupled cluster (MR-AQCC) (Tm and Tm+2) and RCCSD(T) (Yb) methods with small-core relativistic pseudopotentials ECP28MWB combined with the augmented ANO basis sets. The lanthanide atoms are strongly polarizable with the scalar part originating from the 6s electrons and the tensorial part from the open 4f shells. The adiabatic interaction potentials 2Sigma+, 2Pi, 2Delta, and 2Phi of Tm(2F)-He and Tm+2(2F)-He were examined by the multireference approaches, multireference configuration interaction and MR-AQCC, using the basis sets designed in the polarizability calculations. A closed-shell lanthanide system Yb(1S)-He was included for comparison. The Tm-He 2Sigma+, 2Pi, 2Delta, and 2Phi interaction potentials are very shallow and nearly degenerate (within 0.01 cm(-1)), with the well depths in the range of 2.35-2.36 cm(-1) at R=6.17 A. The basis-set saturated well depths are expected to be larger by ca. 25%, as estimated using the bond-function augmented basis set. The interactions of lanthanide atoms with He are one order of magnitude less anisotropic than those involving first-row transition metal atoms. The suppression of anisotropy is chiefly attributed to the screening effected by the 6s shell. When these electrons are removed as in the di-cation complex Tm+2(2F)-He, the potentials deepen to a thousand wave number range and their anisotropy is enhanced 500-fold.     

Low-lying electronic states of FeNC and FeCN: a theoretical journey into isomerization and quartet/sextet competition

With several levels of multireference and restricted open-shell single-reference electronic structure theory, optimum structures, relative energetics, and spectroscopic properties of the low-lying (6)Delta, (6)Pi, (4)Delta, (4)Pi, and (4)Sigma(-) states of linear FeNC and FeCN have been investigated using five contracted Gaussian basis sets ranging from Fe[10s8p3d], C/N[4s2p1d] to Fe[6s8p6d3f2g1h], C/N[6s5p4d3f2g]. Based on multireference configuration interaction (MRCISD+Q) results with a correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis set, appended with core correlation and relativistic corrections, we propose the relative energies: T(e)(FeNC), (6)Delta(0)<(6)Pi (2300 cm(-1))<(4)Delta (2700 cm(-1))<(4)Pi (4200 cm(-1))<(4)Sigma(-); and T(e)(FeCN), (6)Delta(0)<(6)Pi (1800 cm(-1))<(4)Delta (2500 cm(-1))<(4)Pi (2900 cm(-1))<(4)Sigma(-). The (4)Delta and (4)Pi states have massive multireference character, arising mostly from 11sigma-->12sigma promotions, whereas the sextet states are dominated by single electronic configurations. The single-reference CCSDT-3 (coupled cluster singles and doubles with iterative partial triples) method appears to significantly overshoot the stabilization of the quartet states provided by both static and dynamical correlation. The (4,6)Delta and (4,6)Pi states of both isomers are rather ionic, and all have dipole moments near 5 D. On the ground (6)Delta surface, FeNC is predicted to lie 0.6 kcal mol(-1) below FeCN, and the classical barrier for isocyanide/cyanide isomerization is about 6.5 kcal mol(-1). Our data support the recent spectroscopic characterization by Lei and Dagdigian [J. Chem. Phys. 114, 2137 (2000)] of linear (6)Delta FeNC as the first experimentally observed transition-metal monoisocyanide. Their assignments for the ground term symbol, isotopomeric rotational constants, and the Fe-N omega(3) stretching frequency are confirmed; however, we find rather different structural parameters for (6)Delta FeNC:r(e)(Fe-N)=1.940 A and r(N-C)=1.182 A at the cc-pVQZ MRCISD+Q level. Our results also reveal that the observed band of FeNC originating at 27 236 cm(-1) should have an analog in FeCN near 23 800 cm(-1) of almost equal intensity. Therefore, both thermodynamic stability and absorption intensity factors favor the eventual observation of FeCN via a (6)Pi<--(6)Delta transition in the near-UV.     

Mixed-sector intermediate Hamiltonian Fock-space coupled cluster approach

An alternative formulation of the intermediate Hamiltonian Fock-space coupled cluster scheme developed before is presented. The methodological and computational advantages of the new formulation include the possibility of using a model space with determinants belonging to different Fock-space sectors. This extends the scope of application of the multireference coupled cluster method, and makes possible the use of quasiclosed shells (e.g., p2, d4) as reference states. Representative applications are described, including electron affinities of group-14 atoms, ionization potentials of group-15 elements, and ionization potentials and excitation energies of silver and gold. Excellent agreement with experiment (a few hundredths of an electronvolt) is obtained, with significant improvement (by a factor of 5-10 for p3 states) over Fock-space coupled cluster results. Many states not reachable by the Fock-space approach can now be studied.     

An ab initio benchmark study of the H + CO --> HCO reaction

The H + CO --> HCO reaction has been characterized with correlation consistent basis sets at five levels of theory in order to benchmark the sensitivities of the barrier height and reaction ergicity to the one-electron and n-electron expansions of the electronic wave function. Single and multireference methods are compared and contrasted. The coupled cluster method RCCSD(T) was found to be in very good agreement with Davidson-corrected internally-contracted multireference configuration interaction (MRCI+Q). Second-order Moller-Plesset perturbation theory (MP2) was also employed. The estimated complete basis set (CBS) limits for the barrier height (in kcal/mol) for the five methods, including harmonic zero-point energy corrections, are MP2, 4.66; RCCSD, 4.78; RCCSD(T), 4.15; MRCI, 5.10; and MRCI+Q, 4.07. Similarly, the estimated CBS limits for the ergicity of the reaction are: MP2, -17.99; RCCSD, -13.34; RCCSD(T), -13.79; MRCI, -11.46; and MRCI+Q, -13.70. Additional basis set explorations for the RCCSD(T) method demonstrate that aug-cc-pVTZ sets, even with some functions removed, are sufficient to reproduce the CBS limits to within 0.1-0.3 kcal/mol.     

High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems

For the first time high-order excitations (n>2) have been studied in three multireference couple cluster (MRCC) theories built on the wave operator formalism: (1) the state-universal (SU) method of Jeziorski and Monkhorst (JM) (2) the state-specific Brillouin-Wigner (BW) coupled cluster method, and (3) the state-specific MRCC approach of Mukherjee (Mk). For the H4, P4, BeH(2), and H8 models, multireference coupled cluster wave functions, with complete excitations ranging from doubles to hextuples, have been computed with a new arbitrary-order string-based code. Comparison is then made to corresponding single-reference coupled cluster and full configuration interaction (FCI) results. For the ground states the BW and Mk methods are found, in general, to provide more accurate results than the SU approach at all levels of truncation of the cluster operator. The inclusion of connected triple excitations reduces the nonparallelism error in singles and doubles MRCC energies by a factor of 2-10. In the BeH(2) and H8 models, the inclusion of all quadruple excitations yields absolute energies within 1 kcal mol(-1) of the FCI limit. While the MRCC methods are very effective in multireference regions of the potential energy surfaces, they are outperformed by single-reference CC when one electronic configuration dominates.     

Orbital invariance issue in multireference methods

The orbital invariance problem is analyzed from the tensor theory point of view, with an emphasis on multireference coupled cluster methods. Using the transformation properties of second‐quantized operators, we discuss the orbital invariance properties of various methods by examining the tensor properties of the residual equations. A simple self‐consistency‐checking algorithm is proposed. We first establish the orbital invariance properties for the Hartree–Fock, single reference configuration interaction, single reference coupled cluster, complete‐active‐space self‐consistent‐field, and multireference configuration interaction methods, and then discuss the invariance properties of the complete‐active‐space coupled cluster and CCSDt methods. Finally, we demonstrate theoretically the lack of orbital invariance for Jeziorski–Monkhorst ansatz based methods. It appears necessary to modify the ansatz to achieve orbital invariance, and internal contraction serves as one possible solution. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Molecular core-valence correlation effects involving the post-d elements Ga-Rn: benchmarks and new pseudopotential-based correlation consistent basis sets

Correlation consistent basis sets that are suitable for the correlation of the outer-core (n-1)spd electrons of the post-d elements Ga-Rn have been developed. These new sets, denoted by cc-pwCVXZ-PP (X=D,T,Q,5), are based on the previously reported cc-pVXZ-PP sets that were built in conjunction with accurate small-core relativistic pseudopotentials (PPs) and designed only for valence nsp correlation. These new basis sets have been utilized in benchmark coupled cluster calculations of the core-valence correlation effects on the dissociation energies and spectroscopic properties of several small molecules. As expected, the most important contribution is the correlation of the (n-1)d electrons. For example, in the case of the group 13 homonuclear diatomics (Ga(2),In(2),Tl(2)), this leads to a dissociation energy increase compared to a valence-only treatment from 1.5 to 3.2 kcal/mol, bond length shortenings from -0.076 to -0.125 A?, and harmonic frequency increases of 7-8?cm(-1). Even in the group 15 cases (As(2),Sb(2),Bi(2)), the analogous effects of (n-1)d electron correlation are certainly not insignificant, the largest values being +4.4?kcal/mol, -0.049 A?, and +9.6?cm(-1) for the effects on D(e), r(e), and ω(e), respectively. In general, the effects increase in magnitude down a group from 4p to 6p. Correlation of the outer-core (n-1)p electrons is about an order of magnitude less important than (n-1)d but larger than that of the (n-1)s. The effect of additional tight functions for Hartree-Fock and valence sp correlation was found to be surprisingly large, especially for the post-4d and post-5d elements. The pseudopotential results for the molecules containing post-3d elements are also compared to the analogous all-electron calculations employing the Douglas-Kroll-Hess Hamiltonian. The errors attributed to the PP approximation are found to be very small.     

Calculation of electric dipole transition moments using quasi-degenerate variational perturbation theory and averaged coupled-pair functional theory

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH₂, and A1H using multireference singles and doubles configuration interaction, quasi-degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi-degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH₂, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled-pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.     

Toward accurate thermochemical models for transition metals: G3Large basis sets for atoms Sc-Zn

An augmented valence triple-zeta basis set, referred to as G3Large, is reported for the first-row transition metal elements Sc through Zn. The basis set is constructed in a manner similar to the G3Large basis set developed previously for other elements (H-Ar, K, Ca, Ga-Kr) and used as a key component in Gaussian-3 theory. It is based on a contraction of a set of 15s13p5d Gaussian primitives to 8s7p3d, and also includes sets of f and g polarization functions, diffuse spd functions, and core df polarization functions. The basis set is evaluated with triples-augmented coupled cluster [CCSD(T)] and Brueckner orbital [BD(T)] methods for a small test set involving energies of atoms, atomic ions, and diatomic hydrides. It performs well for the low-lying s-->d excitation energies of atoms, atomic ionization energies, and the dissociation energies of the diatomic hydrides. The Brueckner orbital-based BD(T) method performs substantially better than Hartree-Fock-based CCSD(T) for molecules such as NiH, where the starting unrestricted Hartree-Fock wavefunction suffers from a high degree of spin contamination. Comparison with available data for geometries of transition metal hydrides also shows good agreement. A smaller basis set without core polarization functions, G3MP2Large, is also defined.     

The lowest 2A' excited state of the water-hydroxyl complex

Vertical and adiabatic excitation energies of the lowest (2)A(') excited state in the water-hydroxyl complex have been determined using coupled cluster, multireference configuration interaction, multireference perturbation theory, and density-functional methods. A significant redshift of about 0.4 eV in the vertical excitation energy of the complex compared to that of the hydroxyl radical monomer is found with the coupled cluster calculations validating previous results. Electronic excitation leads to a structure with near-equal sharing of the hydroxyl hydrogen by both oxygen atoms and a concomitantly large redshift of the adiabatic excitation energy of approximately 1 eV relative to the vertical excitation energy. The combination of redshifts ensures that the electronic transition in the complex lies well outside the equivalent excitation in the hydroxyl radical monomer. The complex is approximately five times more strongly bound in the excited state than in the ground state.     

Comparison of some multireference electronic structure methods in illustrative applications

The performances of several multireference electronic structure methods including complete active space self-consistent field (CASSCF)-based second-order perturbation theory (CASPT2), multireference configuration interaction with single and double excitations (MR-CISD), MR-CISD with the Davidson correction (MR-CISD+Q), and the CASSCF-based block-correlated coupled cluster method (CAS-BCCC4) we developed recently are compared by applying them to study several different chemical problems involving computation...     

Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism

In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with exact full configuration interaction results for small systems (H(2)O, N(2), and Be(3)). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups.     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Investigation of challenging spin systems using Monte Carlo configuration interaction and the density matrix renormalization group

We investigate if a range of challenging spin systems can be described sufficiently well using Monte Carlo configuration interaction (MCCI) and the density matrix renormalization group (DMRG) in a way that heads toward a more “black box” approach. Experimental results and other computational methods are used for comparison. The gap between the lowest doublet and quartet state of methylidyne (CH) is first considered. We then look at a range of first‐row transition metal monocarbonyls: MCO when M is titanium, vanadium, chromium, or manganese. For these MCO systems we also employ partially spin restricted open‐shell coupled‐cluster (RCCSD). We finally investigate the high‐spin low‐lying states of the iron dimer, its cation and its anion. The multireference character of these molecules is also considered. We find that these systems can be computationally challenging with close low‐lying states and often multireference character. For this more straightforward application and for the basis sets considered, we generally find qualitative agreement between DMRG and MCCI. © 2017 Wiley Periodicals, Inc.     

Electronically excited states of water clusters of 7-azaindole: structures, relative energies, and electronic nature of the excited states

The geometries of 1H-7-azaindole and the 1H-7-azaindole(H(2)O)(1-2) complexes and the respective 7H tautomers in their ground and two lowest electronically excited pi-pi(*) singlet states have been optimized by using the second-order approximated coupled cluster model within the resolution-of-the-identity approximation. Based on these optimized structures, adiabatic excitation spectra were computed by using the combined density functional theory/multireference configuration interaction method. Special attention was paid to comparison of the orientation of transition dipole moments and excited state permanent dipole moments, which can be determined accurately with rotationally resolved electronic Stark spectroscopy. The electronic nature of the lowest excited state is shown to change from L(b) to L(a) upon water complexation.