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.     

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

The recently developed [P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 (2005)] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2Si[Double Bond]SiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R=1-3Re for all of the studied single bond-breaking reactions, where R and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R=1-3Re of the H-SiH3, H-Cl, H3Si-SiH3, Cl-CH3, H-CH3, and H3C-SiH3 bonds. The maximum errors are -2.1, 1.6, and 1.6 mhartree in the R=1-3Re region of the H3C-CH3, Cl-Cl, and H3Si-Cl bonds, respectively, while the discrepancy for the H2Si[Double Bond]SiH2 double bond-breaking reaction is 6.6 (8.5) mhartree at R=2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T).     

Low-lying quartet electronic states of nitrogen dioxide

The environmentally active molecule nitrogen dioxide (NO2) has been systematically studied using high level theoretical methods. The electronic ground state and the low-lying quartet states of NO2 have been investigated. Single reference restricted open-shell self-consistent field (SCF), complete active space SCF (CASSCF), spin-restricted (R) and spin-unrestricted (U) configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), CCSD with perturbative triple excitations [CCSD(T)], and internally contracted multireference configuration interaction (ICMRCI) methods along with Dunning's correlation consistent polarized valence cc-pVXZ and augmented cc-pVXZ (where X=T,Q,5) basis sets were used in this research. At the aug-cc-pV5Z/UCCSD(T) level the classical adiabatic excitation energies (Te values) of the three lowest-lying quartet excited states were predicted to be 83.3 kcalmol (3.61 eV, 29 200 cm(-1)) for the ? 4A2 state, 93.3 kcalmol (4.05 eV, 32 600 cm(-1)) for the b 4B2 state, and 100.8 kcalmol (4.37 eV, 35 300 cm(-1)) for the c 4A1 state. The quantum mechanical excitation energies (T 0 values) were determined to be 81.6 kcalmol (3.54 eV, 28 500 cm(-1)) for the a 4A2 state and 90.7 kcalmol (3.93 eV, 31 700 cm(-1)) for the b 4B2 state. The lowest quartet linear Renner-Teller 4Pi state gives rise to the a 4A2 state with 112.8 degrees and the b 4B2 state with 124.4 degrees <(ONO) bond angles upon bending. The b state shows some peculiar behavior. Although CASSCF, RCISD, UCISD, RCCSD, UCCSD, and RCCSD(T) methods predicted the presence of a Cs equilibrium geometry (a double minimum 4A' state), SCF, UCCSD(T), and ICMRCI wave functions predicted the C2v structure for the b 4B2 state. The importance of both dynamical and nondynamical correlation treatments for the energy difference between C2v and Cs structures of b state is highlighted in this context. The c 4A1 state is predicted to have a very small bond angle of 85.8 degrees . Potential energy diagrams with respect to the bond angles of the ground state and four quartet states are presented.     

Open-shell singlet character of cyclacenes and short zigzag nanotubes

The electronic ground states of [n]cyclacenes, as well as short-zigzag nanotubes, computed at unrestricted broken spin-symmetry density functional theory (UBS-DFT), were found to be open-shell singlets, rather than triplets. Computations for [6]cyclacene at complete active space self-consistent field (CASSCF) and multireference perturbation theory (MRMP2) levels support this conclusion. Along with strain, the radical character of the open-shell singlet with antiferromagnetically coupled electron spins may contribute to the difficulties in synthesizing [n]cyclacenes.     

Performance of the spin-flip and multireference methods for bond breaking in hydrocarbons: a benchmark study

Benchmark results for spin-flip (SF) coupled-cluster and multireference (MR) methods for bond-breaking in hydrocarbons are presented. The nonparallelity errors (NPEs), which are defined as an absolute value of the difference between the maximum and minimum values of the errors in the potential energy along bond-breaking curves, are analyzed for (i) the entire range of nuclear distortions from equilibrium to the dissociation limit and (ii) in the intermediate range (2.5-4.5 A), which is the most relevant for kinetics modeling. For methane, the spin-flip and MR results are compared against full configuration interaction (FCI). For the entire potential energy curves, the NPEs for the SF model with single and double substitutions (SF-CCSD) are slightly less than 3 kcal/mol. Inclusion of triple excitations reduces the NPEs to 0.32 kcal/mol. The corresponding NPEs for the MR-CI are less than 1 kcal/mol, while those of multireference perturbation theory are slightly larger (1.2 kcal/mol). The NPEs in the intermediate range are smaller for all of the methods. The largest errors of 0.35 kcal/mol are observed, surprisingly, for a spin-flip approach that includes triple excitations, while MR-CI, CASPT2, and SF-CCSD curves are very close to each other and are within 0.1-0.2 kcal/mol of FCI. For a larger basis set, the difference between MR-CI and CASPT2 is about 0.2 kcal/mol, while SF-CCSD is within 0.4 kcal/mol of MR-CI. For the C-C bond breaking in ethane, the results of the SF-CCSD are within 1 kcal/mol of MR-CI for the entire curve and within 0.4 kcal/mol in the intermediate region. The corresponding NPEs for CASPT2 are 1.8 and 0.4 kcal/mol, respectively. Including the effect of triples by energy-additivity schemes is found to be insignificant for the intermediate region. For the entire range of nuclear separations, sufficiently large basis sets are required to avoid artifacts at small internuclear separations.     

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76).     

Full CI benchmark calculations for molecular properties

Full CI calculations of first- and second-order properties are presented to provide benchmark results for comparisons with other methods, such as multireference CI(MRCI). The full CI(FCI) polarizability of F^– is computed using a double zeta plus polarization plus diffuse basis set. These FCI results are compared to those obtained at other levels of theory; the CASSCF/MRCI with Davidson correction results are in excellent agreement with the FCI. Differences between the polarizability results computed as a (numerical) second derivative of the energy or as an induced dipole moment are also discussed. FCI calculations are presented for the dipole moment and polarizability of HF, CH₂ and SiH₂ using a DZP basis set. Again, the CASSCF/MRCI values are in excellent agreement with the FCI results, whereas SDCI values, whether computed as an expectation value or as an energy derivative, are much worse. The results obtained using the CPF approach are in considerably better agreement with the FCI results than SDCI, and are similar in quality to the SDCI energy derivative results with the inclusion of Davidson's correction.     

New ab initio coupled potential energy surfaces for the Br(2P(3∕2), 2P(1∕2)) + H2 reaction

The three lowest (1A('), 2A('), and 1A(')) adiabatic potential energy surfaces (PESs) for the Br((2)P) + H(2) reactive system have been computed based on the multi-reference configuration interaction (MRCI) method including the Davidson's correction with a large basis set. These three adiabatic PESs have been transformed to a diabatic representation, leading to four coupling potentials. In addition, the spin-orbit matrix elements were also obtained using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Consequently, six coupling potentials were obtained and their characteristics were extensively discussed. Nonadiabatic quantum dynamics calculations for this system have been realized with these realistic diabatic potentials instead of previous semi-empirical diabatic potentials. Based on two-state model nonadiabatic calculations for the Br((2)P(3∕2), (2)P(1∕2)) + H(2) reaction, the Br((2)P(1∕2)) + H(2) reaction was found to show less reactivity than the Br((2)P(3∕2)) + H(2) reaction at collision energies beyond the threshold of the Br((2)P(3∕2)) + H(2) reaction. Our results are consistent with the previous studies on the XH(2) (X = F, Cl) system, which indicate that the adiabatically forbidden channel is dominant at low energies in the open-shell halogen atom plus H(2) reactions.     

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.     

Spin-orbit configuration interaction study of the electronic structure of the 5f (2) manifold of U(4+) and the 5f manifold of U(5+)

The energy levels of the 5f configuration of U(5+) and 5f(2) configuration of U(4+) have been calculated in a dressed effective Hamiltonian relativistic spin-orbit configuration interaction framework. Electron correlation is treated in the scalar relativistic scheme with either the multistate multireference second-order multiconfigurational perturbation theory (MS-CASPT2) or with the multireference single and double configuration interaction (MRCI) and its size-extensive Davidson corrected variant. The CASPT2 method yields relative energies which are lower than those obtained with the MRCI method, the differences being the largest for the highest state (1)S(0) of the 5f(2) manifold. Both valence correlation effects and spin-orbit polarization of the outer-core orbitals are shown to be important. The satisfactory agreement of the results with experiments and four-component correlated calculations illustrates the relevance of dressed spin-orbit configuration interaction methods for spectroscopy studies of heavy elements.     

A theoretical study of the mechanism and kinetics of F+N3 reactions.

Both the singlet(1A') and triplet(3A') potential energy surfaces (PESs) of F+N(3) reactions are investigated using the complete-active-space self-consistent field (CASSCF) and the multireference configuration interaction (MRCI) methods with a proper active space. The minimum energy crossing point (MECP) at the intersection seam between the 1A' and 3A' PESs is located and used to clarify the reaction mechanisms. Two triplet transition states are found, with one in the cis form and the other one in the trans form. Further kinetic calculations are performed with the canonical unified statistical (CUS) theory on the singlet PES and the improved canonical variational transition-state (ICVT) method on the triplet PES. The rate constants are also reported. At 298 K, the calculated rate constant is in reasonably good agreement with experimental values, and spin-orbit coupling effects lower it by 28 %. The spectroscopic constants derived from the fitted potential-energy curves for the singlet and triplet states of NF are in very good agreement with experimental values. Our calculations indicate that the adiabatic reaction on the singlet PES leading to NF(a(1)Delta)+N(2) is the major channel, whereas the nonadiabatic reaction through the MECP, which leads to NF(X(3)Sigma(-))+N(2), is a minor channel.     

Nonadiabatic quantum reactive scattering of the OH(A 2Σ+) + D2

The seams of conical intersection exist between the ground (1 (2)A(')) and the first-excited (2 (2)A(')) electronic potential energy surfaces (PESs) of OH(A (2)Σ(+),X (2)Π) + H(2) system. This intersection induces the nonadiabatic quenching of OH(A (2)Σ(+)) by D(2). We present nonadiabatic quantum dynamics study for OH(A (2)Σ(+)) + D(2) on new five-dimensional coplanar PESs. The ab initio calculations of PESs are based on multireference configuration interaction (MRCI)/aug-cc-pVQZ level. A back-propagation neural network is utilized to fit the PESs and nonadiabatic coupling. High degrees of rotational excitation of quenched OH(X (2)Π) products are found in nonreactive quenching channel, and the quenched D(2) products are vibrationally excited up to quantum number v(2) (')=8. The theoretical results of nonadiabatic time-dependent wave-packet calculation are in good agreement with the existing experimental data.     

Comparing electronic structure predictions for the ground state dissociation of vinoxy radicals

This paper reports a series of electronic structure calculations performed on the dissociation pathways of the vinoxy radical (CH(2)CHO). We use coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)), complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and MRCI with the Davidson correction (MRCI+Q) to calculate the barrier heights of the two unimolecular dissociation pathways of this radical. The effect of state averaging on the barrier heights is investigated at the CASSCF, MRCI, and MRCI+Q levels. The change in mixing angle along the reaction path is calculated as a measure of derivative coupling and found to be insufficient to suggest nonadiabatic recrossing. We also present a new analysis of previous experimental data on the unimolecular dissociation of ground state vinoxy. In particular, an error in the internal energy distribution of vinoxy radicals reported in a previous paper is corrected and a new analysis of the experimental sensitivity to the onset energy (barrier height) for the isomerization reaction is given. Combining these studies, a final "worst case" analysis of the product branching ratio is given and a statistical model using each of the calculated transition states is found to be unable to correctly reproduce the experimental data.     

Global ab initio potential energy surfaces for the O2(3Σg-)+O2(3Σg-) interaction

Completely ab initio global potential energy surfaces (PESs) for the singlet and triplet spin multiplicities of rigid O(2)((3)Σ(g)(-))+O(2)((3)Σ(g)(-)) are reported for the first time. They have been obtained by combining an accurate restricted coupled cluster theory with singles, doubles, and perturbative triple excitations [RCCSD(T)] quintet potential [Bartolomei et al., J. Chem. Phys. 128, 214304 (2008)] with complete active space second order perturbation theory (CASPT2) or, alternatively, multireference configuration interaction (MRCI) calculations of the singlet-quintet and triplet-quintet splittings. Spherical harmonic expansions, containing a large number of terms due to the high anisotropy of the interaction, have been built from the ab initio data. The radial coefficients of these expansions are matched at long range distances with analytical functions based on recent ab initio calculations of the electric properties of the monomers [M. Bartolomei, E. Carmona-Novillo, M. I. Hernández, J. Campos-Martínez, and R. Hernández-Lamoneda, J. Comput. Chem. (2010) (in press)]. The singlet and triplet PESs obtained from either RCCSD(T)-CASPT2 or RCCSD(T)-MRCI calculations are quite similar, although quantitative differences appear in specific terms of the expansion. CASPT2 calculations are the ones giving rise to larger splittings and more attractive interactions, particularly in the region of the absolute minima (in the rectangular D(2h) geometry). The new singlet, triplet, and quintet PESs are tested against second virial coefficient B(T) data and, their spherically averaged components, against integral cross sections measured with rotationally hot effusive beams. Both types of multiconfigurational approaches provide quite similar results, which, in turn, are in good agreement with the measurements. It is found that discrepancies with the experiments could be removed if the PESs were slightly more attractive. In this regard, the most attractive RCCSD(T)-CASPT2 PESs perform slightly better than the RCCSD(T)-MRCI counterpart.     

Ab initio study of low-lying electronic states of SnCl2+

Complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and restricted-spin coupled-cluster singles-doubles with perturbative triples [RCCSD(T)] calculations have been carried out on low-lying doublet and quartet states of SnCl2+, employing basis sets of up to aug-cc-pV5Z quality. Effects of core correlation and off-diagonal spin-orbit interaction on computed vertical ionization energies were investigated. The best theoretical estimate of the adiabatic ionization energy (including zero-point vibrational energy correction) to the X2A1 state of SnCl2+ is 10.093+/-0.010 eV. The first photoelectron band of SnCl2 has also been simulated by employing RCCSD(T)/aug-cc-pV5Z potential energy functions and including Duschinsky rotation and anharmonicity.     

Reduced multireference coupled cluster method with singles and doubles: Perturbative corrections for triples

The reduced multireference coupled-cluster method with singles and doubles (RMR CCSD) that employs multireference configuration interaction wave function as an external source for a small subset of approximate connected triples and quadruples, is perturbatively corrected for the remaining triples along the same lines as in the standard CCSD(T) method. The performance of the resulting RMR CCSD(T) method is tested on four molecular systems, namely, the HF and F(2) molecules, the NO radical, and the F(2) (+) cation, representing distinct types of molecular structure, using up to and including a cc-pVQZ basis set. The results are compared with those obtained with the standard CCSD(T), UCCSD(T), CCSD(2), and CR CCSD(T) methods, wherever applicable or available. An emphasis is made on the quality of the computed potentials in a broad range of internuclear separations and on the computed equilibrium spectroscopic properties, in particular, harmonic frequencies omega(e). It is shown that RMR CCSD(T) outperforms other triply corrected methods and is widely applicable.     

High-level ab initio studies of the electronic excited states of the hydroxyl radical and water-hydroxyl complex

The lowest-energy electronic transitions in the hydroxyl radical and the hydrogen bound complex H(2)O.HO have been studied using ab initio methods. We have used the complete active-space self-consistent field and multireference configuration interaction (MRCI) methods to calculate vertical excitation energies and oscillator strengths. At the MRCI level the lowest-lying (2)Sigma(+)<--(2)Pi electronic transition is redshifted by about 2500 cm(-1) upon formation of the H(2)O.HO complex. We propose that this transition could be used to identify the complex in the gas phase, which in turn could be used to examine the role of H(2)O.HO in atmospheric reactions.     

Multireference second-order perturbation theory: how size consistent is "almost size consistent"

A systematic study of the deviation from size consistency of the multireference second-order Moller-Plesset perturbation theory (MRMP2) method is presented. The size-consistency error is shown to depend on the number of monomers in a supermolecule calculation, size of basis set, number of correlated valence electrons, and size of active space. HF, F(2), and N(2) are used as test cases, with stretched bonds, to include simple, well-defined multireference character. This is essential in ensuring that MRMP2 is being tested as a multireference method. It is concluded that the MRMP2 and other multireference perturbation theory methods can exhibit significant size-consistency errors, and that the size of the error depends on the manner in which the perturbation theory is implemented.     

The X1Sigmag+, B1Deltag, and B' 1Sigmag+ states of C2: a comparison of renormalized coupled-cluster and multireference methods with full configuration interaction benchmarks

Unusual bonding and electronic near degeneracies make the lowest-lying singlet states of the C2 molecule particularly challenging for electronic structure theory. Here we compare two alternative approaches to modeling bond-breaking reactions and excited states: sophisticated multireference configuration interaction and multireference perturbation theory methods, and a more "black box," single-reference approach, the completely renormalized coupled-cluster method. These approximate methods are assessed in light of their ability to reproduce the full configuration interaction potential energy curves for the X1Sigmag+, B1Deltag, and B' 1Sigmag+ states of C2, which are numerically exact solutions of the electronic Schrodinger equation within the space spanned by a 6-31G* basis set. Both the multireference methods and the completely renormalized coupled-cluster approach provide dramatic improvements over the standard single-reference methods. The multireference methods are nearly as reliable for this challenging test case as for simpler reactions which break only single bonds. The completely renormalized coupled-cluster approach has difficulty for large internuclear separations R in this case, but over the wide range of R=1.0-2.0 A, it compares favorably with the more complicated multireference methods.