Electronic states of NaLi molecule: Benchmark results with Fock space coupled cluster approach.

Accurate potential energy curves (PECs) are obtained for 20 lowest lying electronic states of the NaLi molecule. The computational scheme used here is based on the multireference coupled cluster theory formulated in the (2,0) sector of the Fock space. The latter sector provides the description of states obtained by attachment of two electrons to the reference system. This makes it possible to adopt the doubly ionized NaLi+2 molecule as a Fermi vacuum. The latter has a very concrete advantage in calculations of the PECs since it dissociates into closed shell fragments (NaLi+2 → Na+ + Li+); hence, the restricted Hartree-Fock method can be used within the whole range of interatomic distances. Computed PECs and spectroscopic constants stay very close to the experimental values (if the latter are available) with the accuracy exceeding the other theoretical approaches including those based on the effective core polarization potentials. Relativistic corrections included at the infinite-order two-component level have a non-negligible effect on the accuracy of computed excitation and dissociation energies with contributions up to 50 cm-1.

Extension of the Fock-space coupled-cluster method with singles and doubles to the three-valence sector.

The single-reference coupled-cluster method has proven very effective in the ab initio description of atomic and molecular systems, but its successful application is limited to states dominated by a single Slater determinant, which is used as the reference. In cases where several determinants are important in the wave function expansion, i.e., we have to deal with nondynamic correlation effects, a multi-reference version of the coupled-cluster method is required. The multi-reference coupled-cluster approaches are based on the effective Hamiltonian formulation providing a two-step procedure, in which dynamic correlation effects can be efficiently evaluated by the wave operator, while nondynamic correlation contributions are given by diagonalization of the effective Hamiltonian in the final step. There are two classical multi-reference coupled-cluster formulations. In this paper, the focus is on the so-called Fock-space coupled-cluster method in its basic version with one- and two-particle operators in the exponent. Computational schemes using this truncation of the cluster operator have been successfully applied in calculations in one- and two-valence sectors of the Fock space. In this paper, we show that the approach can be easily extended and effectively employed in the three-valence sector calculations.

Potential Energy Curves for the Low-Lying Electronic States of K2+ from ab Initio Calculations with All Electrons Correlated.

The electron affinity (EA) calculations based on the equation-of-motion coupled cluster method proved to be an efficient scheme in the treatment of potential energy curves (PECs) for alkali molecular ions, Me2+. The EA approach provides description of states obtained by an attachment of one electron to the reference, which for the Me2+ is a doubly ionized Me2+2 system. The latter has a very concrete advantage in the calculations of the PECs, since it dissociates into the closed-shell fragments (Me2+2 → Me+ + Me+); hence, the restricted Hartree-Fock reference can be used in the whole range of interatomic distances. In this work accurate PECs and spectroscopic constants are obtained for the six lowest-lying electronic states of the K2+ ion. The relativistic effects are included by adding appropriate terms of the Douglas-Kroll Hamiltonian to the one-electron integrals.

Equation-of-motion coupled cluster method for the description of the high spin excited states.

The equation-of-motion (EOM) coupled cluster (CC) approach in the version applicable for the excitation energy(EE) calculations has been formulated for high spin components. The EE-EOM-CC scheme based on the restricted Hartree-Fock reference and standard amplitude equations as used in the Davidson diagonalization procedure yields the singlet states. The triplet and higher spin components require separate amplitude equations. In the case of quintets, the relevant equations are much simpler and easier to solve. Out of 26 diagrammatic terms contributing to the R1 and R2 singlet equations in the case of quintets, only R2 operator survives with 5 diagrammatic terms present. In addition all terms engaging three body elements of the similarity transformed Hamiltonian disappear. This indicates a substantial simplification of the theory. The implemented method has been applied to the pilot study of the excited states of the C2 molecule and quintet states of C and Si atoms.

Equation-of-motion coupled cluster method for high spin double electron attachment calculations.

The new formulation of the equation-of-motion (EOM) coupled cluster (CC) approach applicable to the calculations of the double electron attachment (DEA) states for the high spin components is proposed. The new EOM equations are derived for the high spin triplet and quintet states. In both cases the new equations are easier to solve but the substantial simplification is observed in the case of quintets. Out of 21 diagrammatic terms contributing to the standard DEA-EOM-CCSDT equations for the R2 and R3 amplitudes only four terms survive contributing to the R3 part. The implemented method has been applied to the calculations of the excited states (singlets, triplets, and quintets) energies of the carbon and silicon atoms and potential energy curves for selected states of the Na2 (triplets) and B2 (quintets) molecules.

First Principle Calculations of the Potential Energy Curves for Electronic States of the Lithium Dimer.

A multireference coupled cluster (CC) approach formulated in the (2,0) sector of the Fock space (FS) is applied to study electronic states of the Li2 molecule. The CC model including single (S) and double (D) excitations from the reference configuration is considered. The FS-CCSD(2,0) method is applicable to the description of the double electron attached states, which implies that in the neutral molecule studies the doubly ionized reference should be adopted. The results of this study include potential energy curves (PECs) and selected spectroscopic constants for 34 electronic states correlating to five lowest dissociation limits of Li2. Both the PECs and the computed spectroscopic constants agree very well with the experimental data wherever the latter are available. This indicates that the rigorous ab initio method can be successfully applied to study the energetics and molecular properties of the alkali metal diatomics.

Multireference Double Electron Attached Coupled Cluster Method with Full Inclusion of the Connected Triple Excitations: MR-DA-CCSDT.

The multireference (MR) double electron attached (DA) coupled cluster (CC) method with full inclusion of the connected triple excitations has been applied to study various kinds of MR situations. The MR-DA-CCSDT (S, Singles; D, Doubles; T, Triples) equations have been derived and implemented in an efficient way with n(6) scaling for the target multireference states. They can be used for producing potential energy curves (PECs) for some classes of molecules, e.g., when double molecular cations separate into two closed shell fragments, illustrated with the example of the Na2 molecule. Correct PECs have also been obtained on dissociation of the N-N and C-C bonds in N2H4 and C2H6 molecules, respectively. Another application is the behavior of the molecular energy when we change dihedral angle in the ethylene molecule: with the MR-DA-CC, we see immediate improvement of the results with smooth, cusp free, behavior around the 90° region.

Excited and ionized states of the ozone molecule with full triples coupled cluster methods.

The role of connected triple excitations in coupled cluster (CC) calculations of vertical excitation energies, ionization potentials, and the electron affinity of the ozone molecule is evaluated. The equation of motion (EOM) and Fock space (FS) multireference CC approaches with full triples have been used in the calculations. The effect of the T(3) and R(3) operators significantly improve the EOM CCSD results for all considered quantities. A similar behavior is observed in the case of the FS-CC calculations. The FS-CC calculations with full triples have been obtained only for the intermediate Hamiltonian realization of the FS approach as the standard formulation diverges. The latter results are rigorously linked, and less expensive since smaller matrices are diagonalized.

Molecular applications of the intermediate Hamiltonian Fock-space coupled-cluster method for calculation of excitation energies.

The intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculate vertical excitation energies (EEs) for some molecular systems. The calculations are performed for several small molecules, such as H2O, N2, and CO, and for larger systems, such as C2H4, C4H6, and C6H6. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and model spaces are employed permitting a comparison of the calculated vertical EEs with the experimental data.

Where does the planar-to-nonplanar turnover occur in small gold clusters?

Several levels of theory, including both Gaussian-based and plane wave density functional theory (DFT), second-order perturbation theory (MP2), and coupled cluster methods (CCSD(T)), are employed to study Au6 and Au8 clusters. All methods predict that the lowest energy isomer of Au6 is planar. For Au8, both DFT methods predict that the two lowest isomers are planar. In contrast, both MP2 and CCSD(T) predict the lowest Au8 isomers to be nonplanar.