Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial dimensions, this method allows us to obtain an exact characterisation of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (with 1-10 microhartree precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.Comment: 14 pages, 12 figures, tciLaTeX, aip-BibTeX styl

Computation of conical intersections by using perturbation techniques

Multiconfigurational second-order perturbation theory, both in its single-state multiconfigurational second-order perturbation theory (CASPT2) and multistate (MS-CASPT2) formulations, is used to search for minima on the crossing seams between different potential energy hypersurfaces of electronic states in several molecular systems. The performance of the procedures is tested and discussed, focusing on the problem of the nonorthogonality of the single-state perturbative solutions. In different cases the obtained structures and energy differences are compared with available complete active space self-consistent field and multireference configuration interaction solutions. Calculations on different state crossings in LiF, formaldehyde, the ethene dimer, and the penta-2,4-dieniminium cation illustrate the discussions. Practical procedures to validate the CASPT2 solutions in polyatomic systems are explored, while it is shown that the application of the MS-CASPT2 procedure is not straightforward and requires a careful analysis of the stability of the results with the quality of the reference wave functions, that is, the size of the active [email protected] [email protected] [email protected]

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure

Theoretical calculations for solid oxygen under high pressure

The crystal structure of solid oxygen at low temperatures and at pressures up to 7 GPa is studied by theoretical calculations. In the calculations, the adiabatic potential of the crystal is approximated by a superposition of pair-potentials between oxygen molecules calculated by an ab-initio method. The monoclinic alpha structure is stable up to 6 GPa and calculated lattice parameters agree well with experiments. The origin of a distortion and that of an anisotropic lattice compressibility of the basal plane of alpha-O2 are clearly demonstrated. In the pressure range from 6 to 7 GPa, two kinds of structures are proposed by X-ray diffraction experiments: the alpha and orthorhombic delta structures. It is found that the energy difference between these structures becomes very small in this pressure range. The relation between this trend and the incompatible results of X-ray diffraction experiments is discussed.Comment: 12 pages, 6 figure

The crucial importance of the t2gt_{2g}--ege_g hybridization in transition metal oxides

We studied the influence of the trigonal distortion of the regular octahedron along the (111) direction, found in the $\rm CoO_2$ layers. Under such a distortion the $t_{2g}$ orbitals split into one $a_{1g}$ and two degenerated $e_g^\prime$ orbitals. We focused on the relative order of these orbitals. Using quantum chemical calculations of embedded clusters at different levels of theory, we analyzed the influence of the different effects not taken into account in the crystalline field theory; that is metal-ligand hybridization, long-range crystalline field, screening effects and orbital relaxation. We found that none of them are responsible for the relative order of the $t_{2g}$ orbitals. In fact, the trigonal distortion allows a mixing of the $t_{2g}$ and $e_g$ orbitals of the metallic atom. This hybridization is at the origin of the $a_{1g}$--$e_g^\prime$ relative order and of the incorrect prediction of the crystalline field theory

Theoretical study of molecular electronic excitations and optical transitions of C60

We report results on ab initio calculations of excited states of the fullerene molecule by using configuration interaction (CI) approach with singly excited determinants (SCI). We have used both the experimental geometry and the one optimized by the density functional method and worked with basis sets at the cc-pVTZ and aug-cc-pVTZ level. Contrary to the early SCI semiempirical calculations, we find that two lowest $^1 T_{1u} \leftarrow {}^1 A_g$ electron optical lines are situated at relatively high energies of ~5.8 eV (214 nm) and ~6.3 eV (197 nm). These two lines originate from two $^1 T_{1u} \leftarrow {}^1 A_g$ transitions: from HOMO to (LUMO+1) ($6h_u \to 3t_{1g}$) and from (HOMO--1) to LUMO ($10h_g \to 7t_{1u}$). The lowest molecular excitation, which is the $1 ^3 T_{2g}$ level, is found at ~2.5 eV. Inclusion of doubly excited determinants (SDCI) leads only to minor corrections to this picture. We discuss possible assignment of absorption bands at energies smaller than 5.8 eV (or $\lambda$ larger than 214 nm).Comment: 6 pages, 1 figure, 9 Table

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-μ-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion [email protected]

Resonant ion-pair formation in electron recombination with HF^+

The cross section for resonant ion-pair formation in the collision of low-energy electrons with HF^+ is calculated by the solution of the time-dependent Schrodinger equation with multiple coupled states using a wave packet method. A diabatization procedure is proposed to obtain the electronic couplings between quasidiabatic potentials of ^1Sigma^+ symmetry for HF. By including these couplings between the neutral states, the cross section for ion-pair formation increases with about two orders of magnitude compared with the cross section for direct dissociation. Qualitative agreement with the measured cross section is obtained. The oscillations in the calculated cross section are analyzed. The cross section for ion-pair formation in electron recombination with DF^+ is calculated to determine the effect of isotopic substitution.Comment: 12 pages, 12 figure