Extension of total angular momentum representation in energy space

A previously developed representation of total angular momentum in energy space for three atomic systems is extended to include reactions of the type CF₃CN → CF₃ + CN. The effects of internal CF₃ rotation on the angular momentum constraint are shown under different conditions. The representation is used for comparison with recent infrared multiphoton dissociation experiments on this system.     

Reducing CAS-SDCI space. Using selected spaces in configuration interaction calculations in an efficient way

A new method is presented, which allows an important reduction of the size of some Configuration Interaction (CI) matrices. Starting from a Complete Active Space (CAS), the numerous configurations that have a small weight in the CAS wave function are eliminated. When excited configurations (e.g., singly and doubly excited) are added to the reference space, the resulting MR-SDCI space is reduced in the same proportion as compared with the full CAS-SDCI. A set of active orbitals is chosen, but some selection of the most relevant excitations is performed because not all the possible excitations act as SDCI generators. Thanks to a new addressing technique, the computational time is drastically reduced, because the new addressing of the selected active space is as efficient as the addressing of the CAS. The presentation of the method is followed by two test calculations on the N(2) and HCCH molecules. For the N(2) the FCI results are taken as a benchmark reference. The outer valence ionization potentials of HCCH are compared to the experimental values. Both examples allow to test the accuracy of the MR-SDCI compared to that of the corresponding CAS-SDCI, despite the noticeable reduction of the CI space. The algorithm is suitable for the dressing techniques that allow for the correction of the size-extensivity error. The corrected results are also shown and discussed.     

A density functional representation of quantum chemistry. III. Rigorous realization of the program in lattice space

A mathematically rigorous reformulation of molecular quantum mechanics in terms of the particle density operator and a canonically conjugated phase field is given. Using a momentum cutoff, it is shown that the usual molecular Hamiltonian can be expressed in terms of the particle density operator and a rigorously defined phase operator. It is shown that this Hamiltonian converges strongly to the cutoff-free Hamiltonian. In spite of the fact that this Hamiltonian is of second order in the phase operators, all hitherto published expressions are not correct. Unfortunately, the correct formulation destroys the intuitive appeal of using the particle density operator as a coordinate for the many-body problems of quantum chemistry. Unless somebody provides an essential new and clever idea, we propose to resist the fascination of a local quantum field theory of molecular matter in terms of the particle density operator.     

Symmetry simplifications of space types in configuration interaction induced by orbital degeneracy

Symmetry simplifications are introduced in configuration interaction (CI ) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions are derived for enumerating the equivalence classes of space types. A double coset method is expounded which constructs the representatives of all equivalence classes of space types using the cycle index of generalized wreath product and the double cosets of label subgroup with generalized wreath product in the symmetric group S_n, if n is twice the number of occupied and virtual orbitals. Method is illustrated with CI using the localized orbitals of polyenes, CI in benzene, and atomic CI for several reference states.     

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb-Ba)+

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.     

Matrix‐covariant representation of high‐order configuration interaction and coupled cluster theories

We present the closed form of the reduced density matrices (RDMs) of arbitrary order for configuration interaction (CI) wave functions at any excitation level, up to the full CI. A special operator technique due to Bogoliubov is applied and extended. It focuses on constructions of matrix‐covariant expressions independent of the basis set used. The corresponding variational CI equations are given in an explicit form containing the matrices related to conventional excitation operators. A subsequent transformation of the latter to an irreducible form makes it possible to generate the matrix‐covariant representation for coupled cluster (CC) models. Here this transformation is performed for a simplified high‐order CC scheme somewhat reminiscent of the quadratic CI model. A generalized spin‐flip approximation closely related to high‐order CI and CC models is presented, stressing on a possible inclusion of nondynamical and dynamical correlation effects for multiple bond breaking. A derivation of the full CI and simple CC models for systems involving effective three‐electron interactions is also given, thereby demonstrating the capability of the proposed method to deal with complicated many‐body problem. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Content,design, and representation in chemistry

The aim of this paper is to engage with the interplay between representational content and design in chemistry and to explore some of its epistemological consequences. Constraints on representational content arising from the aspectual structure of representation can be manipulated by design. Designs are epistemologically important because representational content, hence our knowledge of target systems in chemistry, can change with design. The significance of this claim is that while it has been recognised that the way one conveys information makes a difference to the inferences one can draw from representations in spite of the invariance of informational content, the present paper argues that in chemistry and biochemistry it is often the case that designs have cognitive priority relative to informational content.     

Analysis of the space correlation factors in a MCSCF representation of LiH and Li2 molecules

The space correlation factor is studied in LiH and Li₂ molecules, using MCSCF wave-functions. The shape of the Fermi hole is related to the localization of molecular space orbitals, while the Coulomb hole study indicates the importance of symmetry properties of the molecular orbitals involved in excited configurations for the representation of the electronic correlation inside the chemical bond.     

Efficient implementation of restricted active space configuration interaction with the hole and particle approximation

The restricted active space configuration interaction (RASCI) formalism with the hole and particle truncation of the wavefunction, that is, RASCI(h,p), holds very nice properties such as balanced treatment of ground and low‐lying excited states, spin‐completeness, large flexibility of the wavefunction, and moderate computational cost. In this article, I present a new implementation of the RASCI(h,p) method using a general algorithm based on the integral‐driven approach. The new implementation allows to choose any electronic configuration as the single reference in combination with an excitation operator with any number of ionization, electron attachment, or spin‐flip (SF) excitations. The applicability and good performance of the new computational code is tested in the ground state calculation of water molecule with increasingly large active spaces and up to the full‐CI limit, the calculation of all‐trans linear polyenes with variable number of SF excitations, and the low‐lying states of fluorine molecule with a double‐ionization potential operator. © 2012 Wiley Periodicals, Inc.     

Microstructures from a mixture of ABC 3-miktoarm star terpolymers and homopolymers in two-dimensional space

Using a 2D real-space self-consistent field theory, we studied the microstructures of the mixture of ABC 3-miktoarm star terpolymer and linear homopolymers. First, we found that the microstructures depend on both the chain length and volume fraction of the linear homopolymer. Second, despite different linear homopolymer lengths, all the mixtures finally converge to the core/shell pattern after the sum of blocks and homopolymer comprises the majority. Third, some novel microstructures that are not found in the pure ABC 3-miktoarm star terpolymer are produced. These calculations are supposed to be helpful for the design of novel microstructures involving star terpolymers that blend with homopolymer.     

Asymmetric synthesis of a diastereomer of the structure proposed for amphidinolide A and the determination of its absolute configuration

An asymmetric synthesis of a diastereomer (2) of the structure (1) proposed for amphidinolide A, a cytotoxic macrolide from the cultured dinoflagellate Amphidinium sp., has been accomplished. The absolute configuration of amphidinolide A was established as 3 from comparison of NMR data, HPLC analysis, and [α]_D values of amphidinolide A, and comparison with the synthetic diastereomers 2 and 3, the latter of which was synthesized previously by Trost's group.     

Transformed Dirac equation for the hydrogen atom,comparison with previous approaches in momentum space,and the anomalous Zeeman effect in momentum representation

The solution of a unitarily transformed Dirac equation for the hydrogenic electron in zero magnetic field is investigated here. The momentum‐space representation is adopted as a natural recourse. The spinor part of the transformed wavefunction in momentum space can be easily prescribed for a central potential. Hence, for the Coulomb potential, a pair of equations is obtained for the radial components in momentum space. It is shown that starting from these radial equations, one can recover the equations previously derived by Rubinowicz, Lévy, and Lombardi for the problem of the Dirac hydrogen atom in momentum space. This establishes equivalence among different approaches based on the momentum representation, including the current treatment. The recovery of the equations due to Rubinowicz permits the exact eigenvalues to be written down and exact expressions to be derived for the radial components of the transformed wavefunction in momentum space. A new approach is adopted to carry out a reduction to the nonrelativistic regime and the nonrelativistic limit. At first the transformed momentum‐space equation for the hydrogen atom is rewritten in terms of the hyperspherical coordinates. The zeroth‐order solutions of the new equation are recovered in the limit c → ∞ where c is the speed of light. These are manifestly separable into positive‐ and negative‐energy forms. For positive energy, these solutions have nonvanishing upper components that are two‐component spinors. The latter exactly correspond to the single‐component, nonrelativistic, momentum‐space solutions derived by Fock. It is shown that when the upper component is corrected through first order in v²/c² but the separability is still maintained for the transformed wavefunction, one retrieves the Pauli equation in momentum space. It is also shown that for a hydrogen atom placed in a uniform magnetic field, the nonvanishing momentum‐space matrix elements representing the anomalous Zeeman effect have a simple form, namely, the product of a radial integral and an angular integral. These integrals are equal to the well‐known radial and angular integrals in coordinate representation. The matrix elements can be easily evaluated. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Generation of a full active configuration space basis in terms of symmetry- and spin-adapted antisymmetrized orbital products

A practical algorithm is described for generating a set of symmetry- and spin-adapted antisymmetrized products of molecular orbitals (SAAPs) which form an orthogonal basis for a full active configuration space. The spin-adaptation is completely general. The space-symmetry adaptation is accomplished for the groups C_∞v and D_∞v.