The use of site symmetry in constructing symmetry adapted functions

It is shown that the application of a projection operator from a given group to a function is equivalent to the successive application of projection operators from factor groups of the starting group to that function. When used with the factor groups representing the site symmetry of a position and the simplest group of interchanges of positions, this concept provides a very simple method for obtaining symmetry adapted linear combinations of basis functions.     

Pseudospectral approach to relativistic molecular theory

The efficient relativistic Dirac-Hartree-Fock (DHF) and Dirac-Kohn-Sham (DKS) methods are proposed by an application of the pseudospectral (PS) approach. The present PS-DHF/DKS method is a relativistic extension of the PS-HF/KS method of Friesner, though we aim at higher numerical accuracy by elimination of superfluous arbitrariness. The relativistic PS-DHF/DKS method is implemented into our REL4D programs. Several PS applications to molecular systems show that the relativistic PS-DHF/DKS approach is more efficient than the traditional approach without a loss of accuracy. The present PS-DKS method successfully assigns and predicts the photoelectron spectra of hexacarbonyl complexes of tungsten and seaborgium theoretically.     

Simple method to obtain symmetry harmonics of point groups

We propose a simple, self-consistent method to obtain basis functions of irreducible representations of a finite point group. Our method is based on eigenproblem formulation of a projection operator represented as a nonhomogeneous polynomial of angular momentum L. The method is shown to be more efficient than the usual numerical methods when applied to the analysis of high-order symmetry harmonics in cubic and icosahedral groups. For low-order symmetry harmonics the method provides rational coefficients of expansion in the Y(L,M) basis.     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

The self-consistent symmetrized OPW method with an application to crystalline selenium

A review of the nonrelativistic self-consistent symmertrized orthogonalized-plane-wave (SCSOPW ) method used for determining electronic energy bands in periodic solids is given. Working equations based on the full use of group theory at all stages are presented for elemental crystals. As an example the method is applied to the trigonal selenium crystal.     

Reduced density matrix hybrid approach: an efficient and accurate method for adiabatic and non-adiabatic quantum dynamics

We present a new approach to calculate real-time quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into "core" and "reservoir" modes with the former to be treated quantum mechanically and the latter classically. The presented method only requires the calculation of the system's reduced density matrix averaged over the quantum core degrees of freedom which is then coupled to a classically evolved reservoir to treat the remaining modes. We demonstrate our approach by applying it to the spin-boson problem using the noninteracting blip approximation to treat the system and core, and Ehrenfest dynamics to treat the reservoir. The resulting hybrid methodology is accurate for both fast and slow baths, since it naturally reduces to its composite methods in their respective regimes of validity. In addition, our combined method is shown to yield good results in intermediate regimes where neither approximation alone is accurate and to perform equally well for both strong and weak system-bath coupling. Our approach therefore provides an accurate and efficient methodology for calculating quantum dynamics in complex systems.     

One-pot reaction as an efficient method for rigid molecular tweezers

Rigid molecular tweezers are compounds of increasing scientific interest. As the structural requirements for such compounds are highly specific, few types of these tweezers are thus far known. The preparation of examples of rigid large-pincered molecular tweezers based on bis Troger's bases derived from 1,4-benzenediamine is described. In addition, evidence is presented of the different binding abilities of the diastereoisomers of such compounds.     

A numerical method to obtain a symmetry-adapted basis from the hamiltonian or a similar matrix

A practical method is proposed which using the hamiltonian matrix, or some other matrix corresponding to any operator with identical symmetry properties, enables one to obtain the transformation matrix, from the given basis to a symmetry-adapted basis. The method is very suitable for applications in the fields of molecular orbital and force constant calculations.     

A virtual vibrational self-consistent-field method for efficient calculation of molecular vibrational partition functions and thermal effects on molecular properties

A new method is described for the calculation of molecular vibrational partition functions and thermal effects on molecular properties including an explicit account of anharmonicity. The approach is based on the vibrational self-consistent-field method. Partition functions and thermal averages of the energies calculated with the new method are generally in good agreement with the result of more accurate methods. At lower temperatures the method gives in addition good results for thermal averages of dipole moments and polarizabilities. The new method is much more efficient than explicit sum-over-states approaches previously used for calculation of thermal averages. Unlike the standard sum-over-states approach, the newly developed method is feasible for larger systems despite the formal exponential increase in the number of states with the size of the system. Thus, it is presently the only practical way for including an explicit treatment of anharmonicity in vibrational wave function based calculations of molecular vibrational partition functions and thermally averaged properties of larger molecules.     

Point chirality functions,symmetry rules for chiral representations in one-centre molecular and field models

There are many problems (e.g. intermolecular forces, molecule-radiation field interactions) in which the separate entities (molecules, photons, or sources of static fields) many be represented by point moments (electric and magnetic. permanent or transition). Such point models lead to expressions containing moment products, which reduce on averaging to orientation-independent product functions that are characteristic of the species and its moment representation. Those functions that change sign when the chirality of the system is changed may be referred to as point chirality functions. In this paper, the point chirality functions generated from a given set of moments are defined, and in turn yield the conditions under which a given moment set is chiral; i.e. gives a chiral representation of the species it represents. They are shown to constitute a set of transferable parameters that lead to a unified approach to orientationally averaged chiral interactions of various kinds. By determining the point chirality functions of isolated chiral systems, the results are applied to interactions between various combinations of molecular, static field and radiation field systems without the need of considering the forms of each interaction in detail.     

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non‐Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z‐component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half‐filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non‐Abelian point group. The C₆₀ molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A general method to obtain Sturmian functions for continuum and bound state problems with Coulomb interactions

In this article, we investigate discretization schemes to represent Sturmian functions for both positive and negative energies in the presence of a long range Coulomb potential. We explore two methods to obtain Sturmian functions for positive energy. The first one involves the expansion of the radial wave function in a L² finite basis set, whereas the second one introduces the discretization of the radial coordinate domain of the Hamiltonian or, alternatively, the Green function. We apply them to find the bound states and scattering phase shift for ‐electron atoms close to the critical charge. Both methods are able to describe bound states near threshold, as well as continuum states with very good convergence properties. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

A method to obtain a near-minimal-volume molecular simulation of a macromolecule, using periodic boundary conditions and rotational constraints

If the rotational motion of a single macromolecule is constrained during a molecular dynamics simulation with periodic boundary conditions it is possible to perform such simulations in a computational box with a minimal amount of solvent. In this article we describe a method to construct such a box, and test the approach on a number of macromolecules, randomly chosen from the protein databank. The essence of the method is that the molecule is first dilated with a layer of at least half the cut-off radius. For the enlarged molecule a near-densest lattice packing is calculated. From this packing the simulation box is derived. On average, the volume of the resulting box proves to be about 50% of the volume of standard boxes. In test simulations this yields on average a factor of about two in simulation speed.     

On the computation of matrix elements between numerical wave functions: The canonical functions method

The problem of the computation of the matrix elements is considered when Ψ_v(r) and Ψ_v(r) are eigenfunctions related to a diatomic potential of the RKR type (defined by the coordinates of its turning points P_i with polynomial interpolations). The eigenfunction Ψ(r) is computed by the canonical functions method making use of the abscissas r_i of P_i uniquely. This limited number of points allows the storage of ψ_v(r_i) for all the required levels v, and reduces greatly the computational effort when v, ν′, and k are varying. The present method maintains all the advantages of a highly accurate numerical method (even for levels near the dissociation), and reduces greatly the computing time. Furthermore, it is shown that it may be extended to analytical potentials like Morse and Lennard-Jones functions, to vibrational-rotational eigenfunctions and to matrix elements between eigenfunctions related to two different potentials. Numerical applications are presented and discussed.     

The molecular approach to heterogeneous nucleation

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.     

Theoretical study of the vertical excited states of benzene, pyrimidine, and pyrazine by the symmetry adapted cluster--configuration interaction method

The ground state and the excited states of benzene, pyrimidine, and pyrazine have been examined by using the symmetry adapted cluster-configuration interaction (SAC-CI) method. Detailed characterizations and the structures of the absorption peaks in the vacuum ultraviolet (VUV), low energy electron impact (LEEI), and electron energy loss (EEL) spectra were theoretically clarified by calculating the excitation energy and the oscillator strength for each excited state. We show that SAC-CI has the power to well reproduce the electronic excitation spectra (VUV, LEEI, and EEL) simultaneously to an accuracy for both the singlet and the triplet excited states originated from the low-lying pi --> pi*, n --> pi*, pi --> sigma* and n --> sigma* excited states of the titled compounds. The present results are compared with those of the previous theoretical studies by methods, such as EOM-CCSD(T), STEOM-CCSD, CASPT2 and TD-B3LYP, etc.     

An efficient ionization method of electrospray mass spectrometry: the development of an aromatic-cored matrix that wraps labile metal complexes through molecular recognition

Compound 1a, which possesses a triphenylene core and six tetraethyleneoxide side chains, shows efficient ionization of M(II)-containing (M=Pd, Pt) complexes in electrospray ionization mass spectrometry (ESI-MS). The molecular ion peaks [M]+, which are hardly detected under common ESI-MS conditions, are clearly observed as their [M x (1a)n]+ (n=1-4) adducts. UV-visible and NMR studies reveal that the electron-rich triphenylene core of 1a binds to the electron-deficient frameworks of the M(II) complexes in solution, giving rise to charge transfer (CT) complexes. We suggest that 1a stabilizes the complexes and promotes efficient ionization through unique donor-acceptor molecular recognition.