As brought to the attention of the community by Hendon et al. and noted by previous workers, the π orbitals of the equilibrium geometry odd-carbon (even number of double bonds = n) [n]cumulenes may be written in either rectilinear or helical form. We trace the origins and detailed composition of the helical orbitals of cumulenes, which emerge in the simplest Hückel model and are not much modified in advanced computations. For the α,ω-disubstituted even [n]cumulenes, the helical representation is obligatory as the symmetry is reduced from D2d to C2. A relationship is apparent between these helical orbitals of the even [n]cumulenes, seen as a Herges coarctate system, and the corresponding Möbius cyclic polyene orbitals. The twist of the orbitals varies in interesting ways along the helix, and so does the contribution of the component atomic orbitals. Though the electronic structures of even [n]cumulenes and Möbius cyclopolyenes are closely related, they differ for higher n in intriguing ways; these are linked to the constrained rotation of the basis orbitals along the helical twist itinerary. Relations are constructed between the level patterns of the π-systems of even [n]cumulenes and ideas of Hückel and Möbius aromaticity.

The performance of the six second order linear response methods RPA(D), SOPPA, SOPPA(CCSD), CIS(D), CC2, and CCSD, which include either noniterative or iterative doubles contributions, has been studied in calculations of vertical excitation energies. The benchmark set consisted of 39 valence and 76 Rydberg states of benzene and five polycyclic aromatic hydrocarbons. As reference values we have used the results of the corresponding calculations with the third order method CCSDR(3), which includes noniterative triples contributions. In addition we have also carried out equivalent calculations at the level of the random phase approximation as well as with the configuration interaction singles and multireference configuration interaction singles and doubles methods.

We have studied the basis set and electron correlation effects on the ab initio calculations of two-photon absorption cross sections of water. Various series of correlation consistent basis sets up to triply augmented basis sets of valence pentuple ζ level as well as the popular 6-31G(d) basis set have been employed in combination with several coupled cluster, configuration interaction, and density functional theory methods. We find that it is very difficult to obtain converged values of the cross sections for even a small molecule such as water. Acknowledging these difficulties in obtaining a fully converged cross section for a given state, we also investigated the possibility of determining relative cross sections for a series of organic molecules. However, we did not find consistency between the relative cross sections calculated at the Hartree-Fock level and several coupled-cluster methods using the 6-31G(d) and aug-cc-pVDZ basis sets. However, we could reproduce the relative ordering of the two-photon absorption cross sections of the molecules studied at the Hartree-Fock level.

The present approach is a graphical procedure for visualizing and addressing determinants and alpha and beta strings for many-electron systems. Compared with previous approaches, the emphasis in the graph is on the vertices and vertex weights. The arcs in the graph are only used for visualization. This leads to a compact representation of the configuration space and provides a computationally efficient and dense indexing scheme. The localization of inter configurational matrix elements are determined directly from the graph by means of segments and shapes similar to other graphical approaches. (C) 2006 Wiley Periodicals, Inc.

In this contribution, we develop and investigate a general 2D hopping model for the photovoltaic action in polymer-based thin films. The model takes a microscopic origin and accounts for the molecular photonic and electronic processes by a simple kinetic scheme that eventually leads a linearized master equation for the time evolution of the photovoltaic system. With an emphasis on the topology of blends of donor/acceptor functionalized polymers, we attempt to characterize the dependence of the short-circuit current, internal quantum efficiency, IV characteristics, and fill factors on the morphology of the blend. Several different morphologies for the polymer film are considered, and they show quite different transport and efficiency behavior (e.g., for so-called double cable structures, nearly quantitative conversion efficiencies are computed, and for other structures similar efficiencies may be found, but with short-circuit currents orders of magnitude lower). The model neglects effects such as exciton migration, the built-in potential, and interaction in the third dimension. Nontheless, significant conclusions can be drawn: in particular, we demonstrate that a viable photovoltaic system driven only by concentration gradients of charge carriers (no built-in field) is possible.

The present approach is a graphical technique for representing and generating primitive configurations of space orbitals for electronic systems. The graph is developed as a tree whose paths define the allowed space configurations of electrons admitting at most double occupancy for each orbital. The emphasis in the graph is on the nodes representing occupied orbitals rather than on the arcs compared with previous graphical procedures used in graphical unitary and symmetric group approaches. This leads to a compact representation of the orbital configurations and provides a computationally very efficient indexing scheme. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

A graphical technique is proposed for generating and addressing all required α and β strings of spin-orbitals for configuration interaction treatments based on determinants. Compared with other treatments, this scheme, as well as reducing to a minimum the number of logical operations, avoids entirely the storage of the massive tables and vectors usually required for addressing the determinants. The generation is proposed of all required addresses to locate the determinants in the CI vectors, before and after application of the Hamiltonian, at run time using graphs and one intermediate table of acceptable dimensions. The scheme, which has been tested on a small personal computer, appears ideal when limited computational resources are available for the CI treatment. It is believed also to be useful for larger applications.

In the present article, we outline a simple scheme for generating configuration interaction matrix elements for spin–orbit interactions in molecules. The procedure leads to a close parallelism with spin-free permutation-group approaches. Unitary shift operators were successfully used on the orbital space to generate the matching permutations necessary to evaluate the required matrix elements. The procedure is adequately illustrated using examples. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 23–27, 1999

The aminomethyl radical was produced by the reaction F-. + CH3NH2 --> HF + (CH2NH2)-C-., which was initiated by pulse radiolysis of CH3NH2-SF6 mixtures. The ultraviolet absorption spectrum of CH2NH2 was recorded on a timescale of 2 mu s using a gated optical multichannel analyzer. The vibronic structure observed in the range 270-380 nm was analyzed by comparison with the results Of ab initio calculations. Kinetics of the self-reaction 2(.)CH(2)NH(2) --> products was studied by monitoring the transient absorption of (CH2NH2)-C-. at 319.5 nm. A value of k = 8.1 x 10(-11) cm(3) molecule(-1) s(-1) was derived from the observed second-order kinetics combined with an estimated yield of the radical. In the presence of oxygen the decay rate was found to increase in accordance with the reaction (CH2NH2)-C-. + O-2 --> products proceeding with a rate constant of 7.8(8) x 10(-11) cm(3) molecule(-1) s(-1).

The general CI code PEDICI has been parallelized by decomposing the occurring summation over two-electron integrals. The parallelization was formulated in terms of a “master/slave'' model, and realized through use of the “PVM'' message passing facility. We have aimed at achieving a reasonably simple implementation for use on machines with intermediate numbers of processors. Exploratory test runs on an IBM SP supercomputer (consisting of RS/6000 model P2SC (120 MHz) nodes) show a very satisfactory performance increase with the number of processors used, as well as encouraging balancing of the workload. Our largest 32-processor test case gives a speed-up factor of 30.27.

Modified virtual orbitals are proposed for multi-reference configuration interaction (MRCI) treatments and a modified Fock operator is defined for the orbital transformation. The main property of the modified orbitals is to improve the convergence properties of the configuration interaction (CI) expansion, which can be exploited to truncate, partially, the expansion in the external space. Simple tests are presented to show that the orbital transformation may be useful to perform FullCI type of treatments for subsets of orbitals and electrons, and to improve the MRCI second-order corrections and energies. Compared to other well-established techniques for accurate MRCI treatments, it is believed that this method offers advantages for electronic structures with many active orbitals and electrons using large orbital basis sets.

Modern valence bond theory, in its spin-coupled form, is used to describe the bonding in o- and m-phenylenedimethylidenes and, in particular, to rationalize the different relative stabilities of the quintet states and lower spin multiplicities.

. It is outlined how the utilization of a basis of projected spin eigenfunctions can lead to increased computational efficiency in the evaluation of matrix elements and density matrices in spin-coupled valence bond calculations.

We find the normalization integral for projected spin eigenfunctions, defined by means of character projection operators of the symmetric group. We also obtain a reduced expression for these spin eigenfunctions.

The classes of the symmetric group 𝒮N are identified by partitions of N. In this work an indexing scheme is presented which provides a dense enumeration of the classes of 𝒮N. The method is based on a graphical representation of partitions of N, which also enables the determination of the class corresponding to a given number. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 421–426, 1997

The representation matrices generated by the projected spin functions have some very interesting properties. All the matrix elements are integers and they are quite sparse. A very efficient algorithm is presented for the calculation of these representation matrices based on a graphical approach and a new indexing scheme for representation of primitive spin functions is introduced. Test calculations show that the method is very fast and suited for calculations on vector computers. (C) 1996 John Wiley & Sons, Inc.