Properties of nearly one-electron molecules. II. Application to the Rydberg spectrum of CaF

The ab initio K matrix method described in the preceding paper (Part I) is applied to the Rydberg electronic structure of calcium monofluoride. The spectroscopic quantum defects for the 2Sigma+, 2Pi, 2Delta, and 2Phi states of CaF are computed using the effective potential of Arif et al. [M. Arif, Ch. Jungen, and A. L. Roche, J. Chem. Phys. 106, 4102 (1997)]. Satisfactory agreement with the experimental values is obtained. The eigenquantum defects obtained from the reaction matrix for the CaF++e- system are found to be strongly energy dependent. The analysis shows that the main features of the energy-dependent structure in the eigenphases are a consequence of a broad molecular shape resonance. Partial-l (orbital angular momentum) characters of two interacting collision eigenchannels vary rapidly as a function of increasing collision energy. This prominent variation leads to interference structure in the intensities for transitions into the ionization continuum, manifesting nodal points in the total ionization cross section in the continuum above the shape resonance. The usefulness of this structure in the ionization cross section as a direct probe of the l-character of the bound state is discussed. In addition, ab initio results for the photoelectron angular distribution and the anisotropy parameter are presented. These computed results are susceptible to direct experimental verification.     

Properties of aromaticity indices based on the one-electron density matrix

Proper normalization of two previously published indices yields aromaticity measures that, when computed within the Hückel molecular orbital (HMO) approximation, closely match the topological resonance energies per pi electron of aromatic annulenes and their ions. The normalized indices, which quantify aromaticity of individual rings in polycyclic systems, are equally applicable to homocyclic and heterocyclic compounds and can be readily computed from 1-matrices calculated at any level of electronic structure theory. However, only the index ING, derived from the Giambiagi formula, produces proper ordering of aromaticities of heterocyclic compounds, provided it is calculated from all-electron wavefunctions in conjunction with the atoms in molecule (AIM) partitioning. Its values are shown to be strongly affected by electron correlation effects. Because of its apparent inability to distinguish between anti- and nonaromatic systems, ING should only be employed for aromatic species.     

An algebraic approach to bound states of simple one-electron systems

A very general realization of the so (2, 1) algebra, which easily follows from the basic commutation relations that are satisfied by any pair of mutually conjugate generalized coordinates and momenta, is constructed. Using special cases of this general realization, and closely following the well known derivation of the eigenvalue spectra of the angular-momentum operators, based on the so (3) algebra, we derive the energy spectrum for the N-dimensional isotropic harmonic oscillator, and for both the nonrelativistic and the relativistic N-dimensional hydrogen atom. Special attention is given to a simple derivation of the form of these Hamiltonians in terms of the so(2, 1) algebra generators. In particular, the usually exploited tilting transformation is avoided, and the whole derivation is presented in an extremely simple and straightforward way. The present approach stresses the similarity and mutual relationship between the systems studied and, in addition to introducing some novel techniques and providing considerable insight into the overall structure of these problems, also has a definite pedagogical value.     

An iterative knowledge-based scoring function to predict protein-ligand interactions: I. Derivation of interaction potentials

Using a novel iterative method, we have developed a knowledge-based scoring function (ITScore) to predict protein-ligand interactions. The pair potentials for ITScore were derived from a training set of 786 protein-ligand complex structures in the Protein Data Bank. Twenty-six atom types were used based on the atom type category of the SYBYL software. The iterative method circumvents the long-standing reference state problem in the derivation of knowledge-based scoring functions. The basic idea is to improve pair potentials by iteration until they correctly discriminate experimentally determined binding modes from decoy ligand poses for the ligand-protein complexes in the training set. The iterative method is efficient and normally converges within 20 iterative steps. The scoring function based on the derived potentials was tested on a diverse set of 140 protein-ligand complexes for affinity prediction, yielding a high correlation coefficient of 0.74. Because ITScore uses SYBYL-defined atom types, this scoring function is easy to use for molecular files prepared by SYBYL or converted by software such as BABEL.     

An iterative approach to the synthesis of thiophene-based organic dyes

We developed an iterative synthetic method for oligo-aryl compounds using an organosilicon-based palladium-catalyzed cross-coupling reaction. Aryl compounds containing a benzyloxy(diisopropyl)silyl group (masked Si group) had sufficient chemical stability, and the unmasking step proceeded in a high yield under mild conditions. Both of the key unmasking/coupling steps required no strict anhydrous or degassed conditions. The developed procedure was used for the synthesis of thiophene-based organic dyes for dye-sensitized solar cells.     

Theory of diffusion-controlled reaction between non-simple molecules. I

A new vibrational principle is presented for reaction rates of diffusion-controlled chemical reaction. The variational principle is obtained by a modification of the closure approximation of Wilemski and Fixman. The closure approximation is found to correspond to a special choice of the trial function in this formation and to yield a lower bound of the reaction rate. This formulation is found to be especially useful for the analysis of reaction between non-simple molecules, such as macromolecules.     

An iterative knowledge-based scoring function to predict protein-ligand interactions: II. Validation of the scoring function

We have developed an iterative knowledge-based scoring function (ITScore) to describe protein-ligand interactions. Here, we assess ITScore through extensive tests on native structure identification, binding affinity prediction, and virtual database screening. Specifically, ITScore was first applied to a test set of 100 protein-ligand complexes constructed by Wang et al. (J Med Chem 2003, 46, 2287), and compared with 14 other scoring functions. The results show that ITScore yielded a high success rate of 82% on identifying native-like binding modes under the criterion of rmsd < or = 2 A for each top-ranked ligand conformation. The success rate increased to 98% if the top five conformations were considered for each ligand. In the case of binding affinity prediction, ITScore also obtained a good correlation for this test set (R = 0.65). Next, ITScore was used to predict binding affinities of a second diverse test set of 77 protein-ligand complexes prepared by Muegge and Martin (J Med Chem 1999, 42, 791), and compared with four other widely used knowledge-based scoring functions. ITScore yielded a high correlation of R2 = 0.65 (or R = 0.81) in the affinity prediction. Finally, enrichment tests were performed with ITScore against four target proteins using the compound databases constructed by Jacobsson et al. (J Med Chem 2003, 46, 5781). The results were compared with those of eight other scoring functions. ITScore yielded high enrichments in all four database screening tests. ITScore can be easily combined with the existing docking programs for the use of structure-based drug design.     

A versatile approach to hybrid thiadiazine-based molecules by the Ugi four-component reaction

Aiming at developing a versatile method for the generation of hybrid heterocyclic molecules, we describe a sequential approach comprising the formation of carboxy-functionalized 1,3,5-thiadiazines followed by the Ugi reaction with variation of the amino and the isonitrile components. The method enables the generation of structurally diverse molecular hybrids including peptide, lipid, steroidal and sugar moieties linked to the 1,3,5-thiadiazine scaffold.     

Calculation of vibronic spectra of polyatomic molecules in the franck—condon and herzberg—teller approximations: Part I. Methods for calculating matrix elements

A number of methods, both accurate and approximate, have been developed to calculate the integrals arising in the theory of vibronic spectra of polyatomic molecules. These methods make it possible to calculate the vibrational structure of the electron spectra of polyatomic molecules in the most general approximations (one-electron, adiabatic) without imposing any particular restrictions (neglect of the Dushinsky effect, temperature distribution of molecules, etc.). A comparison is made of the suggested methods, the approximate methods are analyzed for limits of accuracy, and the optimal fields of application are pointed out.     

An approach to triquinane synthesis using the Pauson-Khand reaction

Tricyclic skeletons have been generated from acyclic enyne precursors by using an intramolecular Pauson-Khand reaction in combination with aldol, Michael and alkylation reactions.     

The electronic structure of molecules by a many-body approach : II. Ionization potentials one-electron properties of pyridine and phosphoridine

The valence ionization potential (IPs) of pyridine and phosphoridine are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the Hartree-Fock approximation. For pyridine the order of the first three IPs is a₂(π), a₁(n), b₁(π), but the IPs of the a₂ and a₁ orbitals are so close together that they have to be regarded as identical in binding energy, which is also concluded from experiment. Whereas for pyridine the ordering of the IPs calculated in the HF approximation is incorrect, it is correct for phosphoridine. For this latter molecule the first three ionization potentials are due to ionization from the b₁(π), a₂(π), and a₁(n) orbitals. Several one-electron properties are calculated and compared with experimental and other theoretical data. The localized molecular orbitals are discussed as well.     

Properties of atoms in molecules. a proposed method for calculating the extent of distortion of an atom

A procedure for calculating the extent of distortion of an atom in a molecule is proposed and applied to the first-and second-row diatomic hydrides. The atomic charges in these molecules were also computed.     

A simple variational-numerical approach to the ro-vibrational spectrum of diatomic molecules. An application to CH+

We describe a simple way of obtaining numerically the manifold of energies for ro-vibrational transitions for a centrifugally distorted oscillator, starting from the potential energy of the non-rotating oscillator calculated by an accurate ab initio method. It is shown that the energies so obtained compare well with those obtained variationally. The species of astrophysical interest methylidyne ion, CH(+), has been selected as an example that allow us to show the computational efficiency of the method with respect to the variational one. It is applied for the determination of ro-vibrational levels up J=6, and the spectroscopic parameters corresponding to the ground electronic state X(1)Sigma(+). From the potential energy surface computed at the MRCI/cc-pV5Z level, the fundamental frequency, B(0) and D(0) are determined to be 2724.8, 13.85688 and -1.53322x10(-3)cm(-1), respectively. We provide also an estimation of anharmonic constants.     

An ab initio approach to the mechanism of the Grignard reaction

The mechanism of the Grignard reaction is investigated for the first time in the light of ab initio SCF MO theory. The possible advantage of a single-electron transfer over a polar mechanism is discussed.