Theoretical development of a Gaussian potential function in the description of the radial portion of isotropic bending vibrations

Analysis of a Gaussian potential function suitable for modeling degenerate bending vibrations in weakly bound molecular complexes is presented. Approximate eigenvalues and eigenvectors are obtained by application of perturbation theory. Comparison to the “exact” eigenvalues obtained via a numerical solution shows that the first- and higher-order perturbation corrections are consistent with variational principles.     

Application of the Sakurai-Sugiura projection method to core-excited-state calculation by time-dependent density functional theory

The Sakurai-Sugiura projection (SS) method was implemented and numerically assessed for diagonalization of the Hamiltonian in time-dependent density functional theory (TDDFT). Since the SS method can be used to specify the range in which the eigenvalues are computed, it may be an efficient tool for use with eigenvalues in a particular range. In this article, the SS method is applied to core excited calculations for which the eigenvalues are located within a particular range, since the eigenvalues are unique to atomic species in molecules. The numerical assessment of formaldehyde molecule by TDDFT with core-valence Becke's three-parameter exchange (B3) plus Lee-Yang-Parr (LYP) correlation (CV-B3LYP) functional demonstrates that the SS method can be used to selectively obtain highly accurate eigenvalues and eigenvectors. Thus, the SS method is a new and powerful alternative for calculating core-excitation energies without high computation costs.     

Hole-burning spectra of phenol-Arn (n = 1, 2) clusters: resolution of the isomer issue

The hole-burning (HB) spectra of phenol-Arn (PhOH-Arn) clusters with n = 1 and 2 have been measured in a molecular beam to clarify the possible existence of isomers. Two species were identified to give rise to signals in the S1-S0 spectrum recorded for the n = 1 cluster; however, one of the species was found to originate from dissociation of an n = 2 cluster. Similarly, three species were observed in the spectrum of the n = 2 cluster, and two of them were assigned to n = 3 and larger clusters. The spectral contamination from larger size clusters was quantitatively explained by the dissociation after photoexcitation. The analysis of the spectra demonstrates that only a single isomer exists in the molecular beam for both the n = 1 and the n = 2 clusters. In addition to two previously detected intermolecular modes, a third low-frequency mode, assigned to an intermolecular bending vibration, is observed for the first time in the HB spectrum of the n = 2 cluster. The assignments of the intermolecular vibrations were confirmed by ab initio MO calculations. The observation of the third intermolecular vibration suggests that the geometry of the n = 2 cluster has Cs or lower symmetry.     

Interaction of ionic biomolecular building blocks with nonpolar solvents: acidity of the imidazole cation (Im+) probed by IR spectra of Im+-Ln complexes (L = Ar, N2; n < or = 3)

The intermolecular interaction between the imidazole cation (Im+ = C3N2H4+) and nonpolar ligands is characterized in the ground electronic state by infrared photodissociation (IRPD) spectroscopy of size-selected Im+-Ln complexes (L = Ar, N2) and quantum chemical calculations performed at the UMP2/6-311G(2df,2pd) and UB3LYP/6-311G(2df,2pd) levels of theory. The complexes are created in an electron impact cluster ion source, which predominantly produces the most stable isomers of a given cluster ion. The analysis of the size-dependent frequency shifts of both the N-H and the C-H stretch vibrations and the photofragmentation branching ratios provides valuable information about the stepwise microsolvation of Im+ in a nonpolar hydrophobic environment, including the formation of structural isomers, the competition between various intermolecular binding motifs (H-bonding and pi-bonding) and their interaction energies, and the acidity of both the CH and NH protons. In line with the calculations, the IRPD spectra show that the most stable Im+-L dimers feature planar H-bound equilibrium structures with nearly linear H-bonds of L to the acidic NH group of Im+. Further solvation occurs at the aromatic ring of Im+ via the formation of intermolecular pi-bonds. Comparison with neutral Im-Ar demonstrates the drastic effect of ionization on the topology of the intermolecular potential, in particular in the preferred aromatic substrate-nonpolar recognition motif, which changes from pi-bonding to H-bonding. .     

Solution of large configuration mixing matrices arising in partitioning technique and applications to the generalized eigenvalue problem

A method is presented that can be used (a) to determine the several lowest eigenvalues and eigenvectors of large symmetric matrices, (b) to solve the generalized eigenvalue problem associated with energy-dependent operators, that arises in computations involving energy-dependent many-body Green's functions and in the evaluation of the true parameters of the effective valence shell hamiltonian, and (c) to directly evaluate the matrices associated with resolvent operators. The applicability to large configuration mixing calculations arises when the N-electron basis functions can be easily broken down to a few dominant configurations (the primary block) and their complement. Using the partitioning technique, the effective hamiltonian within the primary block is directly evaluated. The method is extended to evaluation of the dynamical polarizability tensor, which effectively contains the contributions from all of the eigenstates of a hamiltonian matrix, without the necessity of explicitly calculating its eigenvalues and eigenvectors.     

Hydrogen-bonded structures for self-aggregates of 2,5-dimethylpyrrole and its binary clusters with pyrrole studied by IR cavity ringdown spectroscopy

N-H···π hydrogen-bonded (H-bonded) structures were studied by applying vibrational spectroscopy to self-aggregate clusters of 2,5-dimethylpyrrole (DMPy) and its binary clusters with pyrrole (Py). The NH stretching vibrations of jet-cooled clusters were observed by IR cavity ringdown spectroscopy. A combination of experiments and density functional theory calculations revealed the stable structures, intermolecular binding energies, and harmonic vibrational frequencies. The IR spectrum of the DMPy self-aggregate clusters was very similar in spectral features to that of the Py clusters in a previous work. The observed NH stretching vibrations at 3505, 3420, 3371, and 3353 cm(-1) are simultaneously red-shifted by ～25 cm(-1) from the Py monomer, dimer, trimer, and tetramer, respectively. Based on a spectral analogy of DMPy with Py, and a consistency of the calculated harmonic frequencies with experiments, the H-bonded structures of the DMPy clusters were determined to be of a T-shape for a dimer and a cyclic for a trimer and a tetramer. For the DMPy-Py binary clusters, we discussed the stability and geometry of the N-H···π interactions in the T-shaped dimer and the cyclic trimer. The binary dimer showed the only single NH stretch at 3419 cm(-1) in the IR spectrum. A vibrational analysis of the H-bonded NH stretches as well as the calculated stabilization energies deduced that only the binary dimer by DMPy as an acceptor and Py as a donor can exist in a supersonic jet. For binary trimers, NH stretches were observed due to both (DMPy)(2)-(Py)(1) and (DMPy)(1)-(Py)(2). They were found to have different vibrational patterns from each other; the former showed three dispersed NH stretches, and the other had two quasi-degenerate NH stretches. Throughout this study, we also considered the intermolecular geometries, such as the H-bond distance and the angle in terms of the methyl group substitution effect.     

Guanine crystals: a first principles study

We report first principles density functional theory studies on the basic ground state characteristics, dynamic properties, and the electronic structure of guanine crystals. The effect of water molecules within the crystal is studied in detail, and we discuss their influence on the structural, vibrational, and electronic properties. The geometries calculated for various crystal structures are compared with gas-phase calculations and available experimental data. Phonon frequencies and eigenvectors are predicted for intermolecular and intramolecular lattice vibrations. Vibrational and electronic density-of-states are presented and analyzed. The electronic band structure near the fundamental gap is calculated from the Kohn-Sham approach. We find that the former molecular HOMO states form a dispersive band in the pi-pi stacking direction upon condensation resulting in a large bandwidth of 0.83 eV. Consequences for the charge transport in layered van der Waals bonded organic molecular crystals are discussed.     

Topological analysis of some special graphs: III. Regular polyhedra

A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Not sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.     

Topological analysis of some special graphs. III. Regular polyhedra

A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Net sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.     

Lattice dynamics and interaction potentials in molecular crystals

This paper, based essentially on the work done in recent years in our laboratory, presents a critical analysis of harmonic and anharmonic calculations of crystal vibrations in the determination of intermolecular potentials. The main purpose is to show that the dynamical properties are specifically sensitive to different terms of the potential and thus that information extracted from vibrational spectra of crystals is of the greatest importance for the theory of intermolecular forces. The most important conclusion is that these calculations point to the development of anisotropic short-range potentials and orient future researches towards the more complex and elaborate anharmonic treatment of crystal vibrations.     

New iterative scheme for a simultaneous calculation of m first eigenstates of a real symmetric matrix

A new iterative scheme for a simultaneous calculation of the m lowest eigenvalues together with their eigenvectors has been derived for a real symmetric matrix. The scheme is based on the orthogonal gradient method and is easy to use for large-scale configuration-interaction calculations of electronic wave functions. A variant of the scheme deals with nonorthogonal basis functions, which are particularly simple in the case of the bonded-function method of Boys.     

Electrical anharmonicity and vibronic couplings contributions to optical nonlinearity of N-benzyl-2-methyl-4-nitroaniline crystal studied by FT-IR, polarized FT-NIR, resonance Raman and UV-vis spectroscopy

FT-IR and Raman spectra of the orthorhombic and monoclinic N-benzyl-2-methyl-4-nitroaniline (BNA) single crystals, powders, and BNA solutions were measured in the 15-4000 cm(-1) range, and complete assignments of bands to normal vibrations are proposed. The assignments have been reinforced by density functional theory (DFT) calculations. Polarized FT-NIR spectra of the orthorhombic (010) BNA plate were measured for the overtones and combinations analysis and for the mechanical and electrical anharmonicity estimation. Resonance Raman spectra of the orthorhombic BNA polymorph together with the resonance excitation profiles of fundamental and lattice vibrations, compared with the band maxima in the measured UV-vis-NIR spectra of BNA, have revealed vibronic couplings with intramolecular and intermolecular charge transfers. The role of anharmonicity, vibronic couplings and intermolecular hydrogen bonds as well as of the N-benzyl substituent are discussed and the origin of second harmonic generation in the orthorhombic BNA crystal is proposed.     

The Fukui matrix: a simple approach to the analysis of the Fukui function and its positive character

The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues. At the level of theory used, there is always one dominant eigenvector, with an eigenvalue equal to 1. The remaining eigenvalues are either zero or come in pairs with eigenvalues of the same magnitude but opposite sign. Analysis of the frontier molecular orbital coefficient in the eigenvector with eigenvalue 1 gives information on the quality of the frontier molecular orbital picture. The occurrence of negative Fukui functions can be easily interpreted in terms of the nodal character of the dominant eigenvector versus the characteristics of the remaining eigenvectors and eigenvalues.     

The molecular energy levels of the azoles: A study by photoelectron spectroscopy and ab initio molecular orbital calculations

HeI photoelectron spectroscopy and ab initio calculations have been applied to the azoles, providing sets of energy levels that correlate well with each other in the upper valence shell region. Observed IPs are assigned to the three π- and to the five o-levels that involve (principally) valence shell p orbitals. The observed vibration structure is not particularly informative as an aid to assignment since both π-and σ-levels give some bands with vibration structure. The calculations provide in addition to eigenvalues (energy levels) a set of eigenvectors, permitting analysis of the bonding characteristics of the levels, and trends apparent within the series.     

The structure and vibrational frequencies of the ArH3+ ion and its isotopomers

There is much experimental interest in weakly bound cluster ions. Here we present the first ab initio study of ArH₃⁺, ArD₃⁺, ArHD₂⁺, and ArDH₂⁺. Structures and harmonic frequencies are reported at the MP2 level of theory using large basis sets. SCF anharmonic corrections are also reported. CISD and CPF calculations with the smallest of the basis sets used in this study are used to refine further the MP2 harmonic frequencies. The most intense infrared vibrations are the ν₂ (a₁, H₃⁺ bend) and ν₃ (a₁, intermolecular Ar…H stretch), for which our best predictions of the fundamental vibrations obtained by combining MP2 harmonic and SCF anharmonic corrections are 1819 and 395 cm⁻¹.     

Theoretical investigations of proton-bound cluster ions

Several proton-bound cluster ions have been studied by means of coupled cluster calculations with large basis sets. Among these are complexes of a krypton or xenon atom with the cations HCO+, HN2+ and HNCH+. Various spectroscopic properties have been calculated in all cases. Effects of vibrational anharmonicity are particularly pronounced for the intramolecular stretching vibrations of Kr...HN2+ and Xe...HN2+. The proton stretching vibration of (N2)H+(N2) is predicted around 800 cm-1, with a large transition dipole moment of 1.15 D. Both (N2)H+(N2) and (HCN)H+(NCH) have linear centrosymmetric equilibrium structures. Those of (OC)H+(CO) and (HCC-)H+(CCH-) are asymmetric with barrier heights to the centrosymmetric saddle points of 382 and 2323 cm-1, respectively. The dissociation energy of the anionic complex Cl-...HCCH is calculated to be Do = 3665 cm-1, 650 cm-1 larger than the corresponding value for Br-...HCCH. The complex between a fluoride ion and acetylene is more strongly bound and shows strongly anharmonic behaviour, similar to the bihalides FHF- or ClHCl-. Strong Fermi resonance interaction is predicted between nu 3 (approximately proton stretch) and 2 nu 4 (first overtone of intermolecular stretch).     

Constrained dynamics and extraction of normal modes from ab initio molecular dynamics: application to ammonia

We present a methodology for extracting phonon data from ab initio Born-Oppenheimer molecular dynamics calculations of molecular crystals. Conventional ab initio phonon methods based on perturbations are difficult to apply to lattice modes because the perturbation energy is dominated by intramolecular modes. We use constrained molecular dynamics to eliminate the effect of bond bends and stretches and then show how trajectories can be used to isolate and define in particular, the eigenvalues and eigenvectors of modes irrespective of their symmetry or wave vector. This is done by k-point and frequency filtering and projection onto plane wave states. The method is applied to crystalline ammonia: the constrained molecular dynamics allows a significant speed-up without affecting structural or vibrational modes. All Gamma point lattice modes are isolated: the frequencies are in agreement with previous studies; however, the mode assignments are different.     

The exponents method for calculating equilibrium concentrations of complex species in solution

The exponents method for calculating the concentrations of species in multimetal-multiligand systems is introduced. This method uses the Newton-Raphson method with restricted step iteration, which guarantees a monotonically decreasing objective function. Variable transformation and scaling are performed to avoid underflows and overflows during the calculations. A special linear solver using the eigenvalues and eigenvectors of the Jacobian matrix is implemented for overcoming disastrous singularity of this matrix, and the singular value decomposition method is applied for setting the initial guess. In addition, polynomial extrapolation is used for improving the performance when simulating a diagram of concentrations of species. The method was tested with 14 systems of different sizes over the whole pH range and presented robust and efficient behavior. © 1995 by John Wiley & Sons, Inc.