Resonances and pseudoresonances in a potential with attractive coulomb tail: A study using analytic‐continuation techniques

The performance of the complex absorbing potential (CAP) and the complex scaling (CS) methods in the detection and calculation of complex Siegert energies is studied using a 1‐D long‐range attractive model potential. This potential is constructed to mimic molecular properties, in particular an attractive Coulombic term, to allow one to draw conclusions on molecular ab initio studies. Analyzing the spectrum of the model potential, one compact bound state embedded in the manifold of Rydberg states is found that shows artificial resonance characteristics when applying the CAP and the CS methods. This pseudoresonance problem is less pronounced in the calculation using the CS method than in that using the CAP method. Despite this deficiency, the CAP method is shown to possess advantages over CS when dealing with physical resonances under conditions that simulate the application of standard basis sets in ab initio calculations. The accuracy of the Siegert energy is shown to be maintained when applying a subspace projection technique to the CAP method. This technique reduces the computational demand significantly and leads to an important improvement of the CAP method, which should be of particular significance in molecular applications. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Inter-ring rotational potential of biphenyl and its effect on poly(p-phenylene)

Detailed ab initio studies have been done on the inter-ring torsional states of the biphenyl molecule using self-consistent field molecular orbital method. The potential goes through a minimum at an angle of 38°. The height of the potential barrier for the coplanar state is 2.01 kcal/mol. When the phenyl rings are perpendicular to each other, this height increases to 2.37 kcal/mol. The role of correlation and polarization is found to be important. The shape of the potential suggests that polyparaphenylene may possibly exist as a super helix.     

H+NH3反应势能面的量子化学研究

本文采用UCCSD(T)/aug-cc-pVTZ方法研究了H NH3反应势能面,获得了夺氢反应和交换反应过渡态的的几何结构和振动频率。夺氢反应的过渡态具有Cs对称性,其能垒为61.92 kJ/mol。交换反应的过渡态具有C3v对称性,其能垒为39.69 kJ/mol。H NH3发生形成Td对称性的反应中间体NH4里德堡自由基。与夺氢反应相比,交换反应具有更低的反应能垒,并且NH4自由基在反应中可形成长寿命的共振态,和夺氢反应形成竞争关系,因此在H NH3反应的量子动力学研究中必须同时考虑这两类反应。本文还采用更大的基组aug-cc-pVQZ和aug-cc-pV5Z研究了势能面对基组的收敛行为。     

Experimental and theoretical investigations of the He...I2 rovibronic spectra in the I2 B-X, 20-0 region

The laser-induced fluorescence and action spectra of I2 in a helium supersonic expansion have been recorded in the I2 B-X, 20-0 region. Two features are identified within the spectra. The lower-energy feature arises from transitions between states that are localized in a T-shaped conformation on both the X- and B-state potentials. The higher-energy feature reflects transitions from states that are localized in a linear conformation on the X state to states that have energies that are larger than the barrier for free rotation of the rare gas atom about the I2 molecule on the B-state potential. Ground-state binding energies of 16.6(6) and 16.3(6) cm-1 were determined for the T-shaped and linear conformers, respectively. These spectra are compared to those calculated using the experimentally determined rotational temperatures. Based on the agreement between the experimental and calculated spectra, the binding energies of the J'=0 states with 0 and 2-6 quanta of excitation in the He...I2 bending mode on the B state were determined. Several models for the B-state potential were used to investigate the origins of the shape of the contour of the higher-energy feature in the spectra for He...I2 and He...Br2. The shape of the contours was found to be relatively insensitive to the choice of potential. This leads us to believe that the spectra of these systems are relatively insensitive to the parameters of the B-state potential energy surface and are more sensitive to properties of the halogen molecule.     

Resonances and antibound states in a Morse potential

We calculate the resonant and antibound state energies for a Morse potential with a centrifugal barrier using Siegert boundary conditions. Starting with a complex wave number k (purely imaginary for bound and antibound states), we integrate numerically from the origin up to a matching point using Numerov's method. The inward integration is performed using the corresponding (first-order) Riccati equation. The complex eigenvalues are found by matching the two logarithmic derivatives. We find narrow shape resonances within the well, above the dissociation limit, and broad resonances above the centrifugal barrier. Antibound states are found even with J = 0. © 1997 John Wiley & Sons, Inc.     

The 1s-state analysis applied to high-angle, annular dark-field image interpretation--when can we use it?

A small probe centered on an atomic column excites the bound and unbound states of the two-dimensional projected potential of the column. It has been argued that, even when several states are excited, only the 1s state is sufficiently localized to contribute a signal to the high-angle detector. This article shows that non-1s states do make a significant contribution for certain incident probe profiles. The contribution of the 1s state to the thermal diffuse scattering is calculated directly. Sub-Angstrom probes formed by Cs-corrected lenses excite predominantly the 1s state and contributions from other states are not very large. For probes of lower resolution when non-1s states are important, the integrated electron intensity at the column provides a better estimate of image intensity.     

Torsion angle preference and energetics of small-molecule ligands bound to proteins

Small organic molecules can assume conformations in the protein-bound state that are significantly different from those in solution. We have analyzed the conformations of 21 common torsion motifs of small molecules extracted from crystal structures of protein-ligand complexes and compared them with their torsion potentials calculated by an ab initio DFT method. We find a good correlation between the potential energy of the torsion motifs and their conformational distribution in the protein-bound state: The most probable conformations of the torsion motifs agree well with the calculated global energy minima, and the lowest torsion-energy state becomes increasingly dominant as the torsion barrier height increases. The torsion motifs can be divided into 3 groups based on torsion barrier heights: high (>4 kcal/mol), medium (2-4 kcal/mol), and low (<2 kcal/mol). The calculated torsion energy profiles are predictive for the most preferred bound conformation for the high and medium barrier groups, the latter group common in druglike molecules. In the high-barrier group of druglike ligands, >95% of conformational torsions occur in the energy region <4 kcal/mol. The conformations of the torsion motifs in the protein-bound state can be modeled by a Boltzmann distribution with a temperature factor much higher than room temperature. This high-temperature factor, derived by fitting the theoretical model to the experimentally observed conformation occurrence of torsions, can be interpreted as the perturbation that proteins inflict on the conformation of the bound ligand. Using this model, it is calculated that the average strain energy of a torsion motif in ligands bound to proteins is approximately 0.6 kcal/mol, a result which can be related to the lower binding efficiency of larger ligands with more rotatable bonds. The above results indicate that torsion potentials play an important role in dictating ligand conformations in both the free and the bound states.     

Static atomistic modelling of the structure and ring dynamics of bulk amorphous polystyrene

A detailed static atomistic model of dense, glassy polystyrene is simulated using a well established technique that previously proved successful for simple vinyl polymers. Initial chain conformations that are generated using a Monte Carlo technique including periodic continuation conditions are “relaxed” by potential energy minimization. In total 24 microstructures at densities of 1,07 g/cm³ were obtained with a cube-edge length of 18,65 Å. Detailed analysis of the minimized structures indicates that intermolecular packing influences create a large variety of chain conformations different from the purely intramolecular ground states. The systems are amorphous, exhibiting random coil behavior. The described structures have been used for a quasistatic simulation of localized motions. These motions include stepwise rotation and oscillation of the phenyl groups. The frequency distribution for the simulated ring motions covers many orders of magnitude. It is very rare that an energy barrier with a reorientation angle indicating a ring “flip” is overcome. Motions with small reorientation of the phenyl rings, and therefore not leading to a ring “flip”, dominate with an average reorientation angle of 16° (±12°). The intermolecular effects of the analyzed processes were found very important and far-reaching, widely influencing the cooperative motions of molecular groups.     

Studies on some exponential‐screened coulomb potentials

The generalized pseudospectral method is used to study the bound‐state spectra of some of the exponentially screened Coulomb potentials, namely, the exponential cosine screened Coulomb (ECSC) and general exponential screened Coulomb (GESC) potential, with special emphasis on higher states and stronger interaction. Eigenvalues accurate up to 11 significant figures are obtained through a nonuniform optimal spatial discretization of the radial Schrödinger equation. All the 55 eigenstates of ECSC potential with n ≤ 10 and 36 eigenstates of GESC potential with n ≤ 8 are considered for arbitrary values of the screening parameter, covering a wide range of interaction. Excited states as high as up to n = 18 have been computed with high accuracy for the first time. Excellent agreement with the literature data has been observed in all cases. All the GESC eigenstates are calculated with much greater accuracy than the existing methods available in literature. Many l ≠ 0 states of this potential are reported here. In both cases, a detailed variation of energies with respect to the parameters in potential is monitored. © 2012 Wiley Periodicals, Inc.     

An analytical approximation for the number of states along the reaction coordinate

A variant of a new empirical method, enables one to express a collinear triatomic potential energy surface as a family of Morse curves along “natural” bond order coordinates orthogonal to the reaction coordinate. The procedure depends on a single adjustable parameter which is related to the barrier's height. Because an analytical expression for the number of vibrational states of a Morse oscillator is available, one has an analytical approximation for the number of states along the reaction coordinate. The extrema in the number of states are utilized in various versions of classical microcanonical variational transition state theory (among which is a new version, which is in better agreement with dynamical results), to estimate the probability of a collinear reactions, as a function of the total energy. The analytical expressions are also used to analyze the origins of the maximum and minima in the number of states.     

Potential energy surface for Li+Li2: AN AB initio valence-bond calculation

A potential energy surface, calculated using the ab initio multistructure valence-bond technique, is reported for the collinear Li + Li₂ system. The ground state potential surface of the system is predicted to have no barrier to reaction and to possess a well of 4.62 kcal/mole (0.200 eV) relative to the infinitely separated reactants with the Li₂ at its equilibrium separation. An analytic potential energy surface is derived, which includes empirical corrections for the “diatomic” errors in the ab initio calculation. The empirically corrected surface dissociates to the experimental Li₂ potential energy curve when any one of the three lithium atoms is removed to a large distance. Cuts in the ab initio potential energy surface of the lowest electronically excited states of the system are also reported.     

Negative electron affinities from conventional electronic structure methods

If the potential V describing the interaction between an excess electron and a ground-state neutral or anionic parent is sufficiently attractive at short range, electron-attached states having positive electron affinities (EAs) can arise. Even if the potential is not attractive enough to produce a bound state, metastable electron-attached states may still occur and have lifetimes long enough to give rise to experimentally detectable signatures. Low-energy metastable states arise when the attractive components of V combine with a longer-range repulsive contribution to produce a barrier behind which the excess electron can be temporarily trapped. These repulsive contributions arise from either the centrifugal potential in the excess electron’s angular kinetic energy or long-range Coulomb repulsion in the case of an anionic parent. When there is no barrier, this kind of low-energy metastable state does not arise, but improper theoretical calculations can lead to erroneous predictions of their existence. Conventional electronic structure methods with, at most, minor modifications are described for properly characterizing metastable states and for avoiding incorrectly predicting the existence of metastable states with negative EAs where no barrier is present.     

Schrödinger equation for a dirac bubble potential

The quantum-mechanical problem of a particle moving in a “Dirac bubble potential” U(r) = (λ/r_o)δ(r - r_o) is solved exactly for both bound and continuum states by making use of partial wave Green's functions G_l(r, r₀, k). Phase shifts are expressed in a compact form related to those for an impenetrable sphere.     

Rotational states of the ammonium ion in cubic lattice

The ammonium ion in the alkali halide lattice has the hindered rotational state. The rotational potential is expressed as crystal field, which depends upon only one rotational motion. The tetrahedral ion receives an octahedral field in this system. Four fundamental types of orientation appear due to the symmetry of ion and that of field. As the barrier height increases, the rotational levels approach to the librational levels with tunnel splitting. In particular, the tunneling part in the ground librational level is calculated using both free rotor bases and orientationally localized states. The level structure with the degeneracy is elucidated, which is peculiar in each type of orientation. Thermal properties are shown as model calculations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Random-walk theory for localization

A continuous-time random-walk theory has been developed for Anderson localization. On a continuous time scale random walks are performed along extended (i.e., propagating) and localized (i.e., trap) states. Complete information of disorder is contained in a distribution function called “hopping time distribution function” ψ_nm(t), which gives the probability per unit time for transition from state m to state n in time t. The “stay-put” probability ??(t = ∞), which is the probability to rediscover an excitation at a site “0” at time t = ∞ if it was there at t = 0, is obtained in terms of ψ_nm(t). Appropriate forms for ψ_nm(t) are constructed which are in conformity with the photoconductivity experiments on dispersive transport, and ??(∞) are calculated. The results indicate that the entire spectrum consists of three regimes, namely, those of (i) “diffusion,” (ii) “weak diffusion,” and (iii) “no diffusion,” which, respectively, designate the extension, the power-law localization, and the exponential localization of states. The results also shed light on the question of “continuous or discontinuous (?)” transition across the mobility edge.     

Accurate ab initio potential energy surfaces for the 3A' and 3A' electronic states of the O(3P)+HBr system

In this work, we report the construction of potential energy surfaces for the (3)A(') and (3)A(') states of the system O((3)P) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O((3)P) + HBr → OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A(') electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A(') surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A(') and 4.16 kcal/mol for the (3)A(') state.     

The properties of off-shell coulomb radial wavefunctions

Approximations to exact wave functions for the scattering of few-particle systems often involve components corresponding to the interaction of two of the particles “off the energy-shell”. Several examples arising in the collision of ions and photons with atoms are given. An expansion in partial waves leads to an off-shell radial wave function. The defining differential equation is solved here numerically with particular emphasis on the behaviour arising from two-body potentials of long-range Coulomb form. The transition to shell of the radial wave functions, Jost functions and solutions andT-matrix elements is discussed for both short-range and Coulomb potentials. It is shown that the approximation of a Coulomb potential by a shorter-range form involves little error when sufficiently far off the energy shell.     

An approach to the understanding of radiation chemistry in the condensed phase

This paper describes a purely electronic mechanism by which ≈ 20 eV excitations in condensed phases relax to lower energy states. The mechanism utilizes an “energy fission” process whereby an ionic or excitonic state splits into two lower energy states, at least one being localized. The mechanism explains not only the known rapidity of such processes but also suggests an explanation for the proportionation of the chemistry between ionic and electronically excited states.     

Excited state proton transfer in guanine in the gas phase and in water solution: a theoretical study

Theoretical investigations were performed to study the phenomena of ground and electronic excited state proton transfer in the isolated and monohydrated forms of guanine. Ground and transition state geometries were optimized at both the B3LYP/6-311++G(d,p) and HF/6-311G(d,p) levels. The geometries of tautomers including those of transition states corresponding to the proton transfer from the keto to the enol form of guanine were also optimized in the lowest singlet pipi* excited state using the configuration interaction singles (CIS) method and the 6-311G(d,p) basis set. The time-dependent density function theory method augmented with the B3LYP functional (TD-B3LYP) and the 6-311++G(d,p) basis set was used to compute vertical transition energies using the B3LYP/6-311++G(d,p) geometries. The TD-B3LYP/6-311++G(d,p) calculations were also performed using the CIS/6-311G(d,p) geometries to predict the adiabatic transition energies of different tautomers and the excited state proton transfer barrier heights of guanine tautomerization. The effect of the bulk aqueous environment was considered using the polarizable continuum model (PCM). The harmonic vibrational frequency calculations were performed to ascertain the nature of potential energy surfaces. The excited state geometries including that of transition states were found to be largely nonplanar. The nonplanar fragment was mostly localized in the six-membered ring. Geometries of the hydrated transition states in the ground and lowest singlet pipi* excited states were found to be zwitterionic in which the water molecule is in the form of hydronium cation (H3O(+)) and guanine is in the anionic form, except for the N9H form in the excited state where water molecule is in the hydroxyl anionic form (OH(-)) and the guanine is in the cationic form. It was found that proton transfer is characterized by a high barrier height both in the gas phase and in the bulk water solution. The explicit inclusion of a water molecule in the proton transfer reaction path reduces the barrier height drastically. The excited state barrier height was generally found to be increased as compared to that in the ground state. On the basis of the current theoretical calculation it appears that the singlet electronic excitation of guanine may not facilitate the excited state proton transfer corresponding to the tautomerization of the keto to the enol form.