Ionic vibrational breathing mode of metallic clusters

The energy of the vibrational mode with spherical symmetry, in which the ionic cores oscillate in the radial direction around the equilibrium geometry (ionic breathing mode) is calculated for trivalent (Al_N, 2≤N≤50) and monovalent (Na_N, 2≤N≤73; Cs_N, 2≤N≤74) metallic clusters. The ground-state total energy is calculated using density functional theory, with a spherically averaged pseudopotential to describe the ion–electron interaction and optimizing the geometry by the simulated annealing technique. The energy of the ionic mode is calculated by diagonalization of the dynamical matrix including the electronic relaxation in the linear response approximation. The compressibility and bulk modulus of the metallic cluster are obtained from the energies of the monopole oscillations. These energies present a linear behavior on the inverse of the cluster radius, which is analyzed using a semiclassical liquid drop mass formula for the total energy of the clusters and a scaling model. The values of the vibrational frequencies present electronic shell closing effects for the three metals.©1997 John Wiley & Sons, Inc.     

General theory of vibrational mode mixing and frequency shifts in resonance raman scattering

A general formalism is given for treating vibrational mode mixing, frequency shifts, and atomic equilibrium position shifts under electronic excitation in resonance Raman scattering. The theory is exact for first-order scattering at T = 0 K for all linear and quadratic electron-phonon coupling strengths. Numerical results illustrating mode mixing are presented.     

Optical control of excited-state vibrational coherences of a molecule in solution: The influence of the excitation pulse spectrum and phase in LD690

Spectral and phase shaping of femtosecond laser pulses is used to selectively excite vibrational wave packets on the ground (S0) and excited (S1) electronic states in the laser dye LD690. The transient absorption signals observed following excitation near the peak of the ground-state absorption spectrum are characterized by a dominant 586 cm(-1) vibrational mode. This vibration is assigned to a wave packet on the S0 potential energy surface. When the excitation pulse is tuned to the blue wing of the absorption spectrum, a lower frequency 568 cm(-1) vibration dominates the response. This lower frequency mode is assigned to a vibrational wave packet on the S1 electronic state. The spectrum and phase of the excitation pulse also influence both the dephasing of the vibrational wave packet and the amplitude profiles of the oscillations as a function of probe wavelength. Excitation by blue-tuned, positively chirped pulses slows the apparent dephasing of the vibrational coherences compared with a transform-limited pulse having the same spectrum. Blue-tuned negatively chirped excitation pulses suppress the observation of coherent oscillations in the ground state.     

Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties

An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.     

An unusually large nonadiabatic error in the BNB molecule

The vibronic coupling model of Ko?uppel, Domcke, and Cederbaum in one dimension is introduced as a means to estimate the effects of electronic nonadiabaticity on the vibrational energy levels of molecules that exhibit vibronic coupling. For the BNB molecule, the nonadiabatic contribution to the nominal fundamental vibrational energy of the antisymmetric stretching mode is approximately -80?cm(-1). The surprisingly large effect for this mode, which corresponds to an adiabatic potential that is essentially flat near the minimum due to the vibronic interaction, is contrasted with another model system that also exhibits a flat potential (precisely, a vanishing quadratic force constant) but has a significantly larger gap between interacting electronic states. For the latter case, the nonadiabatic contribution to the level energies is about two orders of magnitude smaller even though the effect on the potential is qualitatively identical. A simple analysis shows that significant nonadiabatic corrections to energy levels should occur only when the affected vibrational frequency is large enough to be of comparable magnitude to the energy gap involved in the coupling. The results provide evidence that nonadiabatic corrections should be given as much weight as issues such as high-level electron correlation, relativistic corrections, etc., in quantum chemical calculations of energy levels for radicals with close-lying and strongly coupled electronic states even in cases where conical intersections are not obviously involved. The same can be said for high-accuracy thermochemical studies, as the zero-point vibrational energy of the BNB example contains a nonadiabatic contribution of approximately -70?cm(-1) (-0.9?kJ mol(-1)).     

An ab initio theoretical study of the optical spectrum of CF2

The ab initio calculation methods have been used to calculate the spectral and electronic characteristics of difluorocarbene in the ground electronic state (¹A₁), the lowest-lying singlet (¹B₁) and triplet (³B₁) states. The optimized equilibrium geometries, rotational constants, harmonic vibrational frequencies and energy gaps, electronic charges, dipole moments of these states have been computed with different basis sets. The calculated vibrational frequency of ³B₁ state (v₂=522 cm^?1) and the energy separation (2.26 eV) between ³B₁ and ¹A₁ states are in good agreement with the experimental results (519 cm^?1, 2.46 eV respectively). According to the calculations the previous assignment of vibrational symmetries of ¹B₁ state was corrected, and some experimentally undetermined vibrational frequencies were predicted.     

Slow periodic oscillations in time domain dynamics of NO2

The authors investigated the time domain nonadiabatic dynamics of NO2 on the coupled X 2A1 and A 2B2 electronic states by launching wave packets on the excited electronic state and focused on the evolution at long times (t>200 fs), which has received little attention up to now. The authors showed that the initial fast spreading of the wave packets is followed at all energies by slow periodic intramolecular vibronic energy redistribution (IVER) with periods in the range of 0.3 to several tens of picoseconds. These energy transfers lead to oscillations with the same periods in the population of each electronic state. Propagation of wave packets indicates that IVER frequencies also dominate the fluctuations of the squared modulus of the autocorrelation function |A(t)|2 at energies not too high above the bottom of the conical intersection, but this is no longer the case at higher energies. For example, for initial wave packets prepared by almost vertical excitation of the vibrational ground state of the ground electronic surface, the oscillations of |A(t)|2 essentially reflect the detuning from 1:2 resonance between the frequency of the bend and that of the symmetric stretch in the excited electronic state. These theoretical results were used to discuss the possible origin of the low-frequency oscillations which were recently observed in time domain experimental spectra of NO2.     

On quantifying the vibronic interaction between electronic states

An accurate estimation of the interstate vibronic coupling strength is of particular relevance for the treatment of nonadiabatic dynamics. This is not a trivial task because direct interactions between electronic states have to be separated from intrinsic frequency shifts. Surprisingly, this issue has not been discussed in detail in the literature so far. An analysis of the error dependence is given for two formulas derived from linear vibronic coupling theory. The difficulty in estimating the interstate coupling parameters is shown to originate from the initially unknown contribution of the diagonal quadratic coupling coefficients to the total vibronic coupling. An interpretation of the error analysis including a numerical case study is followed by a more general discussion of the different mechanisms that can shape adiabatic electronic potential energy functions. Qualitative criteria are formulated for the differentiation between interstate and intrastate vibronic coupling effects based on electronic structure information. These ideas are then applied to investigate vibronic coupling problems in pyrazine as well as trans- and cis-hexatriene.     

FT-IR, FT-Raman, ab initio and DFT structural, vibrational frequency and HOMO-LUMO analysis of 1-naphthaleneacetic acid methyl ester

In this work, the FT-IR and FT-Raman spectra of 1-naphthaleneacetic acid methyl ester (abbreviated as 1-NAAME, C₁₀H₇CH₂CO₂CH₃) have been recorded in the region 3600–10 cm⁻¹. The optimum molecular geometry, normal mode wavenumbers, infrared and Raman intensities, Raman scattering activities, corresponding vibrational assignments, Mullikan atomic charges and other thermo-dynamical parameters were investigated with the help of HF and B3LYP (DFT) method using 6-31G(d,p), 6-311G(d,p) basis sets. Reliable vibrational assignments were made on the basis of total energy distribution (TED) calculated with scaled quantum mechanical (SQM) method. From the calculations, the molecules are predicted to exist predominantly as the C1 conformer. The correlation equations between heat capacity, entropy, enthalpy changes and temperatures were fitted by quadratic formulae. Lower value in the HOMO and LUMO energy gap explains the eventual charge transfer interactions taking place within the molecule. UV–VIS spectral analyses of 1NAAME have been researched by theoretical calculations. In order to understand electronic transitions of the compound, TD-DFT calculations on electronic absorption spectra in gas phase and solvent (DMSO and chloroform) were performed. The calculated frontier orbital energies, absorption wavelengths (λ), oscillator strengths (f) and excitation energies (E) for gas phase and solvent (DMSO and chloroform) are also illustrated.     

Jahn-Teller effect for short-lived states: study of the complex potential energy surfaces

The Jahn-Teller effect for bound electronic states has been investigated for many decades. In contrast, nothing is known regarding its occurrence for short-lived electronic states. Here we investigate the linear and the quadratic E multiply x e Jahn-Teller effect for degenerate resonance states with special regard to the complex potential energy surfaces. We find many new phenomena for both the real and imaginary parts of the potential energy surfaces including additional minima and intersections. Possible simplifications of the equations describing the adiabatic potential energy surfaces are discussed. We also briefly investigate other Jahn-Teller effects in linear approximation. The theoretical concepts are exemplified by calculating ab initio data for the degenerate Pi(*)-type resonance states of the tris(boramethyl)amin anion along two different doubly degenerate vibrational modes.     

Valence-only model potential calculations on copper hydride molecule

Different sets of one-electron functions obtained according to the strong-orthogonal geminal theory (GEM) [1], the Generalized Molecular Orbital (GMO) method [2] and the exchange maximization between virtual and occupied orbitals (EVO) [3], are tested as basis for CI calculations. The efficiency of the three procedures is discussed investigating the electronic structure of the CuH molecule using an effective-core potential. The values computed for the bond length, the dissociation energy and the vibrational frequency of the ground electronic state are compared with the experimental ones. The charge distribution is examined to estimate the contribution of the d electrons to the Cu-H bond. Comparisons are made with the results obtained by other theoretical works in which the copper atom is treated as a one valence electron atom.     

Ab initio scf and Ci study of the electronic structure of the trichlorine radical

Ab initio SCF and CI calculations using a double-zeta plus polarization basis set have been carried out on the trichlorine radical Cl₃ to determine its electronic structure. The minimum in energy is determined for a bent structure at a bond angle of 146° and bond lengths of 2.18 Å (SCF ) or 2.22 Å (CI ). At linear geometry a ²Π_u state is found to be lowest, approximately 7 kcal above the bent minimum, followed by a ²∑_g⁺ state, which is around 4 kcal higher. This situation suggests that already for low quantum numbers a complex vibrational pattern in the Cl₃ infrared spectrum is to be expected due to spin-orbit coupling as well as coupling of electronic, vibrational, and rotational motion.     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [²(²A′ and ²A′)] and ²Σ⁺[²A′] of the C₂F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a ² linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm⁻¹ above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the ²Σ⁺ and the ² lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.     

Aromatic Charge Resonance Interaction Probed by Infrared Spectroscopy

Charge resonance is a strong attractive intermolecular force in aromatic dimer radical ions. Despite its importance, this fundamental interaction has not been characterized at high resolution by spectroscopy of isolated dimers. We employ vibrational infrared spectroscopy of cold aromatic pyrrole dimer cations to precisely probe the charge distribution by measuring the frequency of the isolated N?H stretch mode (ν_NH). We observe a linear correlation between ν_NH and the partial charge q on the pyrrole molecule in different environments. Subtle effects of symmetry reduction, such as substitution of functional groups (here pyrrole replaced by N‐methylpyrrole) or asymmetric solvation (here by an inert N₂ ligand), shift the charge distribution toward the moiety with lower ionization energy. This general approach provides a precise experimental probe of the asymmetry of the charge distribution in such aromatic homo‐ and heterodimer cations.     

Theoretical and experimental studies of collision-induced electronic energy transfer from v=0-3 of the E(0g +) ion-pair state of Br2: collisions with He and Ar

Collisions of Br(2), prepared in the E(0(g)+) ion-pair (IP) electronic state, with He or Ar result in electronic energy transfer to the D, D', and beta IP states. These events have been examined in experimental and theoretical investigations. Experimentally, analysis of the wavelength resolved emission spectra reveals the distribution of population in the vibrational levels of the final electronic states and the relative efficiencies of He and Ar collisions in promoting a specific electronic energy transfer channel. Theoretically, semiempirical rare gas-Br(2) potential energy surfaces and diabatic couplings are used in quantum scattering calculations of the state-to-state rate constants for electronic energy transfer and distributions of population in the final electronic state vibrational levels. Agreement between theory and experiment is excellent. Comparison of the results with those obtained for similar processes in the IP excited I(2) molecule points to the general importance of Franck-Condon effects in determining vibrational populations, although this effect is more important for He collisions than for Ar collisions.     

Hydrogen bonding in the mixed HF/HCl dimer: Is it better to give or receive?

The ClH⋯FH and FH⋯ClH configurations of the mixed HF/HCl dimer (where the donor⋯acceptor notation indicates the directionality of the hydrogen bond) as well as the transition state connecting the two configurations have been optimized using MP2 and CCSD(T) with correlation consistent basis sets as large as aug‐cc‐pV(5 + d)Z. Harmonic vibrational frequencies confirmed that both configurations correspond to minima and that the transition state has exactly one imaginary frequency. In addition, anharmonic vibrational frequencies computed with second‐order vibrational perturbation theory (VPT2) are within 6 cm⁻¹ of the available experimental values and deviate by no more than 4 cm⁻¹ for the complexation induced HF frequency shifts. The CCSD(T) electronic energies obtained with the largest basis set indicate that the barrier height is 0.40 kcal mol⁻¹ and the FH⋯ClH configuration lies 0.19 kcal mol⁻¹ below the ClH⋯FH configuration. While only modestly attenuating the barrier height, the inclusion of either the harmonic or anharmonic zero‐point vibrational energy effectively makes both minima isoenergetic, with the ClH⋯FH configuration being lower by only 0.03 kcal mol⁻¹. © 2018 Wiley Periodicals, Inc.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Correlation between intramolecular bond distances and stretching vibrations for polar molecules: An ab initio study

The correlation between intramolecular bond length and vibrational frequency shifts was calculated at the MP4(aug-cc-PVTZ) ab initio level for a number of molecules (LiH, BH, HF, OH⁻, HDO, BF, CN⁻, and HCI) exposed to uniform electric fields in the range from −0.10 to +0.10 au. The “ω vs. r_e” correlation curves always consist of two branches, each approximately linear. The slopes for the molecules investigated here vary between −2500 and −16600 cm⁻¹/Å. The slopes are well described by an expression containing only the free-molecule second- and third-order force constants and the reduced mass for the stretching mode. Experimental data for polar molecules can be expected to show deviations from a linear “ω vs. r_e” correlation (i) for molecules where the maximum of the frequency vs. field curve occurs at a positive field and (ii) for molecules where the maximum of the frequency vs. field curve falls on the negative-field side but very close to the zero-field case, and (iii) in bonding situations when there is much electron overlap. As opposed to uniform-field situations, anharmonicity and electronic overlap have a substantial influence on the “frequency vs. r_e” slopes in molecular environments. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 537–546, 1997