Normal Vibrational Coordinates Research Articles

DFT Study of Molecular Structure, Electronic and Vibrational Spectra of Tetrapyrazinoporphyrazine, Its Perchlorinated Derivative and Their Al, Ga and In Complexes.

Electronic and geometric structures of metal-free, Al, Ga and In complexes with tetrapyrazinoporphyrazine (TPyzPA) and octachlorotetrapyrazinoporphyrazine (TPyzPACl8) were investigated by density functional theory (DFT) calculations and compared in order to study the effect of chlorination on the structure and properties of these macrocycles. The nature of the bonds between metal atoms and nitrogen atoms was described using the NBO-analysis. Simulation and interpretation of electronic spectra were performed with the use of time-dependent density functional theory (TDDFT). A description of calculated IR spectra was carried out based on the analysis of the distribution of the potential energy of normal vibrational coordinates.

The Effect of Fluorine Substituents on the Intra- and Intermolecular Interaction Parameters of 1,4-Distyrylbenzene Molecules

We have compared and analyzed the parameters of the Franck–Condon (FC) and Herzberg–Teller (HT) interactions, which form the fine-structure spectra of stilbene, 1,4-distyrylbenzene, and tetrafluorodistyrylbenzene—compounds that are similar in their chemical structures but differ in the length of π-conjugation and in the presence of substituents in their benzene rings. The numerical values of the FC intramolecular interaction constants have been obtained, and, simultaneously, the values of the HT parameter have been found as quantitative values of the projections of the electronic transition vector of the dipole moment onto the normal vibrational coordinates. We have solved the question of transferability of these parameters in the homologous series of stilbene molecules containing the same sets of structural elements, which has made it possible to extend the use of the fragmentary approach to describe the fundamental bands of organic molecules of different homological series and to solve the problem of studying the structure of the spectra of large molecules.

High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Titanium Oxides and Their Cations (TiOn/TiOn+, n = 1 and 2).

The ionization energies (IEs) of TiO and TiO2 and the 0 K bond dissociation energies (D0) and the heats of formation at 0 K (ΔH°f0) and 298 K (ΔH°f298) for TiO/TiO+ and TiO2/TiO2+ are predicted by the wave-function-based CCSDTQ/CBS approach. The CCSDTQ/CBS calculations involve the approximation to the complete basis set (CBS) limit at the coupled cluster level up to full quadruple excitations along with the zero-point vibrational energy (ZPVE), high-order correlation (HOC), core-valence (CV) electronic, spin-orbit (SO) coupling, and scalar relativistic (SR) effect corrections. The present calculations yield IE(TiO) = 6.815 eV and are in good agreement with the experimental IE value of 6.819 80 ± 0.000 10 eV determined in a two-color laser-pulsed field ionization-photoelectron (PFI-PE) study. The CCSDT and MRCI+Q methods give the best predictions to the harmonic frequencies: ωe (ωe+) = 1013 (1069) and 1027 (1059) cm-1 and the bond lengths re (re+) = 1.625 (1.587) and 1.621 (1.588) Å, for TiO (TiO+) compared with the experimental values. Two nearly degenerate, stable structures are found for TiO2 cation: TiO2+(C2v) structure has two equivalent TiO bonds, while the TiO2+(Cs) structure features a long and a short TiO bond. The IEs for the TiO2+(C2v)←TiO2 and TiO2+(Cs)←TiO2 ionization transitions are calculated to be 9.515 and 9.525 eV, respectively, giving the theoretical adiabatic IE value in good agreement with the experiment IE(TiO2) = 9.573 55 ± 0.000 15 eV obtained in the previous vacuum ultraviolet (VUV)-PFI-PE study of TiO2. The potential energy surface of TiO2+ along the normal vibrational coordinates of asymmetric stretching mode (ω3+) is nearly flat and exhibits a double-well potential with the well of TiO2+ (Cs) situated around the central well of TiO2+(C2v). This makes the theoretical calculation of ω3+ infeasible. For the symmetric stretching (ω1+), the current theoretical predictions overestimate the experimental value of 829.1 ± 2.0 cm-1 by more than 100 cm-1. This work together with the previous experimental and theoretical investigations supports the conclusion that the CCSDTQ/CBS approach is capable of providing reliable IE and D0 predictions for TiO/TiO+ and TiO2/TiO2+ with error limits less than or equal to 60 meV. The CCSDTQ/CBS calculations give the predictions of D0(Ti+-O) - D0(Ti-O) = 0.004 eV and D0(O-TiO) - D0(O-TiO+) = 2.699 eV, which are also consistent with the respective experimental determination of 0.008 32 ± 0.000 10 and 2.753 75 ± 0.000 18 eV.

ChemInform Abstract: Elementary Electron Transfer Reactions: From Basic Concepts to Recent Computational Advances

AbstractReview: 118 refs.

Elementary electron transfer reactions: from basic concepts to recent computational advances

AbstractThe basic chemicophysical concepts and the most recent developments in the dynamics of the elementary electron transfer reactions are reviewed, posing particular attention to discrete state approaches, which combine use of a few experimental data with reliable ab initio calculations of the equilibrium nuclear configurations and normal coordinates of vibration of the redox partners. WIREs Comput Mol Sci 2013, 3:542–559. doi: 10.1002/wcms.1147This article is categorized under: Structure and Mechanism > Molecular Structures

Effect of the vibrational pattern of out-of-plane vibrational modes on vibronically induced spin-orbit coupling between ππ* states involved in nonradiative intersystem crossing transitions

To describe nonradiative intersystem crossing between excited ππ* states, the matrix elements of the operator of spin-orbit interaction are calculated. Adiabatic electronic functions that depend on out-of-plane normal vibrational coordinates are used as a zero approximation. Using dibenzofuran and tetrachloro-substituted dioxin as examples and taking into account all the out-of-plane vibrational modes, the effects of the vibrational patterns of these modes on the matrix elements under consideration, as well as of the spin-orbit coupling in carbon, oxygen, and chlorine atoms of individual atomic groups of the molecule, are discussed.

Theoretical investigations on valence vibronic transitions

This article reviews previously employed methods to study several valence electronic transitions, optically forbidden or not, enhancing intensity through vibronic coupling. Electronic transition dipole moments were calculated using several ab initio methods including electron correlation. In this method the square of the electronic transition dipole moments are directly calculated along the normal coordinates of vibration and then expanded with a polynomial function. Afterwards, analytical vibrational integration using harmonic wave functions, of the square of the transition moments function, allows us to obtain partial (i.e. for each vibrational mode) and total optical oscillator strengths (OOS), for the vibronic transition of interest. We illustrate the accuracy of the method through valence transitions of benzene (C6H6), formaldehyde (H2CO), acetone (C3H6O) and formic acid (HCOOH).

New method for calculating the moments of thermally averaged densities of distribution of internuclear distances in polyatomic molecules using the Bloch integral equation

A convenient method is suggested for calculating thermally averaged powers of the normal vibrational coordinates Q i by iteratively solving the Bloch integral equation with an anharmonic function of potential energy using multidimensional Hermite polynomials. Analytical formulas of the first approximation regarding anharmonicity constant have been obtained for the following moments of thermally averaged density: 〈Q 1〉, 〈 Q 1 2 〉, 〈Q 1 Q 2〉, 〈Q 1 3 〉 〈Q 1 3 〉, 〈Q 1 Q 2 Q 3〉, 〈Q 1 4 〉, 〈Q 1 2 Q 2 2 〉, 〈Q 1 Q 2/3〉, 〈Q 1 Q 2 Q 3 2 〉, 〈 Q 1 Q 2 Q 3 Q 4〉.

Dynamics of radiationless transitions in large molecular systems: A Franck–Condon-based method accounting for displacements and rotations of all the normal coordinates

An efficient method to study the dynamics of radiationless transition in large molecular systems is proposed. It is based on the use of the whole set of normal coordinates of vibration and allows for taking properly into account both the displacements and the mix of the normal modes upon transition between two electronic states. The Hamiltonian matrix elements are written in terms of generalized Franck–Condon integrals and are analytically evaluated by recursion formulas. Applications to the S2→S1 internal conversion in pyrazine and to long-range electron transfer between quinones in photosynthetic reaction centers are given.

Contributions to the generalized oscillator strength for the inner-shell C1s→3sσgtransition inCO2from the vibronic coupling mechanism

An approach is proposed to account for the general effect of the nuclei motion in the intensity of electronic transitions caused by fast electron collision with molecular targets, following a similar procedure that has recently been used by our group to determine the optical oscillator strength of symmetry-forbidden transition, and which consists of expanding the (squared) transition moment along the normal coordinates of vibration. It is shown that the profile of total generalized oscillator strength as a function of the squared transferred moment can be significantly changed by the inclusion of terms that depend explicitly on the normal coordinates of vibration. The generalized oscillator strength for the inner-shell C $1\stackrel{\ensuremath{\rightarrow}}{s}3s{\ensuremath{\sigma}}_{g}$ transition in ${\mathrm{CO}}_{2}$ is calculated within this approach and compared with experimental results.

Direct Investigation of the Validity of Vertical Approximation in the Calculation of Transition Moment Matrix Elements: n → π* Transition in Methyl Formate

The absolute optical oscillator strength for the n → π* transition in methyl formate is calculated, within a procedure that has recently been used by our group to determine the optical oscillator strength of symmetry-forbidden transitions and which consists of expanding the (squared) transition moment along the normal coordinates of vibration. In the present work, we extend its application to a symmetry-allowed transition and discuss the applicability of the vertical approximation. To validate the present results, the UV photoabsorption cross-section was measured, and the result is compared with the one previously reported.

The interpretation of vibrational spectra of ionic melts

Computer simulations of the short-time, vibrational dynamics of the network-forming ionic melts, LaCl3 and ZnCl2, and of their mixtures with network-breaking alkali halides are described. In the mixtures, high frequency peaks in the vibrational density of states are shown to be describable in terms of the normal coordinates of vibration of transient molecular ion species, like LaCl63− and ZnCl42−. Novel simulation methods are presented which allow this association to be established. In the pure melts, the vibrational motions retain a strong aspect of this local polyhedral unit vibrational character, but the effects of network-induced coupling between the vibrations of different units become pronounced, particularly in ZnCl2. The calculated vibrational spectra are compared with extensive Raman data on these systems, and with infrared and neutron spectra in pure ZnCl2. For the mixtures, remarkably good agreement with experiment is found, confirming the high quality of the representation of the interionic interactions obtained with the polarizable ion model potentials used. For the melts, there are discrepancies between the peak frequencies observed in the vibrational DOS and the Raman spectra. These discrepancies are likely to be due to the network-induced couplings, whose effect on the Raman (and infrared) spectra is not fully included in the calculated DOS.

Density functional computations of the dipole moment derivatives for halogenated silanes

Electric dipole moments for the equilibrium molecular structures and their derivatives along the symmetry coordinates of vibration were computed for SiH 2F 2, SiD 2F 2, SiH 2Cl 2, SiD 2Cl 2, SiH 3F, SiD 3F, SiH 3Cl, SiD 3Cl, SiHF 3, SiDF 3, SiHCl 3, SiDCl 3, SiFCl 3, SiF 3Cl, SiF 4 and SiCl 4 by means of the de mon density functional program (A. St-Amant and D. R. Salahub, Chem. Phys. Lett., 169 (1990) 387). Satisfactory agreement was found between the experimental and computed dipole moments for the equilibrium molecular structures. Perfect agreement was found between the rotational corrections to the dipole moment derivatives calculated by de mon and those obtained independently from the orthogonality relationships between the symmetry coordinates and the rotational coordinates. Derivatives of the dipole moments were transformed into the representation of the normal coordinates of vibration and the results were compared with the experimental data which are available on the infrared intensities of fundamental bands.

EXCITED STATE DYNAMICS OF RETINAL PROTEINS AS STUDIED BY FOURIER TRANSFORM OF OPTICAL ABSORPTION SPECTRUM—II. THEORETICAL ANALYSIS OF WAVEPACKET PROPAGATION OF RHODOPSIN

Abstract— We theoretically calculated the absolute value of the time correlation function (tcf) of the wavepacket propagation in the excited state using the independent harmonic oscillators model for vibration and compared it with the experimental data obtained by the Fourier transform of optical absorption spectrum (FTOA) of rhodopsin in the preceding paper. We found that the theoretically calculated tcf differs significantly from the FTOA data. This fact indicates that the intrinsic harmonic oscillators model is too crude. We showed that better agreement is obtained between the calculated tcf and the FTOA data if we add an extra mode with low frequency and considerable decay constant which is not observable in the resonance Raman spectra. We also proposed that substantial mode‐mixing would take place among normal coordinates of vibrations at the Franck‐Condon state of the excited state and would contribute to the very rapid relaxation of vibrational energies.

Ab initio and localised molecular orbital studies of the integrated intensities of infrared absorption bands of polyatomic molecules. Part 5.—Minimal- and extended-basis-set results for the pyramidal AX3series (A = N, P; X = H, F)

Ab initio SCF-GTO type calculations on the dipole-moment derivatives with respect to the normal coordinates of vibration (∂µ/∂Qi)0 for pyramidal AX3 molecules (A = N, P; X = H, F) are reported. A comparison between theoretical and experimental infrared intensity values Ai shows that double-zeta (DZ) values are generally worse than those obtained with a minimal (STO-3G) basis set, which may be qualified as satisfactory. For NH3 and PH3 calculations with more extended basis sets, including polarization functions, (DZ + P) were also performed. Finally, diffuse functions were included in the calculations for NH3; this leads to a substantial improvement of the DZ or “DZ + P” results. A “DTZPD” basis for NH3(double-zeta for N, triple-zeta for H, including polarization and diffuse functions) was set up; this gives (∂µ/∂Qi)0 values which are close to recently published near-Hartree–Fock results. The sign instability of the stretching derivatives upon change of atomic basis is discussed in terms of derivatives with respect to symmetry coordinates. The “DTZPD” signs for the (∂µ/∂Qi)0 in NH3 are identical to those obtained in the STO-3G case, except for Q3.The STO-3G dipole-moment derivative calculations reproduce the experimental sequence for the A1, A2 and A3 integrated intensities along the AX3 series; this sequence is interpreted via a combined investigation of vibrational and electronic factors. The smaller A1 value for NH3 as compared with NF3 is vibrational in origin, whereas the smaller A1 intensity of NF3 as compared with PF3 is essentially due to electronic factors. The A2 sequence is analysed in terms of the N or P lone-pair behaviour during the bending mode; the lone pairs of the fluorine atoms present in the molecule are seen to have a drastic influence on the intensities; incomplete orbital following of the AX bonds is described. The NH3 LMO results in the minimal basis for (∂µ/∂Q1)0 and (∂µ/∂Q2)0 are quite comparable with those obtained with the larger “DTZPD” basis set. For the asymmetric stretching vibration (Q3), the higher calculated (and experimental) intensity in PF3 as compared with NH3 again mainly resides in an important contribution of the fluorine lone pairs to the intensity of this mode, but also in an inversion of sign in the contributions of the corresponding P—F and N—H bonds.

Vibrational properties of crystals with TlSe type structure

The lattice vibration spectra of TlS and TllnSe 2 crystals were investigated by infrared reflectivity in the wavenumber range from 20 to 5000 cm −1. The frequencies of K = 0 phonons were determined by Kramers-Kronig analysis of the spectra. All five infrared active lattice vibrations predicted by the group theoretical analysis were identified. The normal coordinates of vibrations for five infrared active phonons were determined. In the approximation which does not take into consideration long range Coulomb interaction values of the force constant and effective changes are obtained for TlSe, TlS and TllnSe 2 crystals.

Calculations on the optical activity due to isotopic substitution: [1-D]- and [2- 18O]-α-fenchocamphoronequinone. Relationship to the optical activity of 1-substituted α-diones

It is shown that an electronic rotational strength R( Q) that depends linearly on the normal vibrational coordinates Q can account for optical activity due to isotopic substitution, provided anharmonicities in the nuclear potentials are taken into account. The expression for this rotational strength is cast into a convenient form by expanding R( O) around the average geometry of the molecule in its ground state rather than, as usual, around the equilibrium geometry. For [1-D]-α-fenchocamphoronequinone (H) and [2- 18O]-α-fenchocamphoronequinone (V) the magnitude of the rotational strength of the first singlet—singlet transition is calculated using a polarizability model. The obtained rotational strengths of II and V agree in sign and order of magnitude with the observed values. This result not only supports our description of isotopically induced optical activity but also indicates that the polarizability model is capable of describing adequately the optical activity in the first singlet—singlet transition of α-norbornanediones. This latter conclusion has an interesting implication: when it is assumed that the dicarbonyl moiety in camphorquinone and [1-Br]-α-fenchocamphoronequinone is planar, the calculated rotational strengths agree quite well with the results obtained from experiment. This indicates that in the acquirement of optical activity in the visible absorption band of cisoid α-diketones the effect of vicinal groups may successfully compete with the effect of inherent twist.

Dissociation processes of polyatomic molecules

A general quantum mechanical theory is considered for the diverse dissociation processes of polyatomic molecules. The theory emphasizes the use of the proper normal vibrational coordinates for both the initial state of the polyatomic molecule and the final state of the dissociation fragments. The present theory provides a significant advance over all previous ones that invoke the quasidiatomic hypothesis, wherein the reaction coordinate is taken to be an initial normal mode, the remaining fragment normal modes are assumed to be identical to initial state normal modes, and the dissociation into vibrationally excited fragments is assumed to arise from the final state interactions occurring during the recoil of the fragments. Our more general theory of the vibrational and translational energy distributions in the fragments leads to a generalized Franck–Condon description of dissociation processes in terms of multidimensional bound-continuum matrix elements which can be reduced to one-dimensional ones that are amenable to analytic approximation. The Franck–Condon theory leads to simple criteria for the occurrence of fragment vibrational population inversions. These criteria are dependent on known spectroscopic constants for both the initial molecule and fragments and the repulsive potential between the receding fragments. The effects of final state interactions on the product vibrational distribution are incorporated by the use of a semiclassical model which demonstrates that the Franck–Condon rearrangement type process is dominant for a large number of systems. The theory is explicitly used to evaluate the vibrational distributions for photodissociation of HCN and ICN. The theory may also be applied to predissociation, unimolecular decomposition, and collisional induced dissociation.