Normal Coordinate Analysis in Cartesian Space I. Planar Symmetric Xn Molecules

Normal coordinate analysis of X_n type molecules can be carried out in the Cartesian space as well as in the internal space. Force constants in Cartesian coordinates for aromatic compounds belonging to D_nh group are calculated. The force constants of benzene are evaluated from vibrational frequencies both in the ground state and the ¹B_1u excited state. The calculated frequencies of planar carbon vibration of annulene of any N are tabulated. The normal coordinates derived from the calculation of 10-annulene are roughly the same of naphthalene derived more elaborated by Scherer. The normal modes in 10-annulene are indeed good approximations to the ones in naphthalene. This conclusion is valid for the other aromatic compounds.     

Ab initio vibrational transition dipole moments and intensities of formaldehyde

Vibrational transition dipole moments and absorption band intensities for the ground state of formaldehyde, including the deuterated isotopic forms, are calculated. The analysis is based on ab initio SCF and CI potential energy and dipole moment surfaces. The formalism derives from second-order perturbation theory and involves the expansion of the dipole moment in terms of normal coordinates, as well as the incorporation of point group symmetry in the selection of the dipole moment components for the allowed transitions. Dipole moment expansion coefficients for the three molecule-fixed Cartesian coordinates of formaldehyde are calculated for internal and normal coordinate representations. Transition dipole moments and absorption band intensities of the fundamental, first overtone, combination, and second overtone transitions are reported. The calculated intensities and dipole moment derivatives are compared to experiment and discussed in the context of molecular orbital and bond polarization theory.     

Ab initio calculation of resonance Raman cross sections based on excited state geometry optimization

A method for the calculation of resonance Raman cross sections is presented on the basis of calculation of structural differences between optimized ground and excited state geometries using density functional theory. A vibrational frequency calculation of the molecule is employed to obtain normal coordinate displacements for the modes of vibration. The excited state displacement relative to the ground state can be calculated in the normal coordinate basis by means of a linear transformation from a Cartesian basis to a normal coordinate one. The displacements in normal coordinates are then scaled by root-mean-square displacement of zero point motion to calculate dimensionless displacements for use in the two-time-correlator formalism for the calculation of resonance Raman spectra at an arbitrary temperature. The method is valid for Franck-Condon active modes within the harmonic approximation. The method was validated by calculation of resonance Raman cross sections and absorption spectra for chlorine dioxide, nitrate ion, trans-stilbene, 1,3,5-cycloheptatriene, and the aromatic amino acids. This method permits significant gains in the efficiency of calculating resonance Raman cross sections from first principles and, consequently, permits extension to large systems (>50 atoms).     

Transfer of molecular property tensors in cartesian coordinates: A new algorithm for simulation of vibrational spectra

A direct transfer of Cartesian molecular force fields (FF) and electric property tensors is tested on model systems and compared to transfer in internal coordinates with an aim to improve simulation of vibrational spectra for larger molecules. This Cartesian transformation can be implemented easily and offers greater flexibility in practical computations. It can be also applied for transfer of anharmonic derivatives. The results for model calculations of the force field and vibrational frequencies for N-methylacetamide show that our method removes errors associated with numerical artifacts caused by nonlinearity of the otherwise required Cartesian to internal coordinate transformation. For determination of IR absorption and vibrational circular dichroism intensities, atomic polar and axial tensors were also transferred in the Cartesian representation. For the latter, which are dependent upon the magnetic dipole operator, a distributed origin gauge is used to avoid an origin dependence. Comparison of the results of transferring ab initio FF and intensity parameters from an amide dimer fragment onto a tripeptide with those from a conventionally determined tripeptide FF document some limitations of the transfer method and its possible applications in the vibrational spectroscopy. Finally, application to determination of the FF and spectra for helical heptapeptide are presented and compared to experimental results. © 1997 by John Wiley & Sons, Inc.     

Interpretation of resonance cars and shpolskii spectra with calculated molecular geometries,vibrational frequencies and relative intensities: Chrysene in it's lowest excited singlet and triplet state

Coherent anti-Stokes Raman scattering (CARS) spectra of excited molecules as well as Shpolskii spectra provide information about geometry changes between ground and excited states. Vibrational frequencies and relative intensities from recently obtained CARS spectra of the chrysene S₁ and T₁ state and earlier observed Shpolskii spectra are interpreted in terms of molecular geometry and force-field changes by means of quantum-chemical consistent force field (QCFF) and Franck-Condon factor calculations. The comparison of observed and calculated relative intensities indicates a coupling between the S₁ and S₂ state enhancing some of the vibrational radiative singlet transitions both in absorption and fluorescence spectra whereas within the phosphorescence spectra proportionality to calculated Franck-Condon factors is obeyed. The T₁ state is the more loosely bound state and its geometry change is different from that of the S₁ state. The resonance CARS transitions in the S₁ state are assigned to totally symmetric vibrations getting their intensity by a coupling scheme analogous to the A term of the resonance Raman effect: the relative intensity of a transition is shown to be proportional to the Franck-Condon factor to the higher excited state and to the squared vibrational frequency. Using this relation this state can be identified by means of its finger-print-like intensity pattern.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

Normal coordinate treatment of 1-methyluracil in the crystal state: Use of the ultraviolet resonance Raman intensities to improve the vibrational force field

Normal modes of 1-methyluracil in the crystal state have been determined using a general valence force field. In-plane force constants have been deduced from relations between ultraviolet resonance Raman intensities (UVRR), variations in bond orders from the ground to the electronic excited states and frequencies. Positions for molecules in the orthorhombic system (space group Ibam) were deduced from lattice energy calculations. A very good agreement in the normal modes assignments is obtained with previous works, leading to confidence with the use of UVRR intensities to deduce adequate force-fields.     

Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

Resonance Raman spectra of β-carotene and its molecular structure in the excited electronic state

The resonance Raman spectra of β-carotene have been obtained at low temperature. The excitation profiles of ν₁ (1525 cm^?1) and 2ν₁ (3043 cm^?1) are analysed in terms of the Albrecht theory. The overlap integrals between the vibrational wavefunctions of the ground and the first excited electronic states are shown to be the most important factor in determining the resonance Raman intensities of this molecule. Information on the structure of the electronically excited state has been obtained.     

Diamagnetic Raman Optical Activity of Chlorine,Bromine, and Iodine Gases

Magnetic Raman optical activity of gases provides unique information about their electric and magnetic properties. Magnetic Raman optical activity has recently been observed in a paramagnetic gas (Angew. Chem. Int. Ed. 2012 , 51, 11058; Angew. Chem. 2012 , 124, 11220). In diamagnetic molecules, it has been considered too weak to be measurable. However, in chlorine, bromine and iodine vapors, we could detect a significant signal as well. Zeeman splitting of electronic ground‐state energy levels cannot rationalize the observed circular intensity difference (CID) values of about 10^?4. These are explicable by participation of paramagnetic excited electronic states. Then a simple model including one electronic excited state provides reasonable spectral intensities. The results suggest that this kind of scattering by diamagnetic molecules is a general event observable under resonance conditions. The phenomenon sheds new light on the role of excited states in the Raman scattering, and may be used to probe molecular geometry and electronic structure.     

Diamagnetic Raman Optical Activity of Chlorine,Bromine, and Iodine Gases

Magnetic Raman optical activity of gases provides unique information about their electric and magnetic properties. Magnetic Raman optical activity has recently been observed in a paramagnetic gas (Angew. Chem. Int. Ed. 2012 , 51, 11058; Angew. Chem. 2012 , 124, 11220). In diamagnetic molecules, it has been considered too weak to be measurable. However, in chlorine, bromine and iodine vapors, we could detect a significant signal as well. Zeeman splitting of electronic ground‐state energy levels cannot rationalize the observed circular intensity difference (CID) values of about 10⁻⁴. These are explicable by participation of paramagnetic excited electronic states. Then a simple model including one electronic excited state provides reasonable spectral intensities. The results suggest that this kind of scattering by diamagnetic molecules is a general event observable under resonance conditions. The phenomenon sheds new light on the role of excited states in the Raman scattering, and may be used to probe molecular geometry and electronic structure.     

Green's Function Determination of Force Constants-H2O as Example

Treating isotopically substituted molecule as a perturbed system, Green's function for the perturbation are constructed and related to the force field of vibration. By spectral representation, Green's function is diagonalized in the normal coordinates. Then transforming back to the Cartesian coordinates, the Cartesian force constants are generated without solving the secular equation directly. The relations between the internal force constants and the Cartesian force constants ate given and complete internal force field can be obtained. The results for H₂O are discussed.     

All-trans- and t,T,t,C,t,T,t-deca-1,3,5,7,9-Pentaenes: Ab Initio Structures,Vibrational Analyses,and Some Regularities in the Series of Related Molecules

Total geometry optimization and calculation of the force constants for all-transand t,T,t,C,t,T,tdeca-1,3,5,7,9-pentaene were carried out at the ab initio, HF/6-31G level. The HF/6-31G//HF/ 6-31G force fields were modified using empirical scale factors transferred from trans-buta-1,3-diene augmented by an additional scale factor for the central formal carbon-carbon double bond coordinates (determined previously for all-trans-hexa-1,3,5-triene). The total number of scale factors was seven. The vibrational problems for both decapentaenes were solved using the respective scaled HF/6-31G//HF/6-31G force field. Infrared intensities and Raman activities were calculated from the unscaled HF/6-31G//HF/6-31G force fields. Complete assignment of all the fundamental vibrational frequencies is given. Geometrical parameters, vibrational frequencies and force constants are compared with the corresponding values of buta-1,3-diene, hexa-1,3,5-triene and octa-1,3,5,7-tetraene. Regularities in the properties of this molecular series are discussed. Special attention is given to the possibility of using the vibrational spectra for detection of distortions from the regular trans structure of these oligoenes.     

The use of ultraviolet resonance Raman intensities to test proposed molecular force fields for nucleic acid bases

The harmonic molecular force fields for the nucleic acid bases, cytosine, and guanine, that have been previously published by several investigators are tested by the calculation of the relative intensities of the in-plane modes in the ultraviolet resonance Raman (UVRR) effect from the two lowest lying absorption bands using a theoretical approach devised previously.^1–3 Since only a fraction of the 2N – 3 in-plane vibrations of a molecule are active in the UVRR, the two criteria that are taken for the adjustment of the force constant are: (1) the closest possible agreement between the observed and calculated frequencies of the 2N – 3 in-plane vibrations, and (2) the closest possible agreement between the calculated and observed intensities of those few vibrations that are strongly active in the ultraviolet resonance Raman effect. In particular it is necessary that the force constants be adjusted to avoid the calculation of intense Raman lines with frequencies that are not observed in the UVRR spectrum. Using this criteria, a new force field has been developed that appears to give better agreement with the observed UVRR intensities than previously published ones. It is suggested that this calculation of the UVRR intensities can be used to refine molecular force fields in combination with other methods such as isotopic replacement currently in use to refine force constants.     

Benzyl alcohol-ammonia (1:1) cluster structure investigated by combined IR-UV double resonance spectroscopy in jet and ab initio calculation

Laser-induced fluorescence excitation and IR-UV double resonance spectroscopy have been used to determine the hydrogen-bonded structure of benzyl alcohol-ammonia (1:1) cluster in a jet-cooled molecular beam. In addition,ab initio quantum chemical calculations have been performed at HF/6-31G and HF/6-31G(d,p) levels for different ground state equilibrium structures of the cluster to correlate the calculated OH and NH frequencies and their intensities with experimental results. The broad red-shifted OH-stretching mode in the IR-UV double resonance spectrum suggests strong hydrogen bonding between the hydroxyl hydrogen and the lone pair of the ammonia nitrogen. The position and intensity distribution of the calculated NH and OH modes for the minimum-energy gauche form at HF/6-31G level have better correlation with the experimental results compared to other calculated ground state equilibrium conformers. These results lead to the conclusion that the minimum energy gauche form of the cluster is populated in the jet-cooled condition.     

Using internal coordinates to describe photoinduced geometry changes in MLCT excited states

A resonance Raman intensity analysis of the metal-to-ligand charge-transfer (MLCT) transition for the rhenium compound Re(2-(2'-pyridyl)quinoxaline)(CO)(3)Cl (RePQX) is presented. Photoinduced geometry changes are calculated, and the results are presented using the vibrational normal modes and the redundant internal coordinates. A density functional theory calculation is used to determine the ground-state nonresonant Raman spectrum and a transformation matrix that transforms the redundant internal coordinates into the normal modes. The normal modes nu(37) (rhenium coordination sphere distortion) and nu(75) (ligand skeletal stretch) show the largest photoinduced geometry change (Delta = 1.0 and 0.7, respectively). A single carbonyl mode is enhanced in the resonance Raman spectra. Time-dependent density functional theory is used to calculate excited-state geometry changes, which are subsequently used to determine the signs of the photoinduced normal mode displacements. Transforming to internal coordinates reveals that all the CO bond lengths are displaced in the excited state. The Re-C and C-C ligand bond lengths are also displaced in the excited state. The results are discussed in terms of a simple one-electron picture for the electronic transition. Many bond angles and torsional coordinates are also displaced by the metal-to-ligand charge transfer, and most of these are associated with the rhenium coordination sphere. It is demonstrated that using internal coordinates presents a clear picture of the geometry changes associated with photoinduced electron transfer in metal polypyridyl systems.     

Interpretation of unusual absorption bandwidths and resonance Raman intensities in excited state mixed valence

Excited state mixed valence (ESMV) occurs in molecules in which the ground state has a symmetrical charge distribution but the excited state possesses two or more interchangeably equivalent sites that have different formal oxidation states. Although mixed valence excited states are relatively common in both organic and inorganic molecules, their properties have only recently been explored, primarily because their spectroscopic features are usually overlapped or obscured by other transitions in the molecule. The mixed valence excited state absorption bands of 2,3-di-p-anisyl-2,3-diazabicyclo[2.2.2]octane radical cation are well-separated from others in the absorption spectrum and are particularly well-suited for detailed analysis using the ESMV model. Excited state coupling splits the absorption band into two components. The lower energy component is broader and more intense than the higher energy component. The absorption bandwidths are caused by progressions in totally symmetric modes, and the difference in bandwidths is caused by the coordinate dependence of the excited state coupling. The Raman intensities obtained in resonance with the high and low energy components differ significantly from those expected based on the oscillator strengths of the bands. This unexpected observation is a result of the excited state coupling and is explained by both the averaging of the transition dipole moment orientation over all angles for the two types of spectroscopies and the coordinate-dependent coupling. The absorption spectrum is fit using a coupled two-state model in which both symmetric and asymmetric coordinates are included. The physical meaning of the observed resonance Raman intensity trends is discussed along with the origin of the coordinate-dependent coupling. The well-separated mixed valence excited state spectroscopic components enable detailed electronic and resonance Raman data to be obtained from which the model can be more fully developed and tested.     

Resonance Raman Spectroscopic and Theoretical Study of Geometry Distortion of Thiourea in 21A State

The A-band resonance Raman spectra of thiourea were obtained in water and acetonitrile so-lution. B3LYP/6-311++G(3df,3pd) and RCIS/6-311++G(3df,3pd) calculations were done to elucidate the ultraviolet electronic transitions, the distorted geometry structure and the saddle point of thiourea in 2¹A excited state, respectively. The resonance Raman spectra were assigned. The absorption spectrum and resonance Raman intensities were modeled using Heller's time-dependent wavepacket approach to resonance Raman scattering. The re-sults indicate that largest change in the displacement takes place with the C=S stretch mode ν₆ (|△|=0.95) and noticeable changes appear in the H₅N₃H₆+H₈N₄H₇ wag ν₅ (|△|=0.19), NCN symmetric stretch+C=S stretch+N₃H₆+H₈N₄ wag ν₄ (|△|=0.18), while the moderate intensities of 2ν₁₅ and 4ν₁₅ are mostly due to the large excited state frequency changes of ν₁₅, but not due to its significant change in the normal mode displacement. The mechanism of the appearance of even overtones of the S=CN₂ out of plane deformation is explored. The results indicate that a Franck-Condon region saddle point is the driving force for the quadric phonon mechanism within the standard A-term of resonance Raman scattering, which leads to the pyramidalization of the carbon center and the geometry distortion of thiourea molecule in 2¹A excited state.     

Comment on the <Emphasis Type="Italic">ab initio</Emphasis> vibrational analysis of the rotational isomers of Acrolein

Due to the publication of a number of contradictory assignments of the vibrational wave numbers of rotational isomers of Acrolein in the ground electronic state, the analysis of their vibrational spectra is repeated based on the previously calculated scaled ab initio force fields. With the use of the reported results that predicted the force fields of trans-acrolein in the ¹(n,π*) and ³(n, π*) states at the CASSCF/cc-pVTZ level, the experimental vibrational bands are analyzed in these excited electronic states based on well-established regularities. It is noted that in the assignment of the calculated vibrational wave numbers of the molecule, the isotopic shifts in the ground and excited electronic states ¹(n, π*) and ³(n, π*) are taken into account. The previously considered calculated potential curves of the internal rotation of acrolein in combination with the data on the difference in the enthalpies (ΔH ₀) of conformers allow a choice to be made in favor of one of the variants of the torsional vibration wave numbers that have been reported in the literature.     

Ab initio study of the vibrational assignment and force field of thiosemicarbazide-d0 and -d5

The complete harmonic force field and optimized geometry of thiosemicarbazide have been calculated at the ab initio Hartree—Fock level using the 3-21G basis set. On the basis of this, the frequencies of thiosemicarbazide-d₀ and -d₅ and their ¹⁵N isotopic molecules have been calculated. The calculated frequencies and their band assignments are utilized to critically examine our previous experimental assignments which were based on normal coordinate calculations. The theoretical IR and Raman intensities, together with qualitative experimental band intensities, are also presented.