The importance of ground-state vibronic mixing in molecular Raman scattering

We consider Albrecht's theory for Raman scattering of fundamentals in the far and pre-resonance regions. Destructive interferences inherent to the A and B terms augment the conventionally suppressed C term dramatically. Raman excitation profiles for the ν₁(a_1g) and ν₆(e_2g fundamentals in benzene can be well fitted with theoretical C-term profiles involving the ¹E_1u(π-π^*) state at 1800 A.     

Contraction of the well-tempered Gaussian basis sets: The first-row diatomic molecules

The well-tempered Gaussian basis sets (14s 10p) for atoms from lithium to neon were contracted and used in restricted Hartree–Fock calculations on 13 systems: Li₂(Σ), B₂(Σ), C₂(Σ), N₂(Σ), O₂(Σ), F₂(Σ), Ne₂(Σ), LiF(Σ), BeO(Σ), BF(Σ), CN^?(Σ), CO(Σ), and NO⁺(Σ). Spectroscopic constants (R_e, ω_e, ω_ex_e, B_e, α_e, and k_e) and one-electron properties (dipole, quadrupole, and octupole moments at the center of mass and electric field, electric field gradient, potential, and electron density at the nuclei) were evaluated and compared with the Hartree–Fock results. The largest contracted basis set (7_s6_p3_d) gives results very close to the Hartree–Fock values; the remaining differences are attributed to the absence of the f functions in the present basis sets. For Ne₂, the interaction energy was calculated; the magnitude of the basis-set superposition error was found to be very small (less than 3 μE_h at 2.8 a₀ and less than 2 μE_h at 5.0 a₀).     

Calculated lifetime and decay mechanism of the 991 cm−1 mode in crystalline benzene at 1.6 K

The lifetime of the 991 cm^?1 Ag mode in benzene crystal at 1.6 K has been calculated in good agreement with the experimental value. The main decay mechanism has been shown to consist of a three-phonon scattering involving the ν₁₀ 860 cm^?1 e_2g internal vibration and high-frequency lattice modes.     

Theoretical Study on Resonance Raman Spectra of Tetraoxaporphyrin Dication by TDDFT Calculation

The B state excited resonance Raman scattering of tetraoxaporphyrin dication (TOP²⁺) was theoretically studied with DFT/TDDFT calculations and the sum-over-states approach of polarizability including both the A and B terms contributions. The resonance Raman spectra calculated with PBE1PBE, B3LYP, Cam-B3LYP, and B3LYP-D3 functionals are similar to each other in general, with PBE1PBE and B3LYP being better in reproducing resonance Raman intensities in comparison with the experiment. The calculated relative intensities of the totally symmetric modes are excellently consistent with the experiment. The TDDFT calculations manifested a considerable deformation of the B state along theυ2,υ6, υ7, and υ8 modes, which is responsible for the strong resonance Raman intensities of these modes. The resonance Raman intensities of non-totally symmetric modes were calculated to be weaker than the totally symmetric modes by one or two order of magnitude, whichqualitatively agrees with the experiment. However, the resonance Raman intensity of the υ10 mode (C_βC_β stretch, B_1g symmetry) predicted by TDDFT calculations is unexpectedly small whereas that of the υ11 mode (symmetric C_αC_m stretch, B_1g symmetry) is too large, which is assumed to be caused by the Jahn-Teller instability for the B state of TOP²⁺.     

Experimental and theoretical study on vibrational spectra of nickel and zinc complexes of 5,10-diphenylporphyrin

The vibrational spectra of nickel and zinc 5,10-diphenylporphyrin (NiDaPP and ZnDaPP) have been studied by density functional theory (B3LYP/6-31G(d)) and experimental measurement. The assignment of observed Raman and IR bands are proposed based on theoretical calculation. Theoretical study indicates that 5,10-diphenyl substitution together with out-of-plane distortion diversify the structure of four pyrrole rings and the environment around C_m atoms, which lowers the symmetry of porphyrin skeleton and brings about some variation to vibrational spectra. The first is the activation of all normal modes both in Raman and IR spectra. The second is the lifting of original degenerate E_u representation and its splitting into two A modes in NiDaPP (C₁ group point) and A′/A″ presentation in ZnDaPP (C_s group point), respectively. Furthermore, one or both of the two split components, especially for some vibration involving the motion of C_m atom, undergoes further mixing with original non-degenerate mode (A_1g, A_2g, B_1g, or B_2g) of same vibration. This produces new modes involving only partial motion of original mode. Besides general increasing frequency of NiDaPP with respect to ZnDaPP, different vibrational structure is also indicated by calculation for some structure-sensitive bands, especially ν₈ mode that couples with γ₆ mode and split into two modes for NiDaPP but not for ZnDaPP.     

Interaction of acetonitrile with alkaline metal cations: A density functional,coupled‐cluster,and quadratic configuration interaction study

A systematic quantum chemical study of CH₃CN and its CH₃CN?M⁺ 1:1 model adducts (M⁺∈{Li⁺, Na⁺}) is presented, with respect to binding energetics, structural and vibrational force field changes. Several gradient‐corrected density functional levels of theory were employed (of both “pure” and “hybrid” character), together with the coupled cluster including double substitutions from the Hartree–Fock determinant (CCD) and quadratic configuration interaction including single and double substitutions (QCISD) methods [with the rather large 6‐311G(d,p) basis set], and their performances compared. The binding energy decompositions according to the Kitaura–Morokuma scheme and the reduced variational space self‐consistent field (RVS‐SCF) method have shown that the electrostatic plus polarization interaction terms are primarily responsible for overall stabilization, while the charge‐transfer term is negligibly small and virtually identical for both adducts. The computed harmonic vibrational frequencies for acetonitrile correlate excellently with the experimental ones (r²>0.9998 for almost all cases, while for the BLYP level, r²=1). It is shown for the first time that the experimentally observed blue shifts of the ν_CN mode are caused even by formation of 1:1 adducts, contrary to the previously accepted opinions. The CCD and QCISD, as well as the BPW91 and BP86 levels of theory predict almost excellently the ν_CN mode blue shift upon adduct formation, while the BLYP and B3LYP levels perform significantly poorer. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Lithium isotope effects in the vibrational spectra of Li2SeO4

Polarized Raman scattering spectra have been measured in single crystal ⁷Li₂SeO₄ and ⁶Li₂SeO₄. Based on these data, symmetry-based band assignments are proposed for the ν₂, ν₄ and lithium mode regions. Vibrational coupling interactions are noted between the ν₂, ν₄ and the lithium translatory modes.     

On the assignment of SiH and SiD stretching frequencies: A reanalysis of the ν7 bands of Si2H6 and Si2D6 and a harmonic local mode force field for disilane

Assignments of ν(SiH) and ν(SiD) modes in SiHX₃, SiH₂X₂ and SiH₃X compounds are surveyed. With a few exceptions, ν(SiH)/ν(SiD) ratios are found to be those expected on the basis of harmonic local mode calculations, if ν(SiD) values are first divided by a factor R which normally lies in the range 1.010–1.011. Major deviations from this range indicate misassignments or Fermi resonances. Stretch-stretch interaction constants f′_a are tabulated, and agree excellently with ab initio values, where these are available. Where ν^is (SiH) values are known, the frequency sum rule is found to be obeyed closely. The ν₇ bands of Si₂H₆ and Si₂D₆ are reanalysed to yield an R value of 1.010. The ν(SiH) data for disilanes then yield, in a “6 × 6” refinement, values of the three interaction force constants f′_a, f′_g and f′_g, together with predictions of hitherto unlocated stretching fundamentals. Constancy of the R factor for different types of XH bonds is shown to be a consequence of Dennison's rules, and similar anharmonicity factors.     

Pigment-Protein Interactions in the Antenna-Reaction Center Complex of Heliobacillus mobilis

Membrane fragments of Heliobacillus (Hc.) mobilis were characterized using resonance Raman (RR) spectroscopy in order to determine the configuration of the neurosporene carotenoid, the pigment-protein interactions of the bacteriochlorophyll (BChl) g molecules, and the Chl a-like chlorin pigments present in the antenna-reaction center complex constituting the photosynthetic apparatus. Using 363.8 nm excitation, the Raman contributions of the BChl g molecules were selectively resonantly enhanced over those of the carotenoid and the Chl a-like chlorin pigments. The RR spectrum of BChl g in these membranes excited at 363.8 nm exhibits bands at 1614 and 1688 cm^?1, which correspond to a C_aC_m methine bridge stretching mode and a keto carbonyl group stretching mode, respectively. Both of these bands are 16 cm^?1 wide (full width at half maximum, FWHM), indicating that a sole population of BChl g molecules is being enhanced at this excitation wavelength. The observed frequency of the C_aC_m stretching mode (1614 cm^?1) indicates that the bulk of BChl g molecules is pentacoordinated with only one axial ligand to the central Mg atom while that of the keto carbonyl stretching mode (1668 cm^?1) indicates that these groups are engaged in a hydrogen bond. This homogeneous population of BChl g molecules bound to the heliobacterial core polypeptides is in contrast to the heterogeneous population of Chl a molecules bound to the core polypeptides of the reaction center of photosystem I of Synechocystis 6803 as observed by the inhomogeneously broadened C₉ keto carbonyl band in its RR spectrum. The RR spectrum of the Chl a-like chlorin pigments in Hc. mobilis excited at 441.6 nm exhibits a broad keto carbonyl band (43 cm^?1 FWHM) with components at 1665, 1683 and 1695 cm^?1, indicating several populations of these pigments differing in their protein interactions at the level of the keto carbonyl group. Fourier transform (FT) pre-RR spectroscopic measurements of intact whole cells and membrane fragments at room temperature using 1064 nm excitation indicate that high quality vibrational spectra of the BChl g molecules can be obtained with no photodegradation. Low-temperature FT Raman spectra excited at 1064 nm reveals an inhomogeneously broadened 1665 cm^?1 band corresponding to the C₉ keto carbonyl stretching mode. Spectral deconvolution and second derivative analysis of this band reveal that it is comprised of components at 1665, 1682 and 1695 cm^?1, the latter two most likely arising from BChl g photoconversion products. Excitation using 885 nm to enhance the preresonance effect of the BChl g molecules yields an FT Raman spectrum where the keto carbonyl band at 1665 cm^?1 is narrow, as is the case in the Soret RR spectra, reflecting a sole population of BChl g molecules, which are engaged in an H bond. The RR spectrum of the neurosporene molecule in Hc. mobilis membranes excited at 496.5 nm is compared to that of 1,2-dihydroneurosporene bound in a cis configuration in reaction centers of Rhodopseudomona viridis and to that of the same carotenoid in its all-trans configuration extracted from these reaction centers in the presence of light. The similarity of this latter RR spectrum with that of neurosporene in the Hc. mobilis membranes indicates that it is bound in an all-trans configuration.     

IR,Raman, and Surface‐enhanced Raman Spectroscopic Study on Triruthenium Dipyridylamide Diruthenium Nickel Dipyridylamide Family: Metal‐metal Bonding and Structures

We report the infrared, Raman, and surface‐enhanced Raman scattering (SERS) spectra of triruthenium dipyridylamido complexes and of diruthenium mixed nickel metal‐string complexes. From the results of analysis on the vibrational modes, we assigned their vibrational frequencies and structures. The infrared band at 323–326 cm^?1 is assigned to the Ru₃ asymmetric stretching mode for [Ru₃(dpa)₄Cl₂]^0–2+. In these complexes we observed no Raman band corresponding to the Ru₃ symmetric stretching mode although this mode is expected to have substantial Raman intensity. There is no frequency shift in the Ru₃ asymmetric stretching modes for the complexes with varied oxidational states. No splitting in Raman spectra for the pyridyl breathing line indicates similar bonding environment for both pyridyls in dpa^– , thus a delocalized structure in the [Ru₃]^6–8+ unit is proposed. For Ru₃(dpa)₄(CN)₂ complex series, we assign the infrared band at 302 cm^?1 to the Ru₃ asymmetric stretching mode and the weak Raman line at 285 cm^?1 to the Ru₃ symmetric stretching. Coordination to the strong axial ligand CN^– weakens the Ru‐Ru bonding. For the diruthenium nickel complex [Ru₂Ni(dpa)₄Cl₂]^0–1+, the diruthenium stretching mode ν_Ru‐Ru is assigned to the intense band at 327 and 333 cm^?1 in the Raman spectra for the neutral and oxidized forms, respectively. This implies a strong Ru‐Ru metal‐metal bonding.     

Large-Z and -N dependence of atomic energies from renormalization of the large-dimension limit

By combining Hartree–Fock results for nonrelativistic ground-state energies of N-electron atoms with analytic expressions for the large-dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z^7/2(C₀ + C₁Z^?1/3 + C₂Z^?2/3 + C₃Z^?3/3 + ?), with similar values of the coefficients for the three leading terms. Use of the renormalized large-D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ^4/3(δC₃ + δC₅Z^?2/3 + δC₆Z^?3/3 + ?); comparison with accurate values of δE available for the range Z ? 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.     

Investigation of the frequency‐dispersion effects on the Raman spectra of small polyenes

The time‐dependent Hartree–Fock scheme is applied for determining the frequency‐dependent Raman intensities of C_2nH_2n+2 molecules with n = 1–3. This analytic scheme, recently developed and implemented in the GAMESS program (Quinet, O.; Champagne, B. J Chem Phys 2001, 115, 6293), takes advantage of the 2n + 1 rule to express the polarizability derivatives in terms of first‐order derivatives. It is found that including frequency dispersion strongly modifies the intensity activy coefficients of many vibrational normal modes and therefore changes the aspect of the spectra. On the other hand, the depolarization ratio is much less frequency dependent. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Electronic structure of long cumulene chains

The analysis of the equations of the unrestricted Hartree–Fock (UHF) method for polyenes C_NH_N+2 with even and odd N » 1 is carried out. The equations of the UHF method are shown to be the same in both cases. The comparison of the UHF method with the extended Hartree–Fock (EHF) method applied to large systems is performed. The ground state and π-electron spectra of long cumulene chains C_NH₄ are treated by the EHF Method. The end effects are taken into consideration. It is shown that the EHF method gives a finite value of the first optical transition frequency and, at the same time, zero value of torsion barrier of end CH₂–groups in long cumulene chains (N → ) in contrast to previous calculations of cumulenes by the Huckel method and the restricted Hartree–Fock method.     

Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method

The ground state and the first few excited states of an MnO₆^9? cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is ⁵B_{1 g}, ⁵A_{1 g}, ⁵B_{2 g}, and ⁵E_g as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (⁵E_u) has five unpaired spins on Mn.     

Introduction of the shell structure into the Thomas—Fermi energy density functional for neutral atoms

The Thomas—Fermi energy density functional is constructed for the Na atom using H-like wavefunctions. Minimization of the functional with respect to the Z in the wavefunctions leads to the energy value ot ?166.35 e_O²/a_O, which compares favorably with the Hartree—Fock value of ?161.8 e_O²/a_O.     

Jahn-Teller effect and resonance raman spectra of highly spin-degenerate molecules with application to FeBr4−

We give a model calculation of the resonance Raman amplitude of spin-degenerate molecules that are subject to Jahn-Teller distortion. The method is applied to the resonance Raman excitation profiles of the ν₃(t₂) and ν₁(3_1g) modes of FeBr₄^?.     

Could alkaline–earth-intercalated fullerites actually be semimetals?

Ab initio Hartree–Fock crystal-orbital calculations on three ideal fullerite C₆₀ crystals doped with strontium (C₆₀Sr_N, where N=2, 3, 6) are reported. C₆₀Sr₃ is calculated here to be a semiconductor; C₆₀Sr₂, a zero-gap semiconductor, and C₆₀Sr₆, a one-dimensional metal. The C₆₀Sr_N are found to be highly ionic as well: The total charge transfers are 3.444, 4.956, and 9.228 e for N=2, 3, and 6, respectively. The possible mechanisms of the observed superconductivity in C₆₀Sr₆ are discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 201–208, 1998     

Molecular structure,vibrational spectra,first order hyper polarizability,NBO and HOMO–LUMO analysis of 4-amino-3(4-chlorophenyl) butanoic acid

The Fourier transform infrared (FT-IR) and Fourier transform Raman (FTR) spectra of 4-amino-3(4-chlorophenyl) butanoic acid were recorded in the regions 4000–400 cm⁻¹ and 4000–100 cm⁻¹, respectively, in the solid phase. Molecular electronic energy, geometrical structure, harmonic vibrational spectra, infrared intensities and Raman scattering activities, highest occupied molecular orbital, lowest unoccupied molecular orbital energy, energy gaps and thermodynamical properties such as zero-point vibrational energies, rotational constants, entropies and dipole moment were computed at the Hartree–Fock/6-31G(d,p) and three parameter hybrid functional Lee–Yang–Parr/6-31G(d,p) levels of theory. The vibrational studies were interpreted in terms of potential energy distribution (PED). The results were compared with experimental values with the help of scaling procedures. Most of the modes have wave numbers in the expected range and are in good agreement with computed values. The first order hyperpolarizability (β_total) of this molecular system and related properties (β, μ, 〈α〉 and Δα) are calculated using HF/6-31G(d,p) and B3LYP/6-31G(d,p) methods based on the finite-field approach. Stability of the molecule arising from hyperconjugative interactions, charge delocalization and intramolecular hydrogen bond-like weak interaction has been analyzed using natural bond orbital (NBO) analysis by using B3LYP/6-31G(d,p) method. The results show that electron density (ED) in the σ1 and π1 antibonding orbitals and second-order delocalization energies E⁽²⁾ confirm the occurrence of intramolecular charge transfer (ICT) within the molecule.     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000