Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the low rank perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at atomic sites is considered. Relations which express vibrational frequencies _k and normal modes _k of the perturbed isotopic molecule B in terms of the vibrational frequencies _i and normal modes _i of the unperturbed molecule A are derived. In these relations complete specification of the unperturbed normal modes _i is not required. Only amplitudes | _i of normal modes _i at sites affected by the isotopic substitution are needed.     

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at ρ atomic sites is considered. In the LRP approach vibrational frequencies ω _k and normal modes of the isotopomer B are expressed in terms of the vibrational frequencies ν _i and normal modes of the parent molecule A. In those relations complete specification of the normal modes is not required. Only amplitudes at sites τ affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H,D)-benzene isotopomers are considered. Standard error of the LRP frequencies with respect to the DFT frequencies is on average . This error is due to the uncertainty of the input data (± 0.5 cm⁻¹) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment, one finds that LRP frequencies reproduces experimental frequencies of (H,D)-benzene isotopomers better () than scaled DFT frequencies () which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation.     

Vibrational analysis of a rate-slowing conformational kinetic isotope effect

An enthalpy-entropy approach to analyzing a rate-slowing conformational kinetic isotope effect (CKIE) in a deuterated doubly-bridged biaryl system is described. The computed isotope effect (k_H/k_D?=?1.075, 368?K) agrees well with the measured value (k_H/k_D?=?1.06, 368?K). The rate-slowing (normal isotope effect) nature of the computed CKIE is shown to originate from a vibrational entropy contribution defined by the twenty lowest frequency normal modes in the ground state and transition state structures. This normal entropy contribution is offset by an inverse vibrational enthalpy contribution, which also arises from the twenty lowest frequency normal modes. Zero point vibrational energy contributions are found to be relatively small when all normal modes are considered. Analysis of the H_ZPE, H_vib, and S_vib energy terms arising from the low frequency vibrational modes reveals their signs and magnitudes are determined by larger vibrational energy differences in the labeled and unlabeled ground state structures.     

Some peculiarities of manifestations of the isotope effect in structural transformations of molecules

We consider the effect of the isotopic substitution on the characteristics of structural transformations of molecules. Attention is paid to the probability factor not taken into account in the kinetic isotope effect theory earlier. This factor can prove to be determining in a number of cases, and it results in not only quantitative, but also qualitative changes in the kinetics of the structural transformation process. For example, there may appear or disappear the induction of the reaction and the time dependence of the reaction constant, the inverse ratio of the yields of obtained products, and so on.     

Vibrational isotope effect and molecular structure of M-Xy type molecules

A general theory on the vibrational isotope effect of linear MXY type molecules is presented. Here, XY denotes diatomic species such as CO and CN, while M typically represents a metal atom such as Li and Pt. It is shown that the MXY and MYX structures can be distinguished by comparing the isotope shift of the MXY (or MYX) molecule with that of free XY. Applications of the theory to problems of structure determination and band assignments are made to demonstrate its utility.     

Study of the isotope effect in the isotope exchange reaction between PuIV and PuIII by extraction redox-chromatography

The equilibrium isotope effect in the isotope exchange reaction between Pu^IV extracted with tributyl phosphate and Pu^III in an aqueous nitric acid solution has been studied by extraction chromatography. For the 238/242Pu isotope pair the isotope separation coefficient () at 25 °C has been found to be 1.0022±0.0005.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1557–1558, September, 1994.The authors are grateful to Prof. N. N. Krot for discussion of the results and valuable remarks and to V. P. Perminov for help in designing the computer programs.This work was financially supported by the International Science Foundation (Grant MDB 000).     

乙酰乙酸乙酯在重水和环己烷中的C=O和C=C伸缩振动模式的振动衰减动力学

作为典型的β-二羰基化合物和α,β-烯酮类化合物, 乙酰乙酸乙酯在溶液中以多结构存在. 在本文中, 我们利用飞秒中红外泵浦探测光谱技术, 研究了该化合物在重水和环己烷溶液中不同互变异构体的出现在波长6 μm(频率范围1600～1800 cm^-1)区域的C=O和C=C伸缩振动的振动动力学; 并结合稳态红外实验和量子化学计算, 分析了这些吸收峰的线型特征. 结果表明: 在重水中, 乙酰乙酸乙酯以酮式存在; 而在环己烷中以烯醇式和两种酮式共存. 分析稳态红外光谱可以看到, 烯醇式结构刚性, 其红外光谱线型主要表现为均匀增宽; 而酮式的线型则兼具均匀增宽和非均匀增宽. 而且, 即使在同一种溶剂中, 酮式和烯醇式的表观红外光谱线型也有不同. 通过泵浦探测实验获得了C=O和C=C伸缩振动衰减动力学和各向异性动力学. 重水中酮式的C=O的振动能量弛豫过程比其在环己烷中要快, 这可归因于乙酰乙酸乙酯与溶剂发生的分子间氢键作用. 此外, 烯醇式的C=O伸缩振动和一些振动模式(如COH面内弯曲)之间存在费米共振, 直接影响其快速衰减过程, 这也是造成其振动衰减动力学不同于酮式的原因. 各向异性动力学过程表明, 乙酰乙酸乙酯在重水中的转动速度比其在环己烷中要慢一些, 与它们不同的溶剂化情况有关. 此外, 各向异性动力学过程表现出量子拍频现象, 在酮式中尤为明显, 意味着相关振动模式存在相干激发.     

Vibrational spectrum of a 1D oscillator: The quantum,the Wigner,and the classical ways

Infrared spectra have been used in many chemical applications, and theoretical calculations have been useful for analyzing these experimental results. While quantum mechanics is used for calculating the spectra for small molecules, classical mechanics is used for larger systems. However, a systematic understanding of the similarities and differences between the two approaches is not clear. Previous studies focused on peak position and relative intensities of the spectra obtained by various quantum and classical methods, but here, we included “absolute” intensities in the evaluation. The infrared spectrum of a one-dimensional (1D) harmonic oscillator (HO) and Morse oscillator were examined using four treatments: quantum, Wigner, truncated Wigner, and classical microcanonical treatments. For a 1D HO with a linear dipole moment function (DMF), the quantum and Wigner treatments give nearly the same spectra. On the other hand, the truncated Wigner underestimates the fundamental transition's intensity by half. In the case of cubic DMF, the truncated Wigner and classical methods fail to reproduce the relative intensity between the fundamental and second overtone transitions. Unfortunately, all the Wigner and classical methods fail to agree with the quantum results for a Morse oscillator with just 1% anharmonicity.     

Inverse Ubbelohde effect in the short hydrogen bond of photosystem II: Relation between H/D isotope effect and symmetry in potential energy profile

The short hydrogen bond between tyrosine Y_z and D1‐His190 of photosystem II (PSII) was investigated using multicomponent quantum mechanics, where the quantum fluctuation of a hydrogen nucleus was incorporated into electronic structure calculation. Our computation demonstrated that the deuteration for hydrogen in the short hydrogen bond of PSII led to the reduction of the O…N distance. It indicated an inverse Ubbelohde effect typically recognized in strong and symmetric hydrogen‐bonding clusters such as FHF^– and . We confirmed that the relation between the geometric isotope effect and the symmetry of the potential energy profile of FHF^– was reasonably agreed with that of PSII. According to this agreement, the short hydrogen bond in PSII can be regarded as a short strong hydrogen bond. © 2016 Wiley Periodicals, Inc.     

Reduction of acetophenone using supercritical 2-propanol: the substituent effect and the deuterium kinetic isotope effect

The reductions of several substituted acetophenones using supercritical 2-propanol were carried out to estimate the Hammett's reaction constant (ρ=0.33). Also, the reduction of acetophenone using supercritical deuteriated 2-propanol was carried out to determine the rate-determining step. The kinetic isotope effects were observed in the reduction using 2-deuterio-2-propanol (k_H/k_D=1.6) and O-deuterio-2-propanol (k_H/k_D=2.0). These findings suggest that the reaction proceeds via a cyclic transition state between acetophenone and 2-propanol similar to that of the Meerwein-Ponndorf-Verley reduction.     

UV Spectrum of the Simplest Deuterated Criegee Intermediate CD2OO

The ultraviolet (UV ) absorption spectrum of the simplest deuterated Criegee intermediate CD₂OO has been measured and compared with that of CH₂OO . While the UV spectra of CH₂OO and CD₂OO are similar in the overall shape, distinctive oscillatory structures at the long wavelength side of the absorption band show clear effect of isotopic substitution. The average spacing between the vibrational peaks decreases from 606 cm⁻¹ for CH₂OO to 528 cm⁻¹ for CD₂OO . This large isotope effect cannot be explained by one‐dimensional model along the dissociative O−O bond. Instead, vibrational modes involving motions of the H‐atoms are expected to be responsible for the observed oscillatory structure. This isotope effect offers a stringent test for theoretical investigations on the absorption spectrum and excited‐state dynamics of the simplest Criegee intermediate.     

Vibrational computations beyond the harmonic approximation: performances of the B3LYP density functional for semirigid molecules

The performances of the B3LYP density functional in the computation of harmonic and anharmonic frequencies were tested using 14 standard basis sets of double and triple zeta quality for a set of semirigid molecules containing from 4 to 12 atoms. The quality of the results is assessed by comparison with the most reliable computations available in the literature. The study reveals that the relatively cheap 6-31+G(d,p) basis set performs a very good job for harmonic frequency calculations and that B3LYP anharmonicities are in close agreement with the reference values irrespective of the basis set used. On these grounds "hybrid force fields" are proposed to achieve the best compromise between computer time and quality of the results.     

Solvent and deuterium isotope effects on the decomposition of ammonium nitrite solutions

The rate of decomposition of NH₄NO₂ solutions, at pH 5–7, equals k[NH₃] [HNO₂]² or k[NH ₄ ⁺ ] [NO ₂ ^– ][HNO₂]. A plausible mechanism involves a ratedetermining attack of N₂O₃, derived from HNO₂, on NH₃. H⁺⁺ and S⁺⁺ are 82 kJ-mol^–1 and –27 J-mol^–1-K^–1, respectively. On partially replacing the solvent water by methanol or ethanol, the change G⁺⁺, coupled with the calculated standard Gibbs energy of transfer of the reactants from water to the mixed solvent indicated that, in the latter, there is a greater destabilization of the transition state compared to that of the reactants. This can be explained by assuming two hydrogen bonds from the same water molecule to the transition state and hence a loss of hydrogen bond energy in the mixed solvent compared to the aqueous solution. The rate constant for the reaction of ND₄NO₂ in D₂O compared to the reaction of NH₄NO₂ in water, gave a composite isotope effect involving two acid-base equilibria, suggested in the proposed mechanism; in addition to primary isotope effects in the equilibrium: 2 HNO₂N₂O₃+H₂O.     

Experimental study of the kinetics of reaction of chlorine atoms with tetrahydrofuran and fully deuterated tetrahydrofuran

The overall rate constants for H-abstraction (k_H) from tetrahydrofuran and D-abstraction (k_D) from fully deuterated tetrahydrofuran by chlorine atoms in the temperature range of 298-547 K were determined. In both cases, very weak negative temperature dependences of the overall rate constants were observed, described by the expressions: k_H = (1.55 ± 0.13) × 10⁻¹⁰ exp(52 ± 28/T) cm³ molecule⁻¹ s⁻¹ and k_D = (1.27 ± 0.25) × 10⁻¹⁰exp(55 ± 62/T) cm³ molecule⁻¹ s⁻¹. The experimental results show that the value of the kinetic isotope effect (k_H/k_D), amounting to 1.21 ± 0.10, is temperature independent at 298-547 K.     

The Jahn-Teller effect in icosahedral molecules and complexes

The adiabatic potential surface for icosahedral systems having three-, four- and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v,U-v andV-v problems) is investigated. It is shown that for theT-v andV-v Jahn-Teller cases the potential surface possesses respectively a two- or three-dimensional equipotential continuum of minima. For theU-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on the adiabatic potential surfaces is elucidated. In the linear approximation to theV-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.     

Vibrational Raman optical activity of pi-conjugated helical systems: hexahelicene and heterohelicenes

Helicenes constitute a special class of molecules combining helical conformation with pi-electron delocalization. These confer to helicenes specific chirooptical properties. In this article, we investigate the vibrational signatures thanks to the simulation of vibrational Raman optical activity (VROA) spectra. For that, four representative helicenes: hexahelicene, tetrathia-[7]-helicene, and its pyrrole and furan analogs have been simulated and interpreted using a recently implemented analytical scheme. Helicenes show intense VROA peaks attributed to their pi-conjugated structure and associated with collective vibrational modes. In hexahelicene, the dominant VROA features are due to vibrational modes involving motions of the carbon skeleton and H-wagging, but the intensity finds its source almost exclusively in the former. In the case of the three heterohelicenes, the previous statement is also verified, and on changing the heteroatoms, similar modes presenting comparable atomic contribution patterns have been highlighted, though the vibrational and electronic properties are modified. Some fingerprints could therefore be associated with the helicity of the system. In particular, in forward spectra, most of the VROA bands are positive for left-handed helicenes. Nevertheless, the spectral patterns are quite complex, and no easy rule-of-thumb could distinguish between the different heterohelicenes. Then, considering the fact that most of the contributions originate from the C atoms (group coupling matrices decomposition), it can be concluded that the major role of the heteroatom is restricted to modifying the geometry and the normal modes. At last, the small impact of the gauge-origin on the calculated spectra using a relatively modest basis set (rDPS:3-21G) is demonstrated here in the case of the tetrathia-[7]-helicene molecule presenting a C(2) symmetry. This further demonstrates the adequacy of this basis set for VROA calculations.     

Vibrational and electronic spectra of benzophenone in different phase states: Ab initio calculations and experiment

An ab initio method has been used to perform quantum mechanical calculations of the formation energy of different conformers of benzophenone: planar molecule, twisted molecule, planar molecule dimer, twisted molecule dimer; electronic and vibrational spectra of these conformers were also obtained. An assessment of the medium (solvent) influence on the optimal geometry, dipole moment and stability of different forms of benzophenone was performed in the self-consistent reaction field approximation. It is shown that the twisted conformer is more stable than the planar one (the difference of free energies is 32 kJ/mol for free molecules) and it becomes even more stable with the increase in solvent polarity. The calculated electronic and vibrational spectra agree well with the experimental data and properly reflect the complication of the vibrational spectrum when passing from the gaseous phase to the condensed state of benzophenone. The difference between spectral properties of the two dimer forms allows their identification from the spectra and qualitative explanation of the observed peculiarities of phosphorescence of the amorphous phase of benzophenone by the stabilization of different conformers.     

Coherent Multidimensional Vibrational Spectroscopy of Biomolecules: Concepts,Simulations, and Challenges

Good vibrations : The vibrational response of complex molecules to sequences of infrared pulses provides novel femtosecond snapshots of their structure and dynamics. This technique, which is the optical analogue of multidimensional NMR spectroscopy, gives correlation plots of motions during controlled time intervals between pulses that are applied to study protein folding, chirality, hydrogen‐bonding, phospholipid membranes, and chemical exchange.

     

Vibrational Spectroscopic Study on Ion Solvation and Association of Lithium Perchlorate in 4-Methoxymethyl-ethylene Carbonate

Solvation interaction and ion association in solutions of lithium perchlorate/4-methoxymethyl-ethylene carbonate （MEC） have been studied by using Infrared and Raman spectra as a function of concentration of lithium perchlorate. The splitting of ring deformation band and ring ether asymmetric stretching band, and the change of carbonyl stretching band suggest that there should be a strong interaction between Li^＋ and the solvent molecules, and the site of solvation should be the oxygen atom of carbonyl group. The apparent solvation number of Li^＋ was calculated by using band fitting technique. The solvation number was decreased from 3.3 to 1.1 with increasing the concentration of LiClO4/MEC solutions. On the other hand, the band fitting for the ClO4^- band revealed the presence of contact ion pair, and free ClO4^- anion in the concentrated solutions.