Laurence A. Nafie

Reorientation and Vibrational Relaxation as Line Broadening Factors in Vibrational Spectroscopy

The theory of Gordon which relates the shape of the depolarized components of certain Raman bands to a molecular reorientation correlation function is extended to a number of types of molecular vibrations not previously covered. In addition, the contribution to the line shape for vibrational relaxation and reorientation is obtained for the three types of vibrational spectroscopy, infrared, Raman, and hyper‐Raman, and it is shown that the form of the vibrational relaxation contribution is the same for each spectroscopy. Conditions and assumptions are given under which the line broadening contributions of reorientation and vibrational relaxation can be separated and experimentally determined.

Determination of absolute configuration of chiral molecules using vibrational optical activity: a review.

Determination of the absolute handedness, known as absolute configuration (AC), of chiral molecules is an important step in any field related to chirality, especially in the pharmaceutical industry. Vibrational optical activity (VOA) has become a powerful tool for the determination of the AC of chiral molecules in the solution state after nearly forty years of evolution. VOA offers a novel alternative, or supplement, to X-ray crystallography, permitting AC determinations on neat liquid, oil, and solution samples without the need to grow single crystals of the pure chiral sample molecules as required for X-ray analysis. By comparing the sign and intensity of the measured VOA spectrum with the corresponding ab initio density functional theory (DFT) calculated VOA spectrum of a chosen configuration, one can unambiguously assign the AC of a chiral molecule. Comparing measured VOA spectra with calculated VOA spectra of all the conformers can also provide solution-state conformational populations. VOA consists of infrared vibrational circular dichroism (VCD) and vibrational Raman optical activity (ROA). Currently, VCD is used routinely by researchers in a variety of backgrounds, including molecular chirality, asymmetric synthesis, chiral catalysis, drug screening, pharmacology, and natural products. Although the application of ROA in AC determination lags behind that of VCD, with the recent implementation of ROA subroutines in commercial quantum chemistry software, ROA will in the future complement VCD for AC determination. In this review, the basic principles of the application of VCD to the determination of absolute configuration in chiral molecules are described. The steps required for VCD spectral measurement and calculation are outlined, followed by brief descriptions of recently published papers reporting the determination of AC in small organic, pharmaceutical, and natural product molecules.

Quantum Theory of the Intensities of Molecular Vibrational Spectra

Formulas for the transition probabilities and hence the absolute intensities of molecular vibrational spectra are obtained from a unified quantum field treatment. The theory of infrared, Raman, and hyper‐Raman spectroscopy of molecular vibrations is developed by assuming these processes occur as time‐ordered steps involving the creation or destruction of one quantum of vibrational energy and changes in the occupation number of one, two, or three photons, respectively. The formulas obtained by this method for ir transitions become equivalent to the earlier treatment of Jones and Simpson if the energy difference of the ground and first excited electronic energy levels are very large relative to that of the vibrational quantum. The formulas obtained for Raman transitions are very similar to those obtained by the method originated by Albrecht and developed further by Savin; we get not only the original terms of Albrecht but also the trace terms obtained by Savin. Furthermore by using third‐order time‐dependen...

Vibronic coupling theory of infrared vibrational transitions

The theory of vibronic coupling is developed for infrared vibrational transitions. It is shown that the lowest order nonadiabatic Born–Oppenheimer correction terms contain an important adiabatic component which may be used to describe infrared transition intensity for imaginary Hermitian operators, such as the momentum and angular momentum operators. This previously unrecognized source of adiabatic infrared intensity forms a complement to the traditional Herzberg–Teller vibronic coupling expressions, which are active for the position operator, and resolves the paradox of vanishing electronic intensity for momentum operators in the Born–Oppenheimer approximation. Expressions for infrared absorption and vibrational circular dichroism are derived that utilize only ground electronic state wave functions; LCAO wave functions are used in these expressions to provide a more detailed description of these new momentum intensity contributions.

A confidence level algorithm for the determination of absolute configuration using vibrational circular dichroism or Raman optical activity

Spectral comparison is an important part of the assignment of the absolute configuration (AC) by vibrational circular dichroism (VCD), or equally by Raman optical activity (ROA). In order to avoid bias caused by personal interpretation, numerical methods have been developed to compare measured and calculated spectra. Using a neighbourhood similarity measure, the agreement between a computed and measured VCD or ROA spectrum is expressed numerically to introduce a novel confidence level measure. This allows users of vibrational optical activity (VOA) techniques (VCD and ROA) to assess the reliability of their assignment of the AC of a compound. To that end, a database of successful AC determinations is compiled along with neighbourhood similarity values between the experimental spectrum and computed spectra for both enantiomers. For any new AC determination, the neighbourhood similarities between the experimental spectrum and the computed spectra for both enantiomers are projected on the database allowing an interpretation of the reliability of their assignment.

Dual Polarization Modulation: A Real-Time, Spectral-Multiplex Separation of Circular Dichroism from Linear Birefringence Spectral Intensities

A real-time, spectral-multiplex method for the complete separation of circular dichroism (CD) spectra from linear birefringence (LB) spectra is presented. The method, called dual polarization modulation (DPM), involves the introduction of a second source of polarization modulation after the CD sample. The first source of polarization modulation, as in conventional CD spectrometers, is located before the sample. Intensity signals at the detector in phase with each of the two polarization modulation frequencies are demodulated simultaneously in parallel and combined electronically in opposition to eliminate the LB spectrum by real-time cancellation. The accuracy of the cancellation can be adjusted electronically without the need to change the optical alignment of the instrument. The DPM method permits baseline-corrected CD spectra to be measured without the need for a subsequent CD background measurement.

Theory of High Frequency Differential Interferometry: Application to the Measurement of Infrared Circular and Linear Dichroism via Fourier Transform Spectroscopy

A general method for the direct measurement of differential absorption intensities using a Fourier transform infrared spectrometer is described. The differential intensities must be higher in frequency than the interferogram frequencies and may arise from a periodic variation of the absorption strength of the sample, or by dichroic response of the sample to alternate states of polarization of the infrared beam. Specific expressions are presented for the measurement of circular and linear dichroism. These expressions represent an extension of the Grosjean-Legrand polarization modulation technique to Fourier transform interferometry.

Vibrational Optical Activity

Vibrational optical activity (VOA) is no longer a curious novelty in the field of molecular spectroscopy. After recently celebrating twenty years of development since its early years of discovery, VOA has matured to a point where the phenomenon is well understood theoretically, can be measured and calculated routinely, and is being used to uncover exciting new information about the structure of optically active molecules. Beyond this, VOA has been shown to be a sensitive, noninvasive diagnostic probe of chiral purity or enantiomefic separation with potential use in the synthesis and manufacture of chiral drugs and pharmaceutical products.

Polarized Laser Raman Studies of Biological Polymers

A group‐theoretical analysis of the Raman tensor for helical polymers is given and illustrated for the Pauling α helix which possesses 18 residues in five turns. A detailed determination of the polarized Raman spectra is given for oriented α‐helical poly‐l‐alanine fibers and for four polyribonucleotides in solution. Tentative assignments to A, E1, and E2 symmetry are made on certain Raman bands of poly‐l‐alanine based on the polarization of the Raman light. A detailed comparison of monomer and polymer bands are given for the four polynucleotides. A theory for the angular dependence of Raman light scattered from helical molecules is given.

Adiabatic molecular properties beyond the Born–Oppenheimer approximation. Complete adiabatic wave functions and vibrationally induced electronic current density

The conceptual and mathematical basis for describing adiabatic molecular behavior beyond the Born–Oppenheimer (BO) approximation is presented. The traditional nonadiabatic corrections to the BO approximation are shown to contain a kinetic energy induced adiabatic part and a complete nonadiabatic, or diabatic, part. The lowest order contributions to the new adiabatic terms can be described as momentum adiabatic and are complementary to the traditional BO position adiabatic terms. A complete adiabatic wave function comprised of contributions involving position and momentum is obtained that provides a complete description of the response of the electron probability density to the dynamics of the nuclear motion. This response is comprised of nuclear momentum induced electronic current density and nuclear displacement induced electronic charge flux density for all points in the Cartesian coordinate space of the molecule. These nuclear induced charge fluxes and currents are shown to obey an equation of continui...