Vibrational circular dichroism
Vibrational circular dichroism (VCD) is a spectroscopic technique which detects differences in attenuation of left and right circularly polarized light passing through a sample. It is the extension of circular dichroism spectroscopy into the infrared and near infrared ranges.
Because VCD is sensitive to the mutual orientation of distinct groups in a molecule, it provides three-dimensional structural information. Thus, it is a powerful technique as VCD spectra of enantiomers can be simulated using ab initio calculations, thereby allowing the identification of absolute configurations of small molecules in solution from VCD spectra. Among such quantum computations of VCD spectra resulting from the chiral properties of small organic molecules are those based on density functional theory (DFT) and gauge-invariant atomic orbitals (GIAO). As a simple example of the experimental results that were obtained by VCD are the spectral data obtained within the carbon-hydrogen (C-H) stretching region of 21 amino acids in heavy water solutions. Measurements of vibrational optical activity (VOA) have thus numerous applications, not only for small molecules, but also for large and complex biopolymers such as muscle proteins (myosin, for example) and DNA.
While the fundamental quantity associated with the infrared absorption is the dipole strength, the differential absorption is also proportional to the rotational strength, a quantity which depends on both the electric and magnetic dipole transition moments. Sensitivity of the handedness of a molecule toward circularly polarized light results from the form of the rotational strength. A rigorous theoretical development of VCD was developed concurrently by the late Professor P.J. Stephens, FRS, at the University of Southern California, and the group of Professor A.D. Buckingham, FRS, at Cambridge University in the UK, and first implemented analytically in the Cambridge Analytical Derivative Package (CADPAC) by R.D. Amos. Previous developments by D.P. Craig and T. Thirmachandiman at the Australian National University and Larry A. Nafie and Teresa B. Freedman at Syracuse University though theoretically correct, were not able to be straightfowardly implemented, which prevented their use. Only with the development of the Stephens formalism as implemented in CADPAC did a fast efficient and theoretically rigorous theoretical calculation of the VCD spectra of chiral molecules become feasible. This also stimulated the commercialization of VCD instruments by Biotools, Bruker, Jasco and Thermo-Nicolet (now Thermo-Fisher).
Peptides and proteins
Extensive VCD studies have been reported for both polypeptides and several proteins in solution; several recent reviews were also compiled. An extensive but not comprehensive VCD publications list is also provided in the "References" section. The published reports over the last 22 years have established VCD as a powerful technique with improved results over those previously obtained by visible/UV circular dichroism (CD) or optical rotatory dispersion (ORD) for proteins and nucleic acids.
The effects due to solvent on stabilizing the structures (conformers and zwitterionic species) of amino acids and peptides and the corresponding effects seen in the vibrational circular dichroism (VCD) and Raman optical activity spectra (ROA) have been recently documented by a combined theoretical and experimental work on L-alanine and N-acetyl L-alanine N'-methylamide,. Similar effects have also been seen in the nuclear magnetic resonance (NMR) spectra by the Weise and Weisshaar NMR groups at the University of Wisconsin-Madison.
VCD spectra of nucleotides, synthetic polynucleotides and several nucleic acids, including DNA, have been reported and assigned in terms of the type and number of helices present in A-, B-, and Z-DNA.
VCD can be regarded as a relatively recent technique. Although Vibrational Optical Activity and in particular Vibrational Circular Dichroism, has been known for a long time, the first VCD instrument was developed in 1973 and commercial instruments were available only since 1997.
For biopolymers such as proteins and nucleic acids, the difference in absorbance between the levo- and dextro- configurations is five orders of magnitude smaller than the corresponding (unpolarized) absorbance. Therefore, VCD of biopolymers requires the use of very sensitive, specially built instrumentation as well as time-averaging over relatively long intervals of time even with such sensitive VCD spectrometers. Most CD instruments produce left- and right- circularly polarized light which is then either sine-wave or square-wave modulated, with subsequent phase-sensitive detection and lock-in amplification of the detected signal. In the case of FT-VCD, a photo-elastic modulator (PEM) is employed in conjunction with an FTIR interferometer set-up. An example is that of a Bomem model MB-100 FTIR interferometer equipped with additional polarizing optics/ accessories needed for recording VCD spectra. A parallel beam emerges through a side port of the interferometer which passes first through a wire grid linear polarizer and then through an octagonal-shaped ZnSe crystal PEM which modulates the polarized beam at a fixed, lower frequency such as 37.5 kHz. A mechanically stressed crystal such as ZnSe exhibits birefringence when stressed by an adjacent piezoelectric transducer. The linear polarizer is positioned close to, and at 45 degrees, with respect to the ZnSe crystal axis. The polarized radiation focused onto the detector is doubly modulated, both by the PEM and by the interferometer setup. A very low noise detector, such as MCT (HgCdTe), is also selected for the VCD signal phase-sensitive detection. The first dedicated VCD spectrometer brought to market was the ChiralIR from Bomem/BioTools, Inc. in 1997. Today, Thermo-Electron, Bruker, Jasco and BioTools offer either VCD accessories or stand-alone instrumentation. To prevent detector saturation an appropriate, long wave pass filter is placed before the very low noise MCT detector, which allows only radiation below 1750 cm−1 to reach the MCT detector; the latter however measures radiation only down to 750 cm−1. FT-VCD spectra accumulation of the selected sample solution is then carried out, digitized and stored by an in-line computer. Published reviews that compare various VCD methods are also available.
Modeling VCD Spectra
In 1994, researchers at the University of Southern California (USC), U.S. Army Research Laboratory (USARL), and Lorentzian Inc., reported an accuracy ranking of quantum mechanical analytical techniques to theoretically determine vibrational frequencies, dipole strengths, and rotational strengths of an organic molecule. This ranking claimed density functional theory (DFT) at the B3LYP/6-31G* level of theory was the most accurate and effective computation used to model and vibrational circular dichroism (VCD) spectra.  Electronic structure computations, by solving either the Schrödinger equation or the Kohn-Sham equation, can be used to obtain information about ground state energy, bond vibrational frequency, and electron density (Ψ2), and other characteristics.
Theoretical calculations of vibrational energy often involve the Schrödinger’s equation with the Hamiltonian operator. The computers that process this massive calculation can incorporate the molecule’s kinetic energy as well as the vast number of repulsions and columbic attractions between subatomic particles. The calculations are said to be very costly, as they are difficult and take a long time to accomplish. This is partially because integrating the electron-electron interactions into the equation involves determining electron exchange interactions. Methods like DFT and the Hartree Fock look at a group of atomic orbitals referred to as a basis set to estimate wave function. The wave function can be used to determine frequency, wavelength, energy etc. Hartree Fock operates with a feedback loop called a self-consistent field that continuously refines the wave function estimates until the value falls within a satisfactory change in energy threshold that they converge the calculation and determine an approximated wavefunction. 
The study conducted by USC, USARL, and Lorentzian Inc. analyzed the infrared (FTIR) and VCD spectra of the chiral molecule 4-methyl-2-oxetanone. Lorentzian bands were fit to FTIR and VCD spectra to obtain their peak intensity, line width, and frequency, which may be used to infer properties such as dipole strengths and rotational strengths. These experimental values were then compared to theoretical results. The scientists reported that DFT computations evaluated with the B3LYP functional best modelled FTIR and VCD spectra. To achieve a better cost to benefit ratio the researchers recommended pairing this method with the 6-31* basis set. The second best method reported was the second order Møller–Plesset perturbation theory (MP2). The third and fourth best calculation methods were DFT with the BLYP and LSDA functionals respectively. The researchers stated that Ab initio Hartree Fock Self Consistent Field (HF-SCF) computations modelled FTIR and VCD spectra with the lowest accuracy compared to other methodologies investigated.
The significance in claimed improvement in accuracy of DFT computations over ab initio techniques was that DFT computations were reported to quicken computational speed. By evaluating an effective potential using electron density, which can by specified across three degrees of freedom, DFT sidesteps the evaluation of coulombic potentials between every single electron, which is specified over 3N degrees of freedom (where N is the number of electrons). The B3LYP basis set is a hybrid between direct Hartree-Fock exchange terms as well as local and gradient corrections for exchange and correlation interactions. Therefore, the B3LYP functional is claimed to efficiently model FTIR and VCD of some molecules via DFT at a fraction of the cost. 
Raman optical activity (ROA)
ROA is a technique complementary to VCD especially useful in the 50–1600 cm−1 spectral region; it is considered as the technique of choice for determining optical activity for photon energies less than 600 cm−1.
- Amino acid
- Circular dichroism
- Density functional theory
- DNA structure
- IR spectroscopy
- Magnetic circular dichroism
- Molecular models of DNA
- Nucleic acid
- Optical rotatory dispersion
- Photoelastic modulator
- Protein structure
- Quantum chemistry
- Raman optical activity (ROA)
- Principles of IR and NIR Spectroscopy
- Stephens Philip J (1985). "Theory of vibrational circular dichroism". The Journal of Physical Chemistry. 89: 748–752. doi:10.1021/j100251a006.
- Stephens P. J. (1987). "Gauge dependence of vibrational magnetic dipole transition moments and rotational strengths". The Journal of Physical Chemistry. 91: 1712–1715. doi:10.1021/j100291a009.
- Buckingham A.D., Fowler P.W., Galwas P.A. (1987). "Velocity-dependent property surfaces and the theory of vibrational circular dichroism". Chemical Physics. 112: 1–14. Bibcode:1987CP....112....1B. doi:10.1016/0301-0104(87)85017-6.
- Amos R.D., Handy N.C., Jalkanen K.J., Stephens P.J. (1987). "Efficient calculation of vibrational magnetic dipole transition moments and rotational strengths". Chemical Physics Letters. 133: 21–26. Bibcode:1987CPL...133...21A. doi:10.1016/0009-2614(87)80046-5.
- Craig D.P., Thirunamachandran T. (1978). "A theory of vibrational circular dichroism in terms of vibronic interactions". Molecular Physics. 35: 825–840. doi:10.1080/00268977800100611.
- Nafie Laurence A., Freedman Teresa B. (1983). "Vibronic coupling theory of infrared vibrational transitions". The Journal of Chemical Physics. 78: 7108–7116. Bibcode:1983JChPh..78.7108N. doi:10.1063/1.444741.
- P. Malon; R. Kobrinskaya; T. A. Keiderling (1988). "Vibrational Circular Dichroism of Polypeptides XII. Re-evaluation of the Fourier Transform Vibrational Circular Dichroism of Poly-gamma-Benzyl-L-Glutamate". Biopolymers. 27 (5): 733–746. doi:10.1002/bip.360270503. PMID 2454680.
- T. A. Keiderling; S. C. Yasui; U. Narayanan; A. Annamalai; P. Malon; R. Kobrinskaya; et al. (1988). "Vibrational Circular Dichroism of Biopolymers". In E. D. Schmid; F. W. Schneider; F. Siebert. Spectroscopy of Biological Molecules New Advances. Wiley. pp. 73–76. ISBN 0-471-91934-9.
- S. C. Yasui; T. A. Keiderling (1988). "Vibrational Circular Dichroism of Polypeptides and Proteins". Mikrochimica Acta. II: 325–327. doi:10.1007/BF01349780.
- T. A. Keiderling (1993). I.C. Baianu; H. Pessen; T. Kumosinski, eds. "Physical Chemistry of Food Processes". 2 Advanced Techniques, Structures and Applications. New York: Van Norstrand-Reinhold: 307–337.
- T. A. Keiderling & Qi Xu (2002). "Spectroscopic characterization of Unfolded peptides and proteins studied with infrared absorption and vibrational circular dichroism spectra". In George Rose. Advances in Protein Chemistry. 62. New York: Academic Press. pp. 111–161.
- Keiderling, Timothy A (2002). "Protein and Peptide Secondary Structure and Conformational Determination with Vibrational Circular Dichroism". Current Opinion in Chemical Biology. 6 (5): 682–8. doi:10.1016/S1367-5931(02)00369-1. PMID 12413554.
- Timothy A. Keiderling & R. A. G. D. Silva (2002). "Review: Conformational Studies of Peptides with Infrared Techniques". In M. Goodman; G. Herrman & Houben-Weyl. Synthesis of Peptides and Peptidomimetics. 22Eb. New York: Georg Thiem Verlag. pp. 715–738 (written in 2000.
- Jalkanen K. J., Degtyarenko I. M., Nieminen R. M., Cao X., Nafie L. A., Zhu F., Barron L. D. (2007). "Role of hydration in determining the structure and vibrational spectra of L-alanine and N-acetyl L-alanine N′-methylamide in aqueous solution: a combined theoretical and experimental approach". Theoretical Chemistry Accounts. 119: 191–210. doi:10.1007/s00214-007-0361-z.
- Han Wen-Ge, Jalkanen K. J., Elstner Marcus, Suhai Sándor (1998). "Theoretical Study of AqueousN-Acetyl-l-alanineN'-Methylamide: Structures and Raman, VCD, and ROA Spectra". The Journal of Physical Chemistry B. 102: 2587–2602. doi:10.1021/jp972299m.
- Poon Chi-Duen, Samulski Edward T., Weise Christoph F., Weisshaar James C. (2000). "Do Bridging Water Molecules Dictate the Structure of a Model Dipeptide in Aqueous Solution?". Journal of the American Chemical Society. 122: 5642–5643. doi:10.1021/ja993953+.
- L. A. Nafie, T. A. Keiderling, P. J. Stephens, JACS 1973, 98, 2715
- BioTools Catalog, page 4 Archived December 24, 2014, at the Wayback Machine.
- Laurence A. Nafie (2008). "Vibrational Circular Dichroism: A New Tool for the Solution-State Determination of the Structure and Absolute Configuration of Chiral Natural Product Molecules". Natural Product Communications. 3 (3): 451–466.
- Jovencio Hilario; David Drapcho; Raul Curbelo; Timothy A. Keiderling (2001). "Polarization Modulation Fourier Transform Infrared Spectroscopy with Digital Signal Processing: Comparison of Vibrational Circular Dichroism Methods". Applied Spectroscopy. 55 (11): 1435–1447. Bibcode:2001ApSpe..55.1435H. doi:10.1366/0003702011953810.
- Timothy A. Keiderling; Jan Kubelka; Jovencio Hilario (2006). "Vibrational circular dichroism of biopolymers. Summary of methods and applications". In Mark Braiman; Vasilis Gregoriou. Vibrational spectroscopy of polymers and biological systems. Boca Raton, FL: CRC Press. pp. 253–324. (written in 2000, updated in 2003)
- Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M.J. (1994). "Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields". Journal of Physical Chemistry. 98: 11623–11627.
- Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering. Committee on Challenges for the Chemical Sciences in the 21st Century, National Research Council. 2003. ISBN 0-309-50512-7.
- "1.2 Electronic structure calculations". web.ornl.gov. Retrieved 2018-08-15.
- Cresser, J.D. (2009). Quantum Physics Notes (PDF). pp. 14–26.
- Sherril, David C. (2000). An Introduction to Hartree-Fock Molecular Orbital (PDF). pp. 1–8.
- "- Convergence in Hartree-Fock Calculations". www.cup.uni-muenchen.de. Retrieved 2018-08-15.
- T. A. Keiderling (1981). "Observation of Magnetic Vibrational Circular Dichroism". Journal of Chemical Physics. 75 (7): 3639–41. Bibcode:1981JChPh..75.3639K. doi:10.1063/1.442437.
- T. R. Devine & T. A. Keiderling (1987). "Vibrational Spectral Assignment and Enhanced Resolution Using Magnetic Vibrational Circular Dichroism". Spectrochimica Acta. 43A: 627–629.
- P. V. Croatto; R. K. Yoo; T. A. Keiderling (1989). "Magnetic Vibrational Circular Dichroism with an FTIR". Proceedings of SPIE. 1145: 152–153. Bibcode:1989SPIE.1145..152C. doi:10.1117/12.969401.
- C. N. Tam & T. A. Keiderling (1995). "Direct Measurement of the Rotational g-Value in the Ground State of Acetylene by Magnetic Vibrational Circular Dichroism". Chemical Physics Letters. 243: 55–58. Bibcode:1995CPL...243...55J. doi:10.1016/0009-2614(95)00843-S.
- P. Bour; C. N. Tam; T. A. Keiderling (1995). "Ab initio calculation of the vibrational magnetic dipole moment". Journal of Physical Chemistry. 99: 17810–17813. doi:10.1021/j100051a002.
- P. Bour; C. N. Tam; B. Wang; T. A. Keiderling (1996). "Rotationally Resolved Magnetic Vibrational Circular Dichroism. Experimental Spectra and Theoretical Simulation for Diamagnetic Molecules". Molecular Physics. 87: 299–318. Bibcode:1996MolPh..87..299B. doi:10.1080/00268979600100201.