Abstract

Detailed theoretical analyses are presented for cavity ring-down polarimetry, a recently developed scheme for probing circular birefringence (nonresonant rotatory dispersion) and circular dichroism (resonant differential absorption) with unprecedented sensitivity. Aside from elucidating the nature of time-resolved signals generated by various modes of operation, the influence of instrumental imperfections on polarimetric response is examined. The unique ability of cavity ring-down polarimetry to interrogate nonresonant optical activity in low-pressure chiral vapors is demonstrated by extracting specific rotation parameters at two complementary excitation wavelengths (355 nm and 633 nm) for gaseous samples of α-pinene, β-pinene, and cis-pinane. The resulting isolated-molecule properties are contrasted with those derived from conventional solution-phase experiments and state-of-the-art ab initio calculations.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Müller, K. B. Wiberg, and P. H. Vaccaro, “Cavity ring-down polarimetry (CRDP): a new scheme for probing circular birefringence and circular dichroism in the gas phase,” J. Phys. Chem. A 104, 5959–5968 (2000).
    [CrossRef]
  2. A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
    [CrossRef]
  3. P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
    [CrossRef]
  4. J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
    [CrossRef] [PubMed]
  5. M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
    [CrossRef]
  6. E. L. Eliel and S. H. Wilen, Stereochemistry of Organic Compounds (Wiley, New York, 1994).
  7. K. Mislow, “Molecular chirality,” Top. Stereochem. 22, 1–82 (1999).
  8. O. Schnepp, S. Allen, and E. F. Pearson, “The measurement of circular dichroism in the vacuum ultraviolet,” Rev. Sci. Instrum. 41, 1136–1141 (1970).
    [CrossRef]
  9. W. C. Johnson, “A circular dichroism spectrometer for the vacuum ultraviolet,” Rev. Sci. Instrum. 42, 1283–1286 (1971).
    [CrossRef] [PubMed]
  10. M. G. Mason and O. Schnepp, “Absorption and circular dichroism spectra of ethylenic chromophores: trans-cyclooctene, α- and β-pinene,” J. Chem. Phys. 59, 1092–1098 (1973).
    [CrossRef]
  11. K. P. Gross and O. Schnepp, “Circular dichroism spectra of straight chain mono-olefins. Assignment of ethylene transitions,” Chem. Phys. Lett. 36, 531–535 (1975).
    [CrossRef]
  12. M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
    [CrossRef]
  13. P. L. Polavarapu and D. F. Michalska, “Vibrational circular dichroism in (S)-(−)-epoxypropane. Measurement in vapor phase and verification of the perturbed degenerate mode theory,” J. Am. Chem. Soc. 105, 6190–6191 (1983).
    [CrossRef]
  14. P. J. Stephens and M. A. Lowe, “Vibrational circular dichroism,” Annu. Rev. Phys. Chem. 36, 213–241 (1985).
    [CrossRef]
  15. T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
    [CrossRef]
  16. L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. 48, 357–386 (1997).
    [CrossRef] [PubMed]
  17. J.-B. Biot, “Mémoire sur les rotations que certains substances impriment aux axes de polarisation des rayons lumineux,” Mém. Acad. R. Sci. Inst. France 2, 41–136 (1817).
  18. D. Gernez, “Recherches sur le pouvoir rotatoire des liquides actifs et de leurs vapeurs,” Ann. Sci. Éc. Norm. Sup. 1, 1–38 (1864).
  19. P.-A. Guye and A.-P. do Amaral, “Pouvoirs rotatoires de quelques derivés amyliques à l’état liquide et à l’état de vapeur,” Arch. Sci. Phys. Nat. 33, 513–529 (1895).
  20. T. M. Lowry and H. K. Gore, “Optical rotatory power of vapours. Part I. Rotatory dispersion of camphor and of camphorquinone, especially in the region of absorption,” Proc. R. Soc. London, Ser. A 135, 13–22 (1932).
    [CrossRef]
  21. R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
    [CrossRef]
  22. L. D. Barron, “Fundamental symmetry aspects of molecular chirality,” in New Developments in Molecular Chirality, P. G. Mezey, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1991), Vol. 5, pp. 1–55.
  23. J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
    [CrossRef] [PubMed]
  24. H. Mueller, “The foundation of optics,” J. Opt. Soc. Am. 38, 661 (1948).
  25. M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
    [CrossRef]
  26. W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, Cambridge, Mass., 1962).
  27. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, Boston, 1990).
  28. R. J. Jones, “New calculus for the treatment of optical systems. I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  29. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).
  30. P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988).
  31. J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
    [CrossRef]
  32. C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
    [CrossRef]
  33. G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).
  34. D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Phys. Chem. 99, 6287–6301 (1993).
    [CrossRef]
  35. H. Naus and W. Ubachs, “Experimental verification of Rayleigh scattering cross sections,” Opt. Lett. 25, 347–349 (2000).
    [CrossRef]
  36. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  37. D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring-down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
    [CrossRef]
  38. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [CrossRef]
  39. P. Crabbé, Optical Rotatory Dispersion and Circular Dichroism in Organic Chemistry (Holden-Day, San Francisco, Calif., 1965).
  40. C. Reichardt, Solvents and Solvent Effects in Organic Chemistry (VCH, Weinheim, 1988).
  41. P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
    [CrossRef]
  42. F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
    [CrossRef]
  43. W. Koch and W. C. Holthausen, A Chemist’s Guide to Density Functional Theory (Wiley-VCH, Weinheim, 2000).
  44. J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens (to be published).
  45. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, A. G. Baboul, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian 99, Development Version (Revision B.04) (Gaussian, Inc., Pittsburgh, Pa., 1998).
  46. J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
    [CrossRef]
  47. T. Müller, K. B. Wiberg, and P. H. Vaccaro (unpublished results).
  48. C. Wohlfarth and B. Wohlfarth, “Subvolume B: optical constants,” in Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology (New Series), M. D. Lechner, ed. (Springer-Verlag, Berlin, 1961), Group III: Condensed Matter, Vol. 38, p. 127.

2001 (1)

P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
[CrossRef]

2000 (3)

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
[CrossRef]

H. Naus and W. Ubachs, “Experimental verification of Rayleigh scattering cross sections,” Opt. Lett. 25, 347–349 (2000).
[CrossRef]

T. Müller, K. B. Wiberg, and P. H. Vaccaro, “Cavity ring-down polarimetry (CRDP): a new scheme for probing circular birefringence and circular dichroism in the gas phase,” J. Phys. Chem. A 104, 5959–5968 (2000).
[CrossRef]

1999 (1)

K. Mislow, “Molecular chirality,” Top. Stereochem. 22, 1–82 (1999).

1998 (2)

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
[CrossRef]

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

1997 (5)

R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
[CrossRef]

F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
[CrossRef]

D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring-down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
[CrossRef]

J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
[CrossRef] [PubMed]

L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. 48, 357–386 (1997).
[CrossRef] [PubMed]

1995 (1)

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

1994 (1)

C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
[CrossRef]

1993 (1)

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Phys. Chem. 99, 6287–6301 (1993).
[CrossRef]

1989 (1)

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

1988 (1)

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

1987 (1)

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

1985 (1)

P. J. Stephens and M. A. Lowe, “Vibrational circular dichroism,” Annu. Rev. Phys. Chem. 36, 213–241 (1985).
[CrossRef]

1983 (1)

P. L. Polavarapu and D. F. Michalska, “Vibrational circular dichroism in (S)-(−)-epoxypropane. Measurement in vapor phase and verification of the perturbed degenerate mode theory,” J. Am. Chem. Soc. 105, 6190–6191 (1983).
[CrossRef]

1980 (1)

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

1975 (1)

K. P. Gross and O. Schnepp, “Circular dichroism spectra of straight chain mono-olefins. Assignment of ethylene transitions,” Chem. Phys. Lett. 36, 531–535 (1975).
[CrossRef]

1973 (1)

M. G. Mason and O. Schnepp, “Absorption and circular dichroism spectra of ethylenic chromophores: trans-cyclooctene, α- and β-pinene,” J. Chem. Phys. 59, 1092–1098 (1973).
[CrossRef]

1971 (1)

W. C. Johnson, “A circular dichroism spectrometer for the vacuum ultraviolet,” Rev. Sci. Instrum. 42, 1283–1286 (1971).
[CrossRef] [PubMed]

1970 (1)

O. Schnepp, S. Allen, and E. F. Pearson, “The measurement of circular dichroism in the vacuum ultraviolet,” Rev. Sci. Instrum. 41, 1136–1141 (1970).
[CrossRef]

1954 (1)

M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
[CrossRef]

1948 (1)

H. Mueller, “The foundation of optics,” J. Opt. Soc. Am. 38, 661 (1948).

1941 (1)

1937 (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

1932 (1)

T. M. Lowry and H. K. Gore, “Optical rotatory power of vapours. Part I. Rotatory dispersion of camphor and of camphorquinone, especially in the region of absorption,” Proc. R. Soc. London, Ser. A 135, 13–22 (1932).
[CrossRef]

1895 (1)

P.-A. Guye and A.-P. do Amaral, “Pouvoirs rotatoires de quelques derivés amyliques à l’état liquide et à l’état de vapeur,” Arch. Sci. Phys. Nat. 33, 513–529 (1895).

1864 (1)

D. Gernez, “Recherches sur le pouvoir rotatoire des liquides actifs et de leurs vapeurs,” Ann. Sci. Éc. Norm. Sup. 1, 1–38 (1864).

1817 (1)

J.-B. Biot, “Mémoire sur les rotations que certains substances impriment aux axes de polarisation des rayons lumineux,” Mém. Acad. R. Sci. Inst. France 2, 41–136 (1817).

Allen, S.

O. Schnepp, S. Allen, and E. F. Pearson, “The measurement of circular dichroism in the vacuum ultraviolet,” Rev. Sci. Instrum. 41, 1136–1141 (1970).
[CrossRef]

Ashfold, M. N. R.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
[CrossRef]

Baldwin, J. E.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Basch, H.

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

Berden, G.

R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
[CrossRef]

Biot, J.-B.

J.-B. Biot, “Mémoire sur les rotations que certains substances impriment aux axes de polarisation des rayons lumineux,” Mém. Acad. R. Sci. Inst. France 2, 41–136 (1817).

Bretenaker, F.

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

Cheeseman, J. R.

P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
[CrossRef]

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
[CrossRef]

F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
[CrossRef]

Cianciosi, S. J.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Cohen, D.

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

Condon, E. U.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Deacon, D. A. G.

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

Devlin, F. J.

P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
[CrossRef]

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
[CrossRef]

F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
[CrossRef]

Diping, C.

C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
[CrossRef]

do Amaral, A.-P.

P.-A. Guye and A.-P. do Amaral, “Pouvoirs rotatoires de quelques derivés amyliques à l’état liquide et à l’état de vapeur,” Arch. Sci. Phys. Nat. 33, 513–529 (1895).

Engeln, R.

R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
[CrossRef]

Freedman, T. B.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Frisch, M. J.

P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
[CrossRef]

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
[CrossRef]

F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
[CrossRef]

Gedanken, A.

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

Gernez, D.

D. Gernez, “Recherches sur le pouvoir rotatoire des liquides actifs et de leurs vapeurs,” Ann. Sci. Éc. Norm. Sup. 1, 1–38 (1864).

Goldbeck, R. A.

C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
[CrossRef]

Gore, H. K.

T. M. Lowry and H. K. Gore, “Optical rotatory power of vapours. Part I. Rotatory dispersion of camphor and of camphorquinone, especially in the region of absorption,” Proc. R. Soc. London, Ser. A 135, 13–22 (1932).
[CrossRef]

Gross, K. P.

K. P. Gross and O. Schnepp, “Circular dichroism spectra of straight chain mono-olefins. Assignment of ethylene transitions,” Chem. Phys. Lett. 36, 531–535 (1975).
[CrossRef]

Guye, P.-A.

P.-A. Guye and A.-P. do Amaral, “Pouvoirs rotatoires de quelques derivés amyliques à l’état liquide et à l’état de vapeur,” Arch. Sci. Phys. Nat. 33, 513–529 (1895).

Jensen, H. P.

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

Johnson, W. C.

W. C. Johnson, “A circular dichroism spectrometer for the vacuum ultraviolet,” Rev. Sci. Instrum. 42, 1283–1286 (1971).
[CrossRef] [PubMed]

Jones, R. J.

Kachanov, A. A.

D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring-down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
[CrossRef]

Kliger, D. S.

C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
[CrossRef]

Le Floch, A.

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

Lehmann, K. K.

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Phys. Chem. 99, 6287–6301 (1993).
[CrossRef]

Levi, M.

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

Lowe, M. A.

P. J. Stephens and M. A. Lowe, “Vibrational circular dichroism,” Annu. Rev. Phys. Chem. 36, 213–241 (1985).
[CrossRef]

Lowry, T. M.

T. M. Lowry and H. K. Gore, “Optical rotatory power of vapours. Part I. Rotatory dispersion of camphor and of camphorquinone, especially in the region of absorption,” Proc. R. Soc. London, Ser. A 135, 13–22 (1932).
[CrossRef]

Mason, M. G.

M. G. Mason and O. Schnepp, “Absorption and circular dichroism spectra of ethylenic chromophores: trans-cyclooctene, α- and β-pinene,” J. Chem. Phys. 59, 1092–1098 (1973).
[CrossRef]

McCarthy, C.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

McCauley, S. W.

C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
[CrossRef]

Meijer, G.

R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
[CrossRef]

Michalska, D. F.

P. L. Polavarapu and D. F. Michalska, “Vibrational circular dichroism in (S)-(−)-epoxypropane. Measurement in vapor phase and verification of the perturbed degenerate mode theory,” J. Am. Chem. Soc. 105, 6190–6191 (1983).
[CrossRef]

Mislow, K.

K. Mislow, “Molecular chirality,” Top. Stereochem. 22, 1–82 (1999).

Moore, J. A.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Mueller, H.

H. Mueller, “The foundation of optics,” J. Opt. Soc. Am. 38, 661 (1948).

Müller, T.

T. Müller, K. B. Wiberg, and P. H. Vaccaro, “Cavity ring-down polarimetry (CRDP): a new scheme for probing circular birefringence and circular dichroism in the gas phase,” J. Phys. Chem. A 104, 5959–5968 (2000).
[CrossRef]

Nafie, L. A.

L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. 48, 357–386 (1997).
[CrossRef] [PubMed]

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Naus, H.

Newman, S. M.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
[CrossRef]

O’Keefe, A.

J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
[CrossRef] [PubMed]

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

Orr-Ewing, A. J.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
[CrossRef]

Paul, J. B.

J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
[CrossRef] [PubMed]

Pearson, E. F.

O. Schnepp, S. Allen, and E. F. Pearson, “The measurement of circular dichroism in the vacuum ultraviolet,” Rev. Sci. Instrum. 41, 1136–1141 (1970).
[CrossRef]

Poirson, J.

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

Polavarapu, P. L.

P. L. Polavarapu and D. F. Michalska, “Vibrational circular dichroism in (S)-(−)-epoxypropane. Measurement in vapor phase and verification of the perturbed degenerate mode theory,” J. Am. Chem. Soc. 105, 6190–6191 (1983).
[CrossRef]

Romanini, D.

D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring-down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
[CrossRef]

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Phys. Chem. 99, 6287–6301 (1993).
[CrossRef]

Saykally, R. J.

J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
[CrossRef] [PubMed]

Schellman, J.

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

Scherer, J. J.

J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
[CrossRef] [PubMed]

Schnepp, O.

K. P. Gross and O. Schnepp, “Circular dichroism spectra of straight chain mono-olefins. Assignment of ethylene transitions,” Chem. Phys. Lett. 36, 531–535 (1975).
[CrossRef]

M. G. Mason and O. Schnepp, “Absorption and circular dichroism spectra of ethylenic chromophores: trans-cyclooctene, α- and β-pinene,” J. Chem. Phys. 59, 1092–1098 (1973).
[CrossRef]

O. Schnepp, S. Allen, and E. F. Pearson, “The measurement of circular dichroism in the vacuum ultraviolet,” Rev. Sci. Instrum. 41, 1136–1141 (1970).
[CrossRef]

Schurig, V.

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

Schwab, J. M.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Spencer, K. M.

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Stephens, P. J.

P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
[CrossRef]

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
[CrossRef]

F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
[CrossRef]

P. J. Stephens and M. A. Lowe, “Vibrational circular dichroism,” Annu. Rev. Phys. Chem. 36, 213–241 (1985).
[CrossRef]

Stoeckel, F.

D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring-down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
[CrossRef]

Thépot, J.-Y.

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

Ubachs, W.

Vaccaro, P. H.

T. Müller, K. B. Wiberg, and P. H. Vaccaro, “Cavity ring-down polarimetry (CRDP): a new scheme for probing circular birefringence and circular dichroism in the gas phase,” J. Phys. Chem. A 104, 5959–5968 (2000).
[CrossRef]

Vallet, M.

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

van den Berg, E.

R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
[CrossRef]

Walker, M. J.

M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
[CrossRef]

Wheeler, M. D.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
[CrossRef]

Wiberg, K. B.

T. Müller, K. B. Wiberg, and P. H. Vaccaro, “Cavity ring-down polarimetry (CRDP): a new scheme for probing circular birefringence and circular dichroism in the gas phase,” J. Phys. Chem. A 104, 5959–5968 (2000).
[CrossRef]

Zalicki, P.

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

Zare, R. N.

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

Am. J. Phys. (1)

M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
[CrossRef]

Anal. Chem. (1)

J. Poirson, M. Vallet, F. Bretenaker, A. Le Floch, and J.-Y. Thépot, “Resonant cavity gas-phase polarimeter,” Anal. Chem. 70, 4636–4639 (1998).
[CrossRef] [PubMed]

Ann. Sci. Éc. Norm. Sup. (1)

D. Gernez, “Recherches sur le pouvoir rotatoire des liquides actifs et de leurs vapeurs,” Ann. Sci. Éc. Norm. Sup. 1, 1–38 (1864).

Annu. Rev. Phys. Chem. (2)

L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. 48, 357–386 (1997).
[CrossRef] [PubMed]

P. J. Stephens and M. A. Lowe, “Vibrational circular dichroism,” Annu. Rev. Phys. Chem. 36, 213–241 (1985).
[CrossRef]

Arch. Sci. Phys. Nat. (1)

P.-A. Guye and A.-P. do Amaral, “Pouvoirs rotatoires de quelques derivés amyliques à l’état liquide et à l’état de vapeur,” Arch. Sci. Phys. Nat. 33, 513–529 (1895).

Chem. Phys. Lett. (2)

K. P. Gross and O. Schnepp, “Circular dichroism spectra of straight chain mono-olefins. Assignment of ethylene transitions,” Chem. Phys. Lett. 36, 531–535 (1975).
[CrossRef]

D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring-down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
[CrossRef]

Chem. Rev. (2)

J. J. Scherer, J. B. Paul, A. O’Keefe, and R. J. Saykally, “Cavity ring-down laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–51 (1997).
[CrossRef] [PubMed]

J. Schellman and H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87, 1359–1399 (1987).
[CrossRef]

J. Am. Chem. Soc. (2)

M. Levi, D. Cohen, V. Schurig, H. Basch, and A. Gedanken, “Circular dichroism of an optically active olefin chromophore: (R)-3-methylcyclopentene,” J. Am. Chem. Soc. 102, 6972–6975 (1980).
[CrossRef]

P. L. Polavarapu and D. F. Michalska, “Vibrational circular dichroism in (S)-(−)-epoxypropane. Measurement in vapor phase and verification of the perturbed degenerate mode theory,” J. Am. Chem. Soc. 105, 6190–6191 (1983).
[CrossRef]

J. Chem. Phys. (3)

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

R. Engeln, G. Berden, E. van den Berg, and G. Meijer, “Polarization dependent cavity ring down spectroscopy,” J. Chem. Phys. 107, 4458–4467 (1997).
[CrossRef]

M. G. Mason and O. Schnepp, “Absorption and circular dichroism spectra of ethylenic chromophores: trans-cyclooctene, α- and β-pinene,” J. Chem. Phys. 59, 1092–1098 (1973).
[CrossRef]

J. Chem. Soc., Faraday Trans. (1)

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N. R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc., Faraday Trans. 94, 337–351 (1998).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Chem. (2)

C. Diping, R. A. Goldbeck, S. W. McCauley, and D. S. Kliger, “Optical analysis of an ellipsometric technique for time-resolved magnetic circular dichroism spectroscopy,” J. Phys. Chem. 98, 3601–3611 (1994).
[CrossRef]

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Phys. Chem. 99, 6287–6301 (1993).
[CrossRef]

J. Phys. Chem. A (4)

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens, “Hartree–Fock density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence,” J. Phys. Chem. A 104, 1039–1046 (2000).
[CrossRef]

P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “The calculation of optical rotation using density functional theory,” J. Phys. Chem. A 105, 5356–5371 (2001).
[CrossRef]

F. J. Devlin, P. J. Stephens, J. R. Cheeseman, and M. J. Frisch, “Ab initio prediction of vibrational absorption and circular dichroism spectra of chiral natural products using density functional theory: α-pinene,” J. Phys. Chem. A 101, 9912–9924 (1997).
[CrossRef]

T. Müller, K. B. Wiberg, and P. H. Vaccaro, “Cavity ring-down polarimetry (CRDP): a new scheme for probing circular birefringence and circular dichroism in the gas phase,” J. Phys. Chem. A 104, 5959–5968 (2000).
[CrossRef]

Mém. Acad. R. Sci. Inst. France (1)

J.-B. Biot, “Mémoire sur les rotations que certains substances impriment aux axes de polarisation des rayons lumineux,” Mém. Acad. R. Sci. Inst. France 2, 41–136 (1817).

Opt. Lett. (1)

Proc. R. Soc. London, Ser. A (1)

T. M. Lowry and H. K. Gore, “Optical rotatory power of vapours. Part I. Rotatory dispersion of camphor and of camphorquinone, especially in the region of absorption,” Proc. R. Soc. London, Ser. A 135, 13–22 (1932).
[CrossRef]

Proc. SPIE (1)

T. B. Freedman, K. M. Spencer, C. McCarthy, S. J. Cianciosi, J. E. Baldwin, L. A. Nafie, J. A. Moore, and J. M. Schwab, “Vibrational circular dichroism of simple chiral molecules in the gas phase,” Proc. SPIE 1145, 273–274 (1989).
[CrossRef]

Rev. Mod. Phys. (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Rev. Sci. Instrum. (3)

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

O. Schnepp, S. Allen, and E. F. Pearson, “The measurement of circular dichroism in the vacuum ultraviolet,” Rev. Sci. Instrum. 41, 1136–1141 (1970).
[CrossRef]

W. C. Johnson, “A circular dichroism spectrometer for the vacuum ultraviolet,” Rev. Sci. Instrum. 42, 1283–1286 (1971).
[CrossRef] [PubMed]

Top. Stereochem. (1)

K. Mislow, “Molecular chirality,” Top. Stereochem. 22, 1–82 (1999).

Other (15)

E. L. Eliel and S. H. Wilen, Stereochemistry of Organic Compounds (Wiley, New York, 1994).

P. Crabbé, Optical Rotatory Dispersion and Circular Dichroism in Organic Chemistry (Holden-Day, San Francisco, Calif., 1965).

C. Reichardt, Solvents and Solvent Effects in Organic Chemistry (VCH, Weinheim, 1988).

W. Koch and W. C. Holthausen, A Chemist’s Guide to Density Functional Theory (Wiley-VCH, Weinheim, 2000).

J. R. Cheeseman, M. J. Frisch, F. J. Devlin, and P. J. Stephens (to be published).

M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, A. G. Baboul, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian 99, Development Version (Revision B.04) (Gaussian, Inc., Pittsburgh, Pa., 1998).

L. D. Barron, “Fundamental symmetry aspects of molecular chirality,” in New Developments in Molecular Chirality, P. G. Mezey, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1991), Vol. 5, pp. 1–55.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, Cambridge, Mass., 1962).

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, Boston, 1990).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).

T. Müller, K. B. Wiberg, and P. H. Vaccaro (unpublished results).

C. Wohlfarth and B. Wohlfarth, “Subvolume B: optical constants,” in Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology (New Series), M. D. Lechner, ed. (Springer-Verlag, Berlin, 1961), Group III: Condensed Matter, Vol. 38, p. 127.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).

P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the CRDP apparatus. Pulsed radiation at 355 nm or 633 nm is spatially filtered and mode matched for the CRDP resonator before traversing a circular polarizer consisting of a tandem calcite prism (linear polarizer) and quarter-wave plate. The resulting beam is coupled into a stable linear cavity of L=1.63 m length by passing through the planar rear surface of the input mirror. Intracavity λ/4 retarders, located d=17 cm from each mirror, are aligned to produce a linearly polarized internal field over the intervening l=L-2d=1.29 m region, thereby making this portion of the ring-down apparatus sensitive to the effects of optical activity. Light emerging from the output mirror is imaged onto identical photodetectors that monitor two mutually orthogonal components of linear polarization generated by means of a second circular-polarization analyzer.

Fig. 2
Fig. 2

CRDP modes of operation. Signals predicted to accompany (a) “stationary” and (b) “modulated” implementations of the CRDP scheme are illustrated as functions of the number of round-trip passes, N, experienced by light trapped within the resonator assembly. The solid curves depict ring-down profiles expected for a perfectly aligned, empty apparatus, and the dashed curves represent the response generated upon introduction of a chiral sample possessing nonresonant optical activity (circular birefringence). Although both detection channels are displayed for the “stationary” mode of operation [panel (a)], only the “parallel” signal is shown for the “modulated” configuration [panel (b)] since the complementary “perpendicular” traces will exhibit an identical oscillation pattern that has the same characteristic frequency but is offset in relative phase by half a cycle.

Fig. 3
Fig. 3

Simulation of CB measurement in the presence of strong CD. The solid curve depicts a simulated CRDP trace calculated for the parallel detection channel in the modulated mode of operation (α=π/20) through use of the complete mathematical expression derived for a perfectly aligned apparatus [first equality of Eq. (13a)]. The key resonator properties were fixed at values commensurate with laboratory measurements conducted at 355 nm, and the target medium was presumed to exhibit a mean absorption coefficient of =8×10-5 cm-1 with the CD dissymmetry ratio given by Δ/=1 and the nonresonant optical rotation (CB) specified by ϕ=0. The dashed curve represents the outcome of a nonlinear least-squares regression based upon a functional form [second equality of Eq. (13a)] that ignores overall and differential absorption (=Δ=0) but allows for variation of the CB parameter, ϕ. The best-fit estimate of ϕ=(-0.0085±1.8)×10-4 rad/m confirms that the expected null result for optical rotation is obtained (to within statistical uncertainty).

Fig. 4
Fig. 4

Experimental data acquired in the modulated mode of CRDP operation. The relative intensity of light transmitted through a ring-down polarimeter is plotted as a function of time, t, where t=0 corresponds to the instant of pulsed excitation. Data sets comprising 5000 discrete points were acquired in the perpendicular detection channel of the modulated configuration, with results being displayed for an empty apparatus (solid curves) as well as for one containing ∼1.5 Torr of α-pinene (dashed curves). Panel (a) depicts temporal profiles obtained at 355 nm for (1S, 5S)-(-)-α-pinene, and panel (b) presents analogous measurements at 633 nm for (1R, 5R)-(+)-α-pinene. In both cases, inset (I) provides an expanded view of the response observed in the vicinity of t=0. Likewise, inset (II) shows magnified segments of the signal at t=3.2 µs and t=5.1 µs for panels (a) and (b), respectively, where high-frequency noise has been suppressed by utilizing a Gaussian smoothing procedure.

Fig. 5
Fig. 5

Dependence of measured optical rotation on sample number density. The optical rotation of (1S, 5S)-(-)-α-pinene (expressed in units of mdeg dm-1) is plotted as a function of sample pressure, which, in turn, is directly proportional to the number density of the target species. The filled symbols represent the results of individual CRDP measurements performed at 355 nm with the corresponding error bars indicating estimated two-standard-deviation confidence limits. The solid line follows from a linear least-squares regression analysis that yields a slope of (-1.401±0.076)×10-3 deg dm-1 Torr-1 and an ordinate intercept of (-0.020±0.076)×10-5 deg dm-1 (one-standard-deviation uncertainties).

Tables (2)

Tables Icon

Table 1 Results of Specific Rotation Measurementsa

Tables Icon

Table 2 Influence of Retardation Errors on Specific Rotation Measurementsa

Equations (42)

Equations on this page are rendered with MathJax. Learn more.

Pf=(TnTn-1  T2T1)Pi=TtotPi,
Mmir(R)=R1000010000-10000-1,
Jmir(R)=R-1001.
Mret(θ, δ)=10000cos2 2θ+sin2 2θ cos δcos 2θ sin 2θ(1-cos δ)-sin 2θ sin δ0cos 2θ sin 2θ(1-cos δ)sin2 2θ+cos2 2θ cos δcos 2θ sin δ0sin 2θ sin δ-cos 2θ sin δcos δ,
Jret(θ, δ)=exp(iδ/2)cos2 θ+exp(-iδ/2)sin2 θi sin(δ/2)sin 2θi sin(δ/2)sin 2θexp(-iδ/2)cos2 θ+exp(iδ/2)sin2 θ.
Mlp(θ)=12 1cos 2θsin 2θ0cos 2θcos2 2θsin 2θ cos 2θ0sin 2θsin 2θ cos 2θsin2 2θ00000,
Jlp(θ)=cos2 θcos θ sin θcos θ sin θsin2 θ.
Mcb(ϕl)=10000cos 2ϕl-sin 2ϕl00sin 2ϕlcos 2ϕl00001,
Jcb(ϕl)=cos ϕl-sin ϕlsin ϕlcos ϕl,
Mcd(L, Δ l)=exp(-L)×coshΔ l200sinhΔ l201000010sinhΔ l200coshΔ l2,
Jcd(L, Δ l)=exp(-L/2)×coshΔ l4i sinhΔ l4-i sinhΔ l4coshΔ l4,
Tcd(L, Δ L)Tcb(ϕL)Tmir(R)
×Tcd(L, Δ L)Tcb(ϕL)Tmir(R)
=Tmir(R)Tcd(2L, 0)Tmir(R)=(R exp[-L])σ I,
Tcd(L, Δ l)Tcb(ϕl)Tret(-π/4, π/4)Tmir(R)Tret(π/4, π/4)×Tcd(L, Δ l)Tcb(ϕl)Tret(-(π/4-α), π/4)
×Tmir(R)Tret(π/4-α, π/4),
Tcd(d, Δ d)Tcb(ϕd)Tmir(R)Tcd(d, Δ d)Tcb(ϕd)
=Tcd(d, 0)Tmir(R)Tcd(d, 0)=exp(-d)σ Tmir(R).
MCRDP(N)=R2N exp-N+122L×cosh ξN00sinh ξN0cos ϑN-sin ϑN00sin ϑNcos ϑN0sinh ξN00cosh ξN,
JCRDP(N)=RN exp-N+12Lcos ψN-sin ψNsin ψNcos ψN,
Tlp(γ)Tret(-π/4, π/2)Tret(π/4-α, π/2)TCRDP(N)Pi,
I0,=R2N cos22N+12αα=0R2N,
I0,=R2N sin22N+12αα=00,
I=12R2N exp-N+122LcoshN+12Δl+cos4N+12(α+ϕl)Δ=0R2N×exp-N+122Lcos22N+12(α+ϕl),
I=12R2N exp-N+122LcoshN+12Δl-cos4N+12(α+ϕl)Δ=0R2N×exp-N+122Lsin22N+12(α+ϕl),
Δω=ω-ω0=(α+ϕl)c/L-αc/L=ϕc(l/L),
IIlcp=12R2N exp-N+124d×exp-N+122ll,
IIrcp=12R2N exp-N+124d×exp-N+122rl,
Pi=PX+Punp=1100+a1000=1+a100.
I=12R2N exp-N+122L(1+a)×coshN+12Δl+cos4N+12×(α+ϕl)Δ=0R2N exp-N+122L×a2+cos22N+12(α+ϕl),
I=12R2N exp-N+122L(1+a)×coshN+12Δl-cos4N+12×(α+ϕl)Δ=0R2N exp-N+122L×a2+sin22N+12(α+ϕl),
IIlcp=12(1+a)R2N exp-N+124d×exp-N+122ll,
IIrcp=12(1+a)R2N exp-N+124d×exp-N+122rl.
Pi=12 b+2-b-i(b-2-b),
I=12R2N exp-N+122Lexp-N+12Δl+b sinhN+12Δl+b(2-b)×cos4N+12(α+ϕl)Δ=0R2N×exp-N+122L1-b(2-b)2+b(2-b) cos22N+12(α+ϕl),
I=12R2N exp-N+122L×exp-N+12Δl+b sinhN+12Δl-b(2-b) cos4N+12×(α+ϕl)Δ=0R2N×exp-N+122L1-b(2-b)2+b(2-b) sin22N+12(α+ϕl).
IIlcp=12bR2N exp-N+124d×exp-N+122ll,
IIrcp=1-b2R2N exp-N+124d×exp-N+122rl.
I0,=R2N cos2N+12η,
I0,=R2N sin2N+12η.
I(t)=A exp(-t/τ)[B+sin2(ωt+ς)],
[α]λT=ϕC,

Metrics