Quantum Theory

Katharine Hunt

University Distinguished Professor

17A CEM

517-353-1152


Research webpage


Primary Research Area

Theoretical and Computational (Th)

Other Area(s) of Interest

Biological (Bi)

Chemical Physics (CP)

Material (Ma)

Physical (Ph)

Research

(Research Description PDF)

Quantum systems in time-dependent fields – derived new theoretical results for transition probabilities in quantum systems in time-dependent electromagnetic fields. Beginning with Dirac’s work, the probability that a time-dependent perturbation induces a transition to an excited state has been expressed in terms of the norm-square of the coefficient ck(t) for the excited state | k0 〉 of the original unperturbed Hamiltonian H0. Landau and Lifshitz separated ck(t) into an adiabatic term ak(t) that follows the adiabatic theorem of Born and Fock, and a nonadiabatic term bk(t) that depends on the time-derivative of the perturbation up to time t; they stated that the transition probability is given by the norm-square of bk(t). Our work reinforces the claim of Landau and Lifshitz and goes beyond their results. We proved that the energy separates into 1) the energy of the adiabatically perturbed initial state and 2) the sum over excited states of | bk(t) |2 times the transition energy (Ek – E0), corrected for the perturbation. This is due to the orthogonality of the eigenfunctions of the perturbed Hamiltonian H0 + H′(t); but since we have bk(t), we can give accurate numerical results for the transition probabilities and the nonadiabatic term in the energy. In our more general analysis, a perturbative framework is not needed. We proved that the power absorbed by a molecule from an electromagnetic field is equal to the time-derivative of the nonadiabatic term in the energy; and we note that vibrational wave packets associated with ak(t) and bk(t) evolve on different electronic potential energy surfaces. Our results for transition probabilities differ dramatically from the results of Dirac’s theory, during short perturbing pulses with frequencies that are off-resonant from the transition frequency. For a cosine wave of frequency ω in a Gaussian envelope, | bk(t) |2 is larger than | ck(t) |2 when ω > ωk0, the transition frequency to state k; while the opposite is true when ω < ωk0. These results are independent of the phase of the oscillating wave relative to the peak of the Gaussian envelope. For a perturbing pulse that rises to a level plateau, | bk(t)|2 is constant while the perturbation is constant, but | ck(t) |2 continues to oscillate.

The standard Hamiltonian for a molecule in an electromagnetic field includes an arbitrary gauge potential that is introduced when the vector and scalar potentials of an applied field are altered by a gauge transformation, which leaves the electric and magnetic fields themselves unchanged. The gauge-dependence of the standard molecular Hamiltonian has made it difficult to determine the energy of a molecule in an applied electric field. By analyzing the full Hamiltonian for the molecule and the field, we have found a gauge-dependent term that is normally assigned to the field Hamiltonian, but that exactly cancels the gauge-dependent term in the molecular Hamiltonian. This resolves the quandary and provides a firm footing for future research where accurate energies are needed for molecules in applied fields.

Collision-induced spectroscopic processes – Spectroscopic processes that are forbidden for single molecules are observed in dense gases and liquids, because the electronic charge distorts during molecular collisions. Our work has focused on collision-induced absorption in the IR by H2 gas, H2/He mixtures, N2 gas and O2 gas, with applications in atmospheric profiling, including atmospheres of cool white dwarf stars. We calculate the total dipole moments ab initio and then express them in spherical-tensor form for subsequent line-shape calculations. This work has been carried out in collaboration with Lothar Frommhold and Martin Abel (University of Texas, Austin), Magnus Gustafsson (Luleå, Sweden), and Tijs Karman, Gerrit Groenenboom, and Ad van der Avoird (Nijmegen, the Netherlands).

Manipulation of biomolecules with light – We are also studying the dynamics of fluorescently labeled DNA strands or protein/ DNA complexes in laser fields. Fluorescently labeled DNA strands and proteins fall into a size range where a new approach is needed to calculate the laser-induced forces. This project has involved collaboration with Bob Cukier’s research group, benefiting from their expertise in molecular dynamics simulations. Our current work focuses on DNA strands labeled with an oxazole yellow dye; we plan work on dye-labeled small interfering RNA segments.

Nonadiabatic transition probabilities | bk(t) |2 vs. Dirac's forms for a quantum system perturbed by a cosine wave of frequency ω = 10 (arbitrary units) enclosed in a Gaussian envelope, for transitions with ωk0 = 8, 10, or 12. Results from A. Mandal and K. L. C. Hunt, J. Chem. Phys. 2018, 148, 194107.
Nonadiabatic transition probabilities | bk(t) |2 vs. Dirac’s forms for a quantum system perturbed by a cosine wave of frequency ω = 10 (arbitrary units) enclosed in a Gaussian envelope, for transitions with ωk0 = 8, 10, or 12. Results from A. Mandal and K. L. C. Hunt, J. Chem. Phys. 2018, 148, 194107.

 

Selected Publications

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi’s golden rule forms, Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2018, 148, 194107.

Response to "Comment on 'Gauge-invariant expectation value of the energy of a molecule in an electromagnetic field' ", Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2016, 145, 147103.

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field, Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2016, 144, 044109.

Non-adiabatic current densities, transitions, and power absorbed by a molecule in a time-dependent electromagnetic field, Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2015, 143, 034102.

Quantum mechanical calculation of the collision-induced absorption spectra of N2-N2 with anisotropic interactions, Tijs Karman, Evangelos Miliordos, Katharine L. C. Hunt, Gerrit C. Groenenboom, and Ad van der Avoird, J. Chem. Phys. 2015, 142, 084306.

Ground and excited states of vanadium hydroxide isomers and their cations, VOH0,+ and HVO0,+, Evangelos Miliordos, James F. Harrison, and Katharine L. C. Hunt, J. Chem. Phys. 2013, 138, 114305.

Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation, Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2012, 137, 164109.

Interaction-induced dipoles of hydrogen molecules colliding with helium atoms:  A new ab initio dipole surface for high-temperature applications, Xiaoping Li, Anirban Mandal, Evangelos Miliordos, and Katharine L. C. Hunt, J. Chem. Phys. 2012, 136, 044320.

Infrared absorption by collisional H2-He complexes at temperatures up to 9,000 K and frequencies from 0 to 20,000 cm–1, Martin Abel, Lothar Frommhold, Xiaoping Li, and Katharine L. C. Hunt, J. Chem. Phys. 2012, 136, 044319.

News

Awards/Honors

2001 Senior Faculty Award Sigma Xi Honor Society (Michigan State University)
2000 - 2002 Member Midwest Chemistry Chairs’ Group
1999 Panelist, SBIR Program, Chemistry Division National Science Foundation
1998 - 2003 Selection Committee Member (appointed by British Consul General) Marshall Scholarship Program, Midwest Region
1998 Member National Science Foundation (Committee of Visitors (triennial review of division), Chemistry Division)
1998 - 2002 Chairperson Michigan State University (Department of Chemistry)
1997 Panelist, SBIR Program, Chemistry Division National Science Foundation
1995 - 1997 Councilor for Physical Chemistry American Chemical Society
1993 Panelist, Chemistry 3 (Physical Chemistry), Panel to recommend funding for proposals from scientists in the former Soviet Union International Science Foundation
1992 Panelist, Graduate Research Traineeship Program, Panel to evaluate departmental proposals, Chemistry Division National Science Foundation
1992 Member Midwest Theoretical Chemistry Conference XXV (Conference Organizing Committee)
1992 - 2004 University Distinguished Professor Michigan State University
1991 Junior Faculty Award Sigma Xi Honor Society (Michigan State University)
1991 Panelist, Presidential Young Investigator Award Review Panel, Chemistry Division National Science Foundation
1986 - 1987 Member American Chemical Society (Michigan State University Local Section)
1982 Session Chairperson Fifteenth Annual Midwest Theoretical Chemistry Conference
1978 Ph.D. University of Cambridge, England
1978 - 1979 NSF National Needs Postdoctoral Fellowship National Science Foundation
1975 - 1978 Danforth Fellowship
1975 Bachelor of Science Michigan State University
1975 - 1978 Marshall Scholarship
1971 - 1975 National Merit Scholar
1971 - 1975 Alumni Distinguished Scholarship Michigan State University (Alumni Association)
Board of Trustees Award Michigan State University
Phi Beta Kappa Phi Beta Kappa
Phi Kappa Phi Phi Kappa Phi
Chairperson Michigan State University (Department of Chemistry)