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)

Figure 1. Dirac's transition probability (top) and nonadiabatic transition probability (bottom), for a quantum system in a pulse with a plateau lasting 10 units of time. Different colors correspond to different rates of turning on the perturbation. A. Mandal and K. L. C. Hunt, J. Chem. Phys. 2018, 149, 204110.
Figure 1. Dirac’s transition probability (top) and
nonadiabatic transition probability (bottom), for a
quantum system in a pulse with a plateau lasting 10
units of time. Different colors correspond to different
rates of turning on the perturbation. A. Mandal
and K. L. C. Hunt, J. Chem. Phys. 2018, 149, 204110.

Quantum systems in time-dependent fields — We have derived new theoretical results for transition probabilities in quantum systems in timedependent electromagnetic fields. These results challenge Dirac’s expression for the transition probability, which depends on the norm-square of the coefficient ck(t) for the excited state | k0 〉 of the original unperturbed Hamiltonian H0, in the time-dependent wave function. By integrating by parts, 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. The adiabatic term describes the adjustment of the initial state to the perturbation without actual transitions, while the transition probability is given by the norm-square of bk(t). Our work reinforces this statement and goes beyond the results of Landau and Lifshitz. We proved that the energy separates into adiabatic and nonadiabatic terms. The nonadiabatic term in the energy is given by the sum over excited states of | bk(t) |2 times the transition energy (Ek – E0), corrected for the perturbation. 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. Further, the vibrational wave packets associated with ak(t) and bk(t) evolve on different electronic potential energy surfaces. Our results for transition probabilities differ significantly 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. The differences are also quite stark for a perturbing pulse that rises to a level plateau, and later falls off. While the perturbation is constant, the nonadiabatic transition probability is constant as required physically, since a static perturbation cannot induce transitions; in contrast Dirac’s form of the transition probability continues to oscillate while the perturbation is constant, as shown in Figure 1.

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/H and H2/He mixtures, N2 gas and O2 gas, with applications in astrophysics and in atmospheric profiling. Interaction-induced absorption affects the radiative profiles of gases in star-forming nebulae; very old, very cool white dwarf stars; the outer planets and exoplanets that are termed “hot Jupiters” and “warm Neptunes,” and the atmospheres of satellites of the outer planets. My research group calculates the total dipole moments ab initio and then expresses the results in spherical-tensor form for subsequent line-shape calculations. Dipole surfaces for H2-H are shown in Figure 2. This research area involves collaborations with Lothar Frommhold and Martin Abel (University of Texas, Austin), Magnus Gustafsson (Luleå, Sweden), Tijs Karman, Gerrit Groenenboom, and Ad van der Avoird (Nijmegen, the Netherlands), and Richard Dawes (Missouri University of Science and Technology).

Figure 2. Cartesian components of the dipole of H2-H, figures from AIP Scilight 2019, 220002-1 by Adam Liebendorfer, a report of work by H.-K. Lee, X. Li, E. Miliordos, and K. L. C. Hunt, J. Chem. Phys. 2019, 150, 204307.
Figure 2. Cartesian
components of the
dipole of H2-H, figures
from AIP Scilight 2019,
220002-1 by Adam
Liebendorfer, a report
of work by H.-K. Lee, X.
Li, E. Miliordos, and K. L.
C. Hunt, J. Chem. Phys.
2019, 150, 204307.

 

Selected Publications

The interaction-induced dipole of H2-H: New ab initio results and spherical tensor analysis, Hua-Kuang Lee, Xiaoping Li, Evangelos Miliordos, and Katharine L. C. Hunt, J. Chem. Phys. 2019, 150, 204307, Featured Article.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state, Evangelos Miliordos and Katharine L. C. Hunt, J. Chem. Phys. 2018, 149, 234103.

Nonadiabatic transition probabilities in a time-dependent Gaussian pulse or plateau pulse: Toward experimental tests of the differences from Dirac’s transition probabilities, Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2018, 149, 204110, Editor’s Pick.

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

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 timedependent perturbation, Anirban Mandal and Katharine L. C. Hunt, J. Chem. Phys. 2012, 137, 164109.

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)