PMID- 26156465
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20150914
LR  - 20150709
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 143
IP  - 1
DP  - 2015 Jul 7
TI  - Wave packet propagation across barriers by semiclassical initial value methods.
PG  - 014107
LID - 10.1063/1.4923221 [doi]
AB  - Semiclassical initial value representation (IVR) formulas for the propagator have 
      difficulty describing tunneling through barriers. A key reason is that these 
      formulas do not automatically reduce, in the classical limit, to the version of 
      the Van Vleck-Gutzwiller (VVG) propagator required to treat barrier tunneling, 
      which involves trajectories that have complex initial conditions and that follow 
      paths in complex time. In this work, a simple IVR expression, that has the 
      correct tunneling form in the classical limit, is derived for the propagator in 
      the case of one-dimensional barrier transmission. Similarly, an IVR formula, that 
      reduces to the Generalized Gaussian Wave Packet Dynamics (GGWPD) expression [D. 
      Huber, E. J. Heller, and R. Littlejohn, J. Chem. Phys. 89, 2003 (1988)] in the 
      classical limit, is derived for the transmitted wave packet. Uniform 
      semiclassical versions of the IVR formulas are presented and simplified 
      expressions in terms of real trajectories and WKB penetration factors are 
      described. Numerical tests show that the uniform IVR treatment gives good results 
      for wave packet transmission through the Eckart and Gaussian barriers in all 
      cases examined. In contrast, even when applied with the proper complex 
      trajectories, the VVG and GGWPD treatments are inaccurate when the mean energy of 
      the wave packet is near the classical transmission threshold. The IVR expressions 
      for the propagator and wave packet are cast as contour integrals in the complex 
      space of initial conditions and these are generalized to potentially allow 
      treatment of a larger variety of systems. A steepest descent analysis of the 
      contour integral formula for the wave packet in the present cases confirms its 
      relationship to the GGWPD method, verifies its semiclassical validity, and 
      explains results of numerical calculations.
FAU - Petersen, Jakob
AU  - Petersen J
AD  - Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, 
      Israel.
FAU - Kay, Kenneth G
AU  - Kay KG
AD  - Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
EDAT- 2015/07/15 06:00
MHDA- 2015/07/15 06:01
CRDT- 2015/07/10 06:00
PHST- 2015/07/10 06:00 [entrez]
PHST- 2015/07/15 06:00 [pubmed]
PHST- 2015/07/15 06:01 [medline]
AID - 10.1063/1.4923221 [doi]
PST - ppublish
SO  - J Chem Phys. 2015 Jul 7;143(1):014107. doi: 10.1063/1.4923221.