Extended approximated Born-Oppenheimer equation. I. Theory

The electronic nonadiabatic coupling term: Can it be ignored in dynamic calculations?

“…To examine this assumption we derived a simple expression for the required ͑angular͒ NACTs-see Eq. ͑8͒-based on the adiabatic PESs ͑and the quantization feature 13 …”

“…3 It is now accepted that degeneracy points affect also important processes such as photosynthesis in plants 4 and photochemistry of DNA. 5 Whereas the search for the degeneracy points which are better known as conical intersections ͑or ci points͒ is always carried out with a lot of commitment and devotion [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] ͑nu-merous numerical methods are available for this purpose͒ the nonadiabatic coupling terms ͑NACTs͒ which have their origin in the BO theory are hardly ever considered. 25 It is well accepted that the NACTs are needed to carry out accurate dynamical calculations ͑transition probabilities, cross sections, rate constants, etc.͒ However, in general they are either avoided or replaced by other magnitudes.…”

Topological effects for nonsymmetrical configurations: The C2H2+ as a case study

“…͑2͒ It is well known that topological effects are formed in the vicinity of a point of degeneracy between two adjacent states ͑points of degeneracy are better known as the points of conical/parabolic intersections͒. However, two states may not be enough to form topological effects for larger regions in configuration space 17,25,27,34,35 ͑see also Ref. 33, Chaps.…”

“…1͒. We intend to show that the analytical tools developed for studying the JT multistate intersections 25,27 apply also for the nonsymmetrical multistate intersections.…”

“…[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] The two types differ also in two additional ways: ͑a͒ the BO-RT nonadiabatic coupling terms ͑NACTs͒ are formed by states of opposite symmetry and the resulting topological ͑Berry͒ phase ␣ is equal to 2 . [2][3][4]7 ͑b͒ The BO-JT NACTs are formed by states of same symmetry and the resulting JT phase ␣ is equal to ͑Refs.…”