Quantum Mechanical Insights into Biological Processes at the Electronic Level - Computational Modeling of Biological Systems - page 158

The overlap, right-acting time derivative, and Hamiltonian matrix elements in
this equation are:

D j J ˇ ˇ ˇ k J E ı JK

S JK
jk

D (52)

@t K ı JK

D j J ˇ ˇ ˇ

@ k

S JK
jk

D (53)

D j J ˇ ˇ ˇ H ˇ ˇ ˇ k K E

H JK
jk

D

(54)

_
H here is the full molecular Hamiltonian operator including the nuclear ki-
netic energy, the electronic PES, and nonadiabatic coupling terms. The electronic
Schr odinger equation is solved simultaneously with the nuclear dynamics to obtain
the PESs and couplings. AIMS on a small fragment can be coupled to purely
classical treatment of a large biological molecule surrounding the fragment, i.e.,
in QM/MM.
In general, nonadiabatic dynamics is computationally expensive, algorithmically
complex, but unavoidable for certain kinds of problems in biomolecular simulations.
It is important to be able to recognize when nonadiabatic dynamics would play a
role in a process. First of all, of course, processes involving excited electronic states
are likely candidates. Even fluorescing systems may exhibit excited state population
leaks through nonradiative internal conversion. Also, in principle, any time a system
crosses an activation barrier, chances are that at the transition state the two surfaces
come close enough for nonadiabatic coupling to become significant. A quick check
for the adiabaticity of the process is to run a CASSCF calculation and assess the
contribution of different states to the CAS expansion.

5.2 Examples of Applications

There are myriads of reported dynamics studies, especially employing ab initio
classical adiabatic dynamics. Here, we will highlight some exciting studies that
employ more complicated simulation engines, and account for nuclear quantum
effects, or go beyond the BAO.
QM/MM adiabatic dynamics simulations were performed on the thymine dimer
radical anion splitting in the photoactivated self-repair process in DNA [ 39 ]. The
simulations were done in explicit water. The QM region was treated with DFT, and
the MM region was treated with the AMBER force field. The calculations revealed
that the upper-bound of the free energy barrier to this process is 2.5 kcal/mol.
The mechanism was found to be asynchronous, with one bond in the dimer
breaking earlier in the process (Fig. 16 ). This work, along with experimental studies
contributed to the general appreciation of the general stability and ability to self-
repair of the natural DNA structure.