Biology Reference

In-Depth Information

X

Þ¼
@

E
KS

@

ij
L
ij
@

M
I
R
I
ð

t

R
I
þ

R
I
hf
i
jf
j
i

@

X

j
L
ij
jf
j
i:

Þ¼
d

E
KS

dhf
i
j
þ

mf
i
ð

t

This allows evolving the electronic and nuclear system at the same time: after

the full electronic optimization at the starting nuclear step, there is no need to re-

optimize the electronic system, which is simply evolved with a single electronic

calculation for each nuclear step. Since the electronic part is the bottleneck of the

calculation, this generally allows a save in computational cost. The electron system

dynamics is driven by the value of the fictitious electron mass. The exact BO

approximation is recovered if

0, but this would need an infinitesimally small

timestep for the evolution of the whole system. Exact BO or CP can be used for the

step (a) and to generate a long trajectory for step (b).

Once a dynamical trajectory of the system is available, the vibrational spectrum

can be obtained by the Fourier transform (FT) of the velocity self-correlation

function [point (c)] [
33
]:

m ¼

S

ðoÞ¼

FT

½

c

ðtÞ ¼

FT

½h

v

ð

t

Þ

v

ð

t

þ tÞi:

S
(

) will have resonances (peaks) at the frequencies corresponding to the vibra-

tional modes of the system, whose height will be larger for the modes that have

larger superposition with the starting displacement generated by the perturbation,

i.e., the spectrum will reflect the external perturbation. The width of the peaks

includes several effects. One is the necessarily finite length of the simulation, which

implies a numerical enlargement of the peaks in the Fourier space. This adds up to

the physical broadening due to anharmocity that implies also interactions between

the modes and displacement of the frequencies from those evaluated within the

harmonic approach. In addition if the dynamics is evaluated within the CP scheme

an additional softening of the frequencies of about 1-3% is due to the fictitious

electron mass

o

that has the effect of slowing down the dynamics [
34
].

A schematic representation of the IR, Raman, and Resonance Raman processes

is reported in Fig.
1c
, together with the corresponding spectra of the same mole-

cule, i.e., the GFP model chromophore HDBI. The difference between IR and

Raman spectra is apparent: the selection rules for the two processes are very

different, thus the Raman active modes in this molecule are much less than the IR

active modes. The difference between Raman and Resonance Raman spectra

are less evident in this kind of molecule. They are more evident, e.g., when the

chromophore is in the protein, where the ResonanceRamantechniqueisableto

select the modes of the chromophore, related to the electronic excitation, from

those of the protein.

m

Search WWH ::

Custom Search