<s>
Surface	B-Algorithm
hopping	I-Algorithm
is	O
a	O
mixed	O
quantum-classical	O
technique	O
that	O
incorporates	O
quantum	O
mechanical	O
effects	O
into	O
molecular	O
dynamics	O
simulations	O
.	O
</s>
<s>
Surface	B-Algorithm
hopping	I-Algorithm
partially	O
incorporates	O
the	O
non-adiabatic	O
effects	O
by	O
including	O
excited	O
adiabatic	O
surfaces	O
in	O
the	O
calculations	O
,	O
and	O
allowing	O
for	O
'	O
hops	O
 '	O
between	O
these	O
surfaces	O
,	O
subject	O
to	O
certain	O
criteria	O
.	O
</s>
<s>
Surface	B-Algorithm
hopping	I-Algorithm
accounts	O
for	O
these	O
limitations	O
by	O
propagating	O
an	O
ensemble	O
of	O
trajectories	O
,	O
each	O
one	O
of	O
them	O
on	O
a	O
single	O
adiabatic	O
surface	O
at	O
any	O
given	O
time	O
.	O
</s>
<s>
This	O
effect	O
is	O
incorporated	O
in	O
the	O
surface	B-Algorithm
hopping	I-Algorithm
algorithm	O
by	O
considering	O
the	O
wavefunction	O
of	O
the	O
quantum	O
degrees	O
of	O
freedom	O
at	O
time	O
t	O
as	O
an	O
expansion	O
in	O
the	O
adiabatic	O
basis	O
:	O
</s>
<s>
Surface	B-Algorithm
hopping	I-Algorithm
can	O
develop	O
nonphysical	O
coherences	O
between	O
the	O
quantum	O
coefficients	O
over	O
large	O
time	O
which	O
can	O
degrade	O
the	O
quality	O
of	O
the	O
calculations	O
,	O
at	O
times	O
leading	O
the	O
incorrect	O
scaling	O
for	O
Marcus	O
theory	O
.	O
</s>
<s>
In	O
practice	O
,	O
surface	B-Algorithm
hopping	I-Algorithm
is	O
computationally	O
feasible	O
only	O
for	O
a	O
limited	O
number	O
of	O
quantum	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
Most	O
of	O
the	O
formal	O
critique	O
of	O
the	O
surface	B-Algorithm
hopping	I-Algorithm
method	O
comes	O
from	O
the	O
unnatural	O
separation	O
of	O
classical	O
and	O
quantum	O
degrees	O
of	O
freedom	O
.	O
</s>
