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<div class="moz-cite-prefix">On 13/11/13 15:58, Qinghua Cao wrote:<br>
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<div dir="ltr">Hey, everyone,<br>
<br>
I'm working on the vertical transition energy in two ways:<br>
<br>
1. a state-averaged CASSCF calculation of all states in one
calculation (i also tried to include different numbers of
states, and the result may vary significantly with the number of
state!!)<br>
2. CASSCF calculations of ground state and excited states
individually<br>
<br>
it turns out that the transition energies are very different
from the above ways, and they could differ as large as 1 eV.
Moreover, including 10 states and 20 states in a state-averaged
CASSCF calculation also lead to very different results.<br>
<br>
I don't know whether this ever occurs to any of you. If so, are
there any reasons or explanations for this? Which is the most
reliable way to calculate the energy?<br>
<br>
Thanks in advance!<br>
<br>
Qinghua<br>
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<br>
<br>
Dear Qinghua,<br>
as no one more competent than me has yet commented on your question,
I'll give you my opinion on the matter. <br>
It is to be expected that vertical excitation energies of
state-averaged CASSCF differ depending on the number of states
included (and on the active space used); that said, a difference of
1 eV looks indeed quite large, but not knowing which system you are
studying it is difficult to comment on that. I also think it is
impossible to blindly say which strategy gives the `best' (=closest
to experiment) excitation energies. <br>
<br>
Leaving aside numerical problems of incorrect convergence to local
minima, the reason for these difference is due to the orbital
optimization. It seems to be the case that for your system and for
the active space you are using (for example, the `full valence' one
used by molpro by default) the electronic states you are considering
have rather different optimal orbitals.<br>
<br>
As an idealized example, suppose there are three electronic states,
a ground state G and two excited ones A and B, and that when you do
CASSCF for each state one state at a time you get orbitals O1 for G,
again O1 for A and O2 for B. In other words G and A have the same
optimal CASSCF orbitals while B's optimal orbitals are different.<br>
When you do a state-average CASSCF calculation with all three states
you get orbitals which are intermediate between O1 and O2 (closer to
O1 if you use standard weights as two states `want' O1 and only one
O2); the absolute energies of all states will be increased with
respect to the one-at-a-time values, but presumably the energy of B
will be increased more than G and A because the intermediate
orbitals are less optimal for that state.<br>
If you do a calculation with G+B the orbitals will be `half way'
between O1 and O2, and with respect to the three-state-averaged
calculation G will be higher in energy and B lower, and as a
consequence E(B)-E(A) [G+A+B state-averaged] > E(B)-E(A) [G+B
state-averaged].<br>
<br>
In your case where you have 20 states (each with different optimal
orbitals) the situation is more complicated but the idea is the
same. If the optimal orbitals are very different for different
states you'll see large differences depending on which states are
included in the state-averaging.<br>
A possibles, straightforward suggestion is to try a different
reference space (e.g., larger) to see if it reduces the differences
between state-averaged and two-states-at-a-time excitation energies.
<br>
On a more complicated level one could also try to group together
states which have similar optimal orbitals and get the relative
energies within each group, and then carefully perform
two-state-averaged calculations to link the networks (I don't know
if this strategy has been used in the literature).<br>
<br>
In any case one should not expect CASSCF energies to give very
accurate (e.g., accurate to ~0.25 eV or so) excitation energies
because of the lack of dynamical electron correlation. You should
also try a post-CASSCF method (RS2, MRCI, CIPT2) and see what
difference it makes to your results.<br>
<br>
I hope it helps.<br>
<br>
Kind regards, <br>
Lorenzo<br>
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