problems in choosing nstates in SA-CASSCF calculation and MS-MR-CASPT2 calculation

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Bin Han

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Jun 6, 2022, 8:54:37 AM6/6/22
to molpro-user
Dear all,

I am a beginner of doing SA-CASSCF and MS-MR-CASPT2 calculations, and recently I want to study the f-d transtion of  a molecule centering the Eu2+ and surrounding the ligand. The Eu2+ ([Xe] 4f7) has 7 4f electrons and I want to do SA-CASSCF calculation to get the excited state energy, so I choose 7 4f orbitals and 5 5d orbitals as my active space using AVAS. And I choose nstate=36 to include the ground state and all single excitation states. But the calculation result shows that the lowest 14 states are 4f^6 5d^1 ones, the 4f^7 state is only the 15th, and I have tried different number of states range from 1 to 36, and I plot the energy of each state in my each calculation with different 'nstates', this is my input,

***,caspt2
memory,1000,m

direct
gprint,basis,orbital,civector

symmetry,nosym
geomtyp=xyz
geometry=R-MeN8-EuI2.xyz

***,caspt2
memory,1000,m

direct
gprint,basis,orbital,civector

symmetry,nosym
geomtyp=xyz
geometry=R-MeN8-EuI2.xyz

set,charge=2
include,svp.incl

cfit,basis=qzvpp/jkfit
{df-hf
occ,147
closed,140
wf,287,1,7}
{avas
start,2100.2
orbital,2110.2
center,81,5d,4f}

nstate=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
i=0
do istate=1,#nstate
i=i+1
state(i)=nstate(istate)

{df-multi
closed,140
occ,152
wf,287,1,7
start,2110.2
state,state(i)
canonical}
multi(i)=energy(2)-energy(1)

enddo
{table,state,multi
head,state,multi}

the energy is ploted in <nstates.png>(see attachment), I choose different nstate range from 1 to 36, and the x-axis is the each state in each nstate calculation, y-axis is the energy of the state (for example, if nstate=20, the SA-CASSCF calculation will give the energy of 20 states, the x and y axis is the state and the state's energy accordingly).


I am puzzled about the result, when the nstates < 16 the first CASSCF sate is the 4f^7 state and the energy difference between the first state and the second state become lower  ( 0.088hartree to 0.007 hartree) when nstates increase. But when nstates ≥ 16 , the first 14 states become 4f^6 5d^1 ones, the 4f^7 state is only the 15th. and there is a energy gap (~0.055 hartree) between 14th and 16th state. The experimental value of the f-d transition in my molecule is ~0.1 hartree. I am so confused about the results.

I know the basis set may be a problem, so I have changed to another basis set, cc-pVQZ-DK3 for Eu atom and cc-pVTZ for other atoms, and this is my input,

***,caspt2
memory,2000,m

direct
gprint,basis,orbital,civector

symmetry,nosym
geomtyp=xyz
geometry=R-MeN8-EuI2.xyz

set,charge=2

basis=cc-pVTZ,Eu=cc-pVQZ-DK3

{hf
closed,154
occ,161
wf,315,1,7
avas
center,81,4f,5d}

{multi,SO-SCI
closed,154
occ,166
wf,315,1,7
state,36
canonical}

However, I get a more strange result, in <pvdz.png>(see attachment)

the first state is  4f^7 state but the energy difference between first state and second state is 0.28 hartree which is far away with the experimental value (~0.1 hartree), and also, there is a energy gap between 15th and 16th state while they are all 4f^6 5d^1 states.

I have several questions and conjectures about this,
1) The total energy seems not decrease while including more states, it seems that the high energy state diffuse to every other state, which changes the ground state greatly, and make the result unphysical. But I can't understand this in the algorithm of CASSCF. I really hope you can give me some advice.
2) I guess the energy gap in the middle may come from the ligand field? But I can't figure out why it is in the 15th state, maybe the 5 5d orbitals is divided into 2 near degenerate low energy orbitals and 3 near degenerate high energy orbitals due to energy splitting , so there are 15 low energy state including the ground state?
3) I have no idea about why the reault using cc-pVQZ-DK3 for Eu atom and cc-pVTZ for other atoms will be so strange. It is my first time to use the relativistic correlation consistent basis sets, may be this error comes from the unsuitable basis set.
4) Can MS-MR-CASPT2  deal with such a large molecule? And I don't know how many states I should use in my next MS-MR-CASPT2 calculation, I have done some tests in single atom Eu2+, I find the influence of the number of states on energy is huge, so I want to ask if it is better to use more states?

Best regards,
Bin
R-MeN8-EuI2_36.out
R-MeN8-EuI2_pvqz.out
pvqz.png
R-MeN8-EuI2.xyz
svp.incl
R-MeN8-EuI2.out
nstates.png

Peterson, Kirk

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Jun 6, 2022, 11:31:21 AM6/6/22
to Bin Han, molpro-user

Hi,

 

I can comment on the 2nd set of calculations. While you chose a relativistically contracted basis set for Eu,  you didn't actually turn on the relativistic Hamiltonian. Please use cc-pVTZ-DK for the light atoms and specify dkho=3 before your first energy calculation.

 

regards,

 

-Kirk

 

From: <molpr...@googlegroups.com> on behalf of Bin Han <ice86...@gmail.com>
Date: Monday, June 6, 2022 at 5:54 AM
To: molpro-user <molpr...@googlegroups.com>
Subject: [molpro-user] problems in choosing nstates in SA-CASSCF calculation and MS-MR-CASPT2 calculation

 

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Bin Han

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Jul 4, 2022, 10:31:19 AM7/4/22
to molpro-user
Dear all,

I have found that if I change the weight of each state, the SA-CASSCF result seems right. My first try is to assign equal weight for ground state and the total other 35 single excited states (both for SA-CASSCF and MS-MR-CASPT2), but I find it is hard to use all orbitals in MS-MR-CASPT2, I think the dynamic correlation between f otbitals and Inner orbitals may be very small, so I freeze all occupied orbitals except the 7 f-orbitals, this is the input:

 {df-multi
 MAXITER,400
 closed,140
 occ,152
 wf,287,1,7
 start,2110.2
 state,36;WEIGHT,1,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143
 canonical}

 {df-rs2c,shift=0.1,IPEA=0.3,mix=36,xms=1,noprop,maxit=100,maxiti=400
 closed,140
 occ,152
 core,140
 wf,287,1,7
 state,36;WEIGHT,1,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143,0.02857143}

the SA-CASSCF result reveals the first state is  4f^7 state and the others are excited state, and the energy gap is 0.095 hartree which is relatively closed to the experimental value (~0.11 hartree), but the energy gap in MS-MR-CASPT2 result is 0.075 hartree which is not right. And I also calculate only 2 state, although it take far more number of iterations to converge, but the reasult seems more reasonable. SA-CASSCF reveals the 2 states are 4f^7 and 4f^6 5d^1, the energy gap is 0.088 hartree in SA-CASSCF and 0.106 hartree in MS-MR-CASSCF which is extremely closed to the experimental value (~0.11 hartree), this is the input,

 {multi,SO_SCI
 MAXITER,400
 closed,140
 occ,152
 wf,287,1,7
 start,2110.2
 state,2
 canonical}

 {rs2c,shift=0.1,IPEA=0.3,mix=2,xms=1,maxit=100,maxiti=400
 closed,140
 occ,152
 core,140
 wf,287,1,7
 state,2}

I am not sure about those results, and I want to ask that,
1) Using only 2 states in SA-CASSCF and MS-MR-CASPT2 seems right although the number of iterations (129) to converge SA-CASSCF is far more than 36 states (14). So is it OK to use 2 states results?
2) The dynamic correlation effects in the two calculation behaves totally different which decrease energy gap 0.02 hartree in 36 states while increase 0.018 hartree in 2 states. So I guess I may make some mistakes in MS-MR-CASPT2 calculation?
3) I read the paper about the dynamically weighted MCSCF(https://doi.org/10.1063/1.1667468), I have a question that if we change the weight according to the energy gap which influence the final energy of each state, so shall this method lead the dynamic correlation effects into MCSCF calculation artificially? Will this influence the results of the next MS-MR-CASPT2 calculation?

Really hope you can give me some suggestions about this, thanks a lot.

Best regards,
Bin
R-MeN8-EuI2_2states.out
R-MeN8-EuI2_df_36states.out
svp.incl
R-MeN8-EuI2.xyz
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