[molpro-user] Strange Occupation Numbers for CIS Natural Orbitals
Tatiana Korona
tania at tiger.chem.uw.edu.pl
Fri Mar 1 03:21:43 GMT 2013
Dear Ben,
The CIS excited-state density matrix (DM) is a sum of three parts: the SCF
ground-state density, the CI-coefficient density (fills occupied-occupied and
virtual-virtual parts of the DM), and the contribution from the orbital
relaxation. The latter part may cause a (usually) small deviation from the
commonsense occupation numbers, because it fills the occupied-virtual (OV) and
VO parts of the DM. If only two first parts are used, the NATORB results are as
one can expect: occupation numbers .le. 2 for low-lying orbitals and two
orbitals with occupation numbers about 1, plus the rest with very small
occupation numbers. For CIS the orbital-unrelaxed properties are however
completely unreliable (see the CIS paper of Foresman et al. in JPC), so I
decided to show only results with the orbital relaxation included in my CIS
implementation. These orbital-relaxed properties are by the way the same as you
can get from the numerical differentiation of the CIS energy. If you have
access to Molpro sources, you can calculate the orbital-unrelaxed DM by
commenting
if(jtrm.eq.0)call daxpy_X(ntqgcx(1),z1,q1,1,d,1)
in cis.F at the very end of the subroutine dens1. I can also unblock this
feature with some command, if there is a need for this. In your particular case
the deviations from common sense are large, because a poor molecule you call
ethylene:-) is veeeeery deformed (e.g. one of C-C-H angles equal to 91 etc.),
and the description given by CIS is totally inadequate. I have checked that also
for the ground-state density on the MP2 level (also orbital-relaxed), you would
get 2.3 as the "occupation number" for the natural orbital 1.1.
Best wishes,
Tatiana
On Wed, 27 Feb 2013, Benjamin Levine wrote:
> Dear Molrpo Users,
> We've recently been calculating CIS natural orbitals using the command:
>
> {cis,-2,trans=2
> natorb,2150.2}
>
> and we find something very strange. For some geometries, some of the occupation numbers of the natural orbitals are greater than 2, and the occupation numbers sum to a number significantly larger than the number of electrons. I would expect CIS natural orbital occupation numbers to be well behaved (0<=n<=2), but maybe I am incorrect? I'm writing to ask if anyone else has had this experience, or if they might have any insights or explanations. Example input and partial output files for a particularly striking case are below. Thank you for your time and consideration.
>
> All the best,
> Ben
>
> --
> Benjamin G. Levine
> Assistant Professor
> Department of Chemistry
> Michigan State University
> East Lansing, MI
>
> 517-355-9715 x169
> http://levinegroup.chemistry.msu.edu
>
> Input File:
>
> memory,200,m
> gprint,civector,orbital
> nosym,noorient
> geomtyp=xyz
> angstrom
>
> geometry={
> 6
> ethylene xyz input
> C 0.0000000000 0.0000000000 0.0000000000
> C 1.4052545888 0.0000000000 0.0000000000
> H -3.0318249E-02 -0.3909261 -1.0828689362
> H -0.6231545 -0.7603594 0.4650986906
> H 1.9721052763 0.9307625 0.000000
> H 2.0425070093 -0.8726716 -0.1706819
> }
>
> basis=6-31g**
>
> {multi
> occ,8
> closed,8
> orbital,2140.2}
>
> {hf
> save,2102.2}
>
> {cis,-2,trans=2
> natorb,2150.2}
>
> put,molden,e-cas-221.molf
> ---
>
> Partial Output:
>
> ...
> States requested for CIS calculation: 2.1
> Spin symmetry: singlet
>
> Convergence thresholds: THRVAR = 1.00D-08 THRDEN = 1.00D-06
>
> Number of core orbitals: 2 ( 2 )
> Number of closed-shell orbitals: 6 ( 6 )
> Number of external orbitals: 40 ( 40 )
>
> Molecular orbitals read from record 2102.2 Type=RHF/CANONICAL (state 1.1)
>
> Number of N-1 electron functions: 6
> Number of N-2 electron functions: 0
> Number of singly external CSFs: 240
> Number of doubly external CSFs: 0
> Total number of CSFs: 241
>
> Length of J-op integral file: 0.00 MB
> Length of K-op integral file: 0.19 MB
>
> Integral transformation finished. Total CPU: 0.04 sec, npass= 1 Memory used: 0.58 MW
>
>
> CIS FOR 1 SINGLET EXCITED STATES OF SYMMETRY 1 STATES: 1
>
> Number of CSF: 240
>
>
> Iter. Vector |HC-EC| E_new-E_old Excitation energy Total energy
>
> 0 1 0.609007E-01 0.211566E-01 0.0211565984 -77.8329390544
>
> 1 1 0.104942E-01 -0.633429E-02 0.0148223093 -77.8392733435
>
> 2 1 0.215701E-02 -0.235623E-03 0.0145866862 -77.8395089666
>
> 3 1 0.594312E-03 -0.135905E-04 0.0145730957 -77.8395225571
>
> 4 1 0.125467E-03 -0.675507E-06 0.0145724202 -77.8395232326 Converged
>
> CIS-Results for state 2.1: Excitation energy 0.01457242 au 0.397 eV 3198.28 cm-1
>
> Coefficient Excitation
> 0.99267 8.1 -> 9.1
>
> Starting CIS properties program. Author: T. Korona (2006)
>
>
> 1st order properties for state 2.1, spin symmetry singlet
>
>
> Starting Coupled-perturbed Hartree-Fock, convergence threshold= 1.0D-06
>
> ITER MIC DIIS VAR VARC CPU
> 1 0 1 0.15D+00 0.21D-02 0.01
> 2 9 2 0.99D-02 0.28D-02 0.02
> 3 2 3 0.36D-03 0.39D-04 0.03
> 4 9 4 0.12D-04 0.23D-05 0.04
> 5 6 5 0.45D-06 0.57D-07 0.05
>
> CPHF convergence reached in 5 macroiterations and 26 microiterations. Accuracy: 4.5210D-07
>
> CPHF solution written to record 8501.2
>
> State 2.1 Dipole moment CIS 0.96776762 -0.60478737 -0.14580920
> State 2.1 <RR(SCF)>= 0.275381E+02 <RR(CIS)>= 0.280551E+02 <RR(CIS)>/<RR(SCF)>= 1.02
>
> Density matrix saved on record 2150.2 (density set 1)
>
> Natural orbitals
> ================
>
> Orb Occ Coefficients
>
> 1 1s 1 1s 1 1s 1 2px 1 2py 1 2pz 1 2px 1 2py 1 2pz 1 3d0
> 1 3d2- 1 3d1+ 1 3d2+ 1 3d1- 2 1s 2 1s 2 1s 2 2px 2 2py 2 2pz
> 2 2px 2 2py 2 2pz 2 3d0 2 3d2- 2 3d1+ 2 3d2+ 2 3d1- 3 1s 3 1s
> 3 2px 3 2py 3 2pz 4 1s 4 1s 4 2px 4 2py 4 2pz 5 1s 5 1s
> 5 2px 5 2py 5 2pz 6 1s 6 1s 6 2px 6 2py 6 2pz
>
> 1.1 3.5061636 -0.060854 0.131965 0.190108 -0.121394 0.361108 0.115844 -0.160893 0.384271 0.089419 -0.000724
> 0.016854 -0.014980 0.010437 -0.018479 0.010750 -0.033988 0.044585 0.022594 -0.020489 -0.291179
> -0.057646 0.062891 -0.337526 -0.002779 -0.036415 -0.004187 0.002414 -0.000503 -0.136485 -0.205417
> 0.001014 0.008204 -0.006682 0.012854 0.061103 -0.006675 0.009540 0.006406 -0.082016 -0.161725
> 0.000323 0.001634 -0.007400 0.106245 0.206417 0.000945 0.003297 -0.006341
>
> 2.1 2.0055045 0.015169 -0.029378 -0.032248 -0.076659 -0.047009 0.351827 -0.056081 -0.036683 0.160076 -0.023941
> -0.002386 0.014747 0.001802 -0.027531 -0.008956 0.041245 0.076439 0.029993 -0.096651 0.183669
> -0.014779 -0.102193 0.138544 -0.005361 0.004123 -0.023745 -0.006883 -0.000324 -0.251589 -0.272510
> -0.008044 -0.008404 -0.010089 0.151680 0.145153 0.006678 0.006217 0.004893 -0.010215 0.027782
> 0.001378 0.000636 0.003177 0.043380 0.006534 -0.001991 0.000660 0.002849
>
> 3.1 2.0010903 -0.020521 0.020410 -0.037093 0.248681 0.175746 0.079061 0.062998 0.077781 0.016937 -0.011778
> -0.004551 0.002088 0.020936 -0.012074 -0.071353 0.126963 0.143428 -0.271660 0.274653 0.114874
> -0.117870 0.075559 0.057360 -0.005602 0.013983 0.006940 0.009816 -0.011555 -0.114264 -0.134881
> 0.003767 0.001592 -0.005865 -0.126202 -0.077184 -0.002238 -0.003258 0.008663 0.106309 0.071260
> -0.007420 -0.003931 0.002026 -0.188076 -0.171475 0.003753 -0.007862 -0.000532
>
> 4.1 2.0000939 0.031622 -0.101069 -0.141489 0.146192 0.041530 -0.029942 0.048017 0.016854 -0.011786 -0.002983
> -0.012352 0.004088 0.009375 -0.000629 0.022052 0.334283 0.292087 0.117608 -0.138169 -0.044128
> 0.045807 -0.067581 -0.019055 -0.010887 -0.009579 -0.009065 -0.004014 0.008631 -0.037153 -0.027501
> 0.001321 0.000840 -0.004195 -0.129829 -0.083838 -0.002758 -0.006390 0.004054 0.079365 0.001257
> -0.003112 -0.009017 0.000714 0.235094 0.119114 -0.009535 0.013813 0.000495
>
> 5.1 2.0000016 0.984612 0.031293 -0.012143 0.013131 -0.000978 0.000352 0.001124 0.003705 0.002129 -0.000656
> -0.000121 -0.000324 0.001219 0.000022 -0.124964 0.019256 0.024481 -0.005256 -0.005553 0.001896
> -0.003989 -0.005117 0.000871 -0.000479 -0.000326 -0.000569 -0.000105 -0.000064 -0.001476 -0.001645
> 0.000072 -0.000389 -0.000801 -0.002481 0.001008 -0.000088 -0.000546 0.000456 0.003637 0.000319
> -0.000324 -0.000556 0.000080 0.008795 0.002340 -0.000473 0.000670 0.000099
>
> 6.1 1.9999987 0.120765 0.004003 0.008430 -0.021407 -0.000175 0.004580 -0.004776 0.001406 0.002295 0.000848
> 0.001659 -0.000274 -0.001963 -0.000057 1.004785 -0.046081 -0.069749 -0.021499 0.026538 0.006767
> -0.010500 0.011823 0.004750 0.001580 0.001600 0.001289 0.000398 -0.001323 -0.000442 0.003702
> -0.000006 -0.000184 0.000035 0.010435 0.008595 -0.000018 0.000500 -0.000248 -0.018213 0.000888
> 0.000893 0.002401 -0.000049 -0.047123 -0.020773 0.002188 -0.003305 -0.000323
>
> 7.1 1.9998260 -0.202527 0.324986 0.304041 0.029583 -0.085378 0.025350 -0.006588 -0.040542 0.009649 -0.006605
> 0.006457 -0.006365 0.007358 -0.002453 -0.043427 0.202191 0.125983 -0.151709 -0.010506 0.036674
> -0.027313 -0.008958 0.015720 -0.009023 0.003765 0.000725 0.012868 -0.005036 0.101928 0.007665
> 0.002007 0.001479 0.012300 0.174424 0.088431 0.008197 0.009133 -0.005959 0.030553 0.005186
> -0.003279 -0.003054 0.000753 0.021481 -0.018525 -0.003499 0.002757 0.001381
>
> 8.1 1.9995955 0.022111 -0.025714 0.032452 -0.220567 -0.015617 0.007605 -0.076210 -0.023215 -0.007077 0.004920
> 0.017629 -0.002519 -0.011576 -0.001258 -0.011836 0.042627 0.016175 0.330812 0.321938 -0.017557
> 0.161026 0.148774 -0.011521 -0.004681 0.021557 0.002040 -0.014755 -0.000510 0.013645 0.046797
> -0.004211 -0.000155 -0.000611 0.097448 0.086209 -0.001208 0.003409 -0.002526 0.286379 0.196287
> -0.004566 -0.014495 -0.000409 -0.039189 -0.050308 0.004060 0.002867 -0.001338
>
> 9.1 0.0010096 0.050665 -0.387381 0.021947 -0.468369 -0.262320 -0.483818 -0.181414 0.128435 -0.376147 0.006368
> -0.014782 -0.022676 -0.059769 -0.029994 -0.056992 0.343362 0.048698 -0.518953 0.071319 0.290069
> -0.306098 0.283593 -0.111820 0.008576 -0.063855 0.013868 -0.040879 -0.107074 -0.121882 -0.755722
> -0.033983 -0.029999 0.019161 -0.006907 0.385387 -0.002768 0.000591 -0.005741 -0.046235 -0.129901
> -0.025511 0.008212 -0.018689 0.112216 0.438792 0.002727 -0.000300 0.021658
>
> 10.1 0.0005363 -0.074515 0.229255 0.856816 0.137970 -0.007040 -0.448926 0.009842 -0.196226 -0.202987 -0.114109
> -0.047689 0.205467 -0.082124 0.119768 -0.004208 0.229035 -0.315184 0.274178 -0.312194 -0.460379
> 0.221581 -0.125436 0.411933 0.021357 -0.092168 -0.114892 0.022339 0.121248 -0.143342 -0.648099
> 0.018608 -0.113853 0.042054 0.050943 -0.295076 -0.000592 0.010065 -0.033039 -0.003526 0.310762
> -0.014161 -0.000570 -0.022959 0.002073 -0.616268 0.009243 0.013792 0.020642
>
> Electronic charge: 16.000000
>
> Natural orbitals saved on record 2150.2 (orbital set 1)
>
> Starting CIS properties program. Author: T. Korona (2006)
>
>
> 1st order properties for state 2.1, spin symmetry singlet
>
>
> State 2.1 Transition dipole moment CIS -0.19268290 0.06979694 0.02140916
> Oscillator strength 0.00082493
>
>
> Final Results:
> ==============
>
> State Exc. Energy Total Energy Weight(S) Weight(D) Delta E Conv Max. Coef. Excitation
> 2.1 0.01457242 -77.83952323 0.100E+01 0.000E+00 -0.676E-06 Y 0.99267 8.1 -> 9.1
>
>
>
>
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>
Dr. Tatiana Korona http://tiger.chem.uw.edu.pl/staff/tania/index.html
Quantum Chemistry Laboratory
University of Warsaw
Pasteura 1, PL-02-093 Warsaw, POLAND
`The man who makes no mistakes does not usually make anything.'
Edward John Phelps (1822-1900)
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