[molpro-user] Strange Occupation Numbers for CIS Natural Orbitals
Benjamin Levine
levine at chemistry.msu.edu
Fri Mar 1 12:05:34 GMT 2013
Dear Tatiana,
Thank you so much for your extremely thorough reply! It is extremely
helpful.
All the best,
Ben
On 2/28/2013 10:21 PM, Tatiana Korona wrote:
> 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)
--
Benjamin G. Levine
Assistant Professor
Department of Chemistry
Michigan State University
East Lansing, MI
517-355-9715 x169
http://levinegroup.chemistry.msu.edu/
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