[molpro-user] Why the MCSCF energy is lower than Full-CI?
Peter Knowles
KnowlesPJ at Cardiff.ac.uk
Sun Feb 14 13:50:03 GMT 2010
In this example, you are a victim of the relatively primitive initial
wavefunction guess in the FCI code. It picks the lowest energy
determinant, which happens to be an open-shell configuration that is
of different symmetry to the ground state. The MCSCF code uses a
different algorithm and correctly finds the singlet A_g state.
Everything comes right if you either remove the 'nosym' card, or
displace the geometry very slightly to break the symmetry. In either
case, you'll get the same energy from both programs, although if you
were to do this in a bigger basis set it would be necessary to run fci
after mcscf in order to use the same orbitals.
Peter
On 13 Feb 2010, at 15:28, cong.wang wrote:
> Dear everyone,
>
> Hello,
>
> Excuse me, I did a HF, CASSCF(4,8), and Full-CI calculations for
> H4 square molecule with 6-31G basis set on molpro 2009. The CASSCF
> energy is lower than FCI by 0.02 a.u., what would be the explanation
> for that? Should the CASSCF(4,8) and FCI be equivalent in this case?
>
> Here are the input and output files
>
> Thank you very much in advance
> Best regards
> Sincerely,
> Cong Wang
>
> Ph. D. Student
> Department of Chemistry
> Laboratory for Instruction in Swedish
> University of Helsinki
> A.I. Virtanens plats 1
> P.O. Box 55
> FI-00014 University of Helsinki
> FINLAND
>
> ***,h4 !A title
> symmetry,nosym
> geomtyp=xyz
> geometry={
> 4
> title
> H 0. 0. 0.
> H 0. 0. 0.5
> H 0. 0.5 0.
> H 0. 0.5 0.5
> }
>
> basis={
> !
> ! HYDROGEN (4s) -> [2s]
> s, H , 18.7311370, 2.8253937, 0.6401217, 0.1612778
> c, 1.3, 0.03349460, 0.23472695, 0.81375733
> c, 4.4, 1
> }
>
>
> hf !closed-shell scf
> {fci;occ,8;core,0;wf,4,1}
> {multi;occ,8}
>
> *******************
>
> Here is the output file
>
> ***,h4
> symmetry,nosym
> geomtyp=xyz
> geometry={
> 4
> title
> H 0. 0. 0.
> H 0. 0. 0.5
> H 0. 0.5 0.
> H 0. 0.5 0.5
> }
>
> basis={
>
> !
>
> ! HYDROGEN (4s) -> [2s]
> s, H , 18.7311370, 2.8253937, 0.6401217, 0.1612778
> c, 1.3, 0.03349460, 0.23472695, 0.81375733
> c, 4.4, 1
> }
>
>
> hf
> !closed-shell scf
> {fci;occ,8;core,0;wf,4,1}
> {multi;occ,8}
>
>
> Variables initialized (631), CPU time= 0.02 sec
> Commands initialized (426), CPU time= 0.03 sec, 469 directives.
> Default parameters read. Elapsed time= 0.12 sec
> Checking input...
> Passed
> 1
>
>
> *** PROGRAM SYSTEM MOLPRO
> ***
> Copyright, University College Cardiff
> Consultants Limited, 2008
>
> Version 2009.1 linked 11 Dec 2009
> 10:14:28
>
>
> **********************************************************************************************************************************
> LABEL * h4
> Linux-2.6.9-67.9hp.8sp.XCsmp/c18(x86_64) 64 bit mpp version
> DATE: 13-Feb-10 TIME: 17:19:36
> **********************************************************************************************************************************
>
> Patch level: 26
> **********************************************************************************************************************************
>
> Variable memory set to 8000000 words, buffer space 230000 words
>
> SETTING GEOMTYP = XYZ
> ZSYMEL=NOSYM
>
> SETTING BASIS = USERDEF
>
>
> Recomputing integrals since basis changed
>
>
> Using spherical harmonics
>
>
> 1PROGRAM * SEWARD (Integral evaluation for generally contracted
> gaussian basis sets) Author: Roland Lindh, 1990
>
> Geometry written to block 1 of record 700
>
>
> Point group C1
>
>
>
> ATOMIC COORDINATES
>
> NR ATOM CHARGE X Y Z
>
> 1 H 1.00 0.000000000 0.000000000 0.000000000
> 2 H 1.00 0.000000000 0.000000000 0.944863066
> 3 H 1.00 0.000000000 0.944863066 0.000000000
> 4 H 1.00 0.000000000 0.944863066 0.944863066
>
> Bond lengths in Bohr (Angstrom)
>
> 1-2 0.944863066 1-3 0.944863066 1-4 1.336238162 2-3
> 1.336238162 2-4 0.944863066
> (0.500000000) (0.500000000) (0.707106781)
> (0.707106781) (0.500000000)
>
> 3-4 0.944863066
> (0.500000000)
>
> Bond angles
>
> 1-2-3 45.00000000 1-2-4 90.00000000 1-3-2 45.00000000
> 1-3-4 90.00000000
>
> 1-4-2 45.00000000 1-4-3 45.00000000 2-1-3 90.00000000
> 2-1-4 45.00000000
>
> 2-3-4 45.00000000 2-4-3 90.00000000 3-1-4 45.00000000
> 3-2-4 45.00000000
>
> NUCLEAR CHARGE: 4
> NUMBER OF PRIMITIVE AOS: 16
> NUMBER OF SYMMETRY AOS: 16
> NUMBER OF CONTRACTIONS: 8 ( 8A )
> NUMBER OF CORE ORBITALS: 0 ( 0A )
> NUMBER OF VALENCE ORBITALS: 4 ( 4A )
>
>
> NUCLEAR REPULSION ENERGY 5.73015684
>
>
> Eigenvalues of metric
>
> 1 0.424E-02 0.895E-01 0.895E-01 0.116E+00 0.559E+00 0.559E+00
> 0.901E+00 0.568E+01
>
>
> Contracted 2-electron integrals neglected if value below 1.0E-11
> AO integral compression algorithm 1 Integral accuracy 1.0E-11
>
> 0.524 MB (compressed) written to integral file (100.0%)
>
> Node minimum: 0.262 MB, node maximum: 0.262 MB
>
>
> NUMBER OF SORTED TWO-ELECTRON INTEGRALS: 342. BUFFER
> LENGTH: 32768
> NUMBER OF SEGMENTS: 1 SEGMENT LENGTH: 342 RECORD
> LENGTH: 524288
>
> Memory used in sort: 0.56 MW
>
> SORT1 READ 1040. AND WROTE 342. INTEGRALS IN 1
> RECORDS. CPU TIME: 0.00 SEC, REAL TIME: 0.03 SEC
> SORT2 READ 666. AND WROTE 666. INTEGRALS IN 2
> RECORDS. CPU TIME: 0.00 SEC, REAL TIME: 0.01 SEC
>
> Node minimum: 324. Node maximum: 342. integrals
>
> OPERATOR DM FOR CENTER 0 COORDINATES: 0.000000 0.000000
> 0.000000
>
>
> **********************************************************************************************************************************
> DATASETS * FILE NREC LENGTH (MB) RECORD NAMES
> 1 18 2.24 500 610 700
> 900 950 970 1000 129 960 1100
> VAR BASINP GEOM
> SYMINP ZMAT AOBASIS BASIS P2S ABASIS S
> 1400 1410 1200
> 1210 1080 1600 1650 1700
> T V H0
> H01 AOSYM SMH MOLCAS OPER
>
> PROGRAMS * TOTAL INT
> CPU TIMES * 0.25 0.04
> REAL TIME * 0.86 SEC
> DISK USED * 8.40 MB
> GA USED * 0.00 MB (max) 0.00 MB (current)
> **********************************************************************************************************************************
>
> 1PROGRAM * RHF-SCF (CLOSED SHELL) Authors: W. Meyer, H.-J.
> Werner
>
>
> NUMBER OF ELECTRONS: 2+ 2- SPACE SYMMETRY=1 SPIN
> SYMMETRY=Singlet
> CONVERGENCE THRESHOLDS: 1.00E-05 (Density) 1.00E-07 (Energy)
> MAX. NUMBER OF ITERATIONS: 60
> INTERPOLATION TYPE: DIIS
> INTERPOLATION STEPS: 2 (START) 1 (STEP)
> LEVEL SHIFTS: 0.00 (CLOSED) 0.00 (OPEN)
>
>
>
> Orbital guess generated from atomic densities. Full valence
> occupancy: 2
>
> Molecular orbital dump at record 2100.2
>
> ITERATION DDIFF GRAD ENERGY 2-EL.EN.
> DIPOLE MOMENTS DIIS
> 1 0.000E+00 0.000E+00 -1.01850516 6.476015
> 0.000000 0.000000 0.000000 0
> 2 0.000E+00 0.587E-01 -1.05651369 6.784778
> 0.000000 0.000000 0.000000 1
> 3 0.896E-01 0.923E-02 -1.05796300 6.767464
> 0.000000 0.000000 0.000000 2
> 4 0.378E-01 0.216E-02 -1.05826410 6.761665
> 0.000000 0.000000 0.000000 3
> 5 0.253E-01 0.141E-02 -1.05951712 6.765025
> 0.000000 0.000000 0.000000 4
> 6 0.139E+00 0.112E-02 -1.06074940 6.788974
> 0.000000 0.000000 0.000000 5
> 7 0.401E+00 0.221E-02 -1.06066222 6.794301
> 0.000000 0.000000 0.000000 6
> 8 0.231E-01 0.273E-02 -1.06088156 6.765436
> 0.000000 0.000000 0.000000 6
> 9 0.111E+00 0.912E-04 -1.06088511 6.767986
> 0.000000 0.000000 0.000000 7
> 10 0.299E-01 0.198E-03 -1.06088680 6.766019
> 0.000000 0.000000 0.000000 7
> 11 0.862E-02 0.819E-05 -1.06088680 6.765931
> 0.000000 0.000000 0.000000 7
> 12 0.598E-03 0.458E-06 -1.06088680 6.765936
> 0.000000 0.000000 0.000000 4
> 13 0.113E-04 0.833E-08 -1.06088680 6.765936
> 0.000000 0.000000 0.000000 3
> 14 0.816E-06 0.145E-08 -1.06088680 6.765936
> 0.000000 0.000000 0.000000 0
>
> Final occupancy: 2
>
> !RHF STATE 1.1 Energy -1.060886803967
> Nuclear energy 5.73015684
> One-electron energy -10.17401176
> Two-electron energy 3.38296811
> Virial quotient -0.30535441
> !RHF STATE 1.1 Dipole moment 0.00000000 0.00000000
> 0.00000000
> Dipole moment /Debye 0.00000000 0.00000000
> 0.00000000
>
> Orbital energies:
>
> 1.1 2.1 3.1 4.1
> -1.484903 -0.219135 0.118997 0.347029
>
>
> **********************************************************************************************************************************
> DATASETS * FILE NREC LENGTH (MB) RECORD NAMES
> 1 19 2.24 500 610 700
> 900 950 970 1000 129 960 1100
> VAR BASINP GEOM
> SYMINP ZMAT AOBASIS BASIS P2S ABASIS S
> 1400 1410 1200
> 1210 1080 1600 1650 1700 960(1)
> T V H0
> H01 AOSYM SMH MOLCAS OPER ABASIS
>
> 2 3 0.30 700 1000 2100
> GEOM BASIS RHF
>
> PROGRAMS * TOTAL HF INT
> CPU TIMES * 0.27 0.01 0.04
> REAL TIME * 0.93 SEC
> DISK USED * 14.05 MB
> SF USED * 0.00 MB
> GA USED * 0.00 MB (max) 0.00 MB (current)
> **********************************************************************************************************************************
>
> 1PROGRAM * FCI (Full CI) Author: P.J. Knowles, 1984
>
> *** Initialisation ***
>
> Molecular orbitals read from record 2100.2 Type=RHF/CANONICAL
> (state 1.1)
>
> Frozen orbitals: 0 ( 0 0 0 0 0 0 0 0)
> Active orbitals: 8 ( 8 0 0 0 0 0 0 0)
> Active electrons: 4
> Spin quantum number: 0.0
> Orbital pairs: 36 0 0 0 0
> 0 0 0
> Strings: 28 0 0 0 0
> 0 0 0
> 28 0 0 0 0
> 0 0 0
> Determinants: 784 0 0 0 0
> 0 0 0
>
> Load integrals 0.3 sec
> Transform integrals 0.3 sec
> Storage for integrals: 1432
> Remaining memory: 7998276
>
> Core energy: 5.73015684
> Run Hamiltonian processor DAVIDSON
> Symmetry: 1
> Trial vector: 0.00
> Result vector: 0.00
> Maximum iterations: 90
> Convergence threshold: 0.0000100
> RHS vector: 0.00
> Hamiltonian shift: 0.0000000
> Output threshold: 0.0500000
> Options: 0
> Number of roots: 1
> 0Hamiltonian diagonaliser entered at time 0.29
> 0Initial configuration generated:
> 2 0.7071068 -1.0926897
> 29 0.7071068 -1.0926897
>
> It Tr CPU Convergence Energy Pop dE(next)
>
> 1 1 0.3 1.00000000 -1.06497453
> + 0.07 -0.04894565 -0.04845022
> 2 1 0.3 0.16243432 -1.10830923
> + 0.13 -0.00201200 -0.00194720
> 3 1 0.3 0.03189825 -1.11019693
> + 0.15 -0.00009890 -0.00009653
> 4 1 0.3 0.00619425 -1.11029626
> + 0.11 -0.00000431 -0.00000415
> 5 1 0.3 0.00113560 -1.11030039
> + 0.13 -0.00000024 -0.00000024
> 6 1 0.3 0.00026966 -1.11030063
> + 0.13 -0.00000001 -0.00000001
> 7 1 0.3 0.00006100 -1.11030064
> + 0.14 0.00000000 0.00000000
> 8 1 0.3 0.00001235 -1.11030064
> + 0.13 0.00000000 0.00000000
> 9 1 0.3 0.00000273 -1.11030064
>
>
> RESULTS FOR STATE 1.1
> =====================
>
> Correlation energy -0.045326113978
> !FCI STATE 1.1 Energy -1.110300643555
> CI Vector (threshold= 0.500E-01)
> 0.697298777599 1 2 1 3
> 0.059500107090 1 2 1 7
> 0.697298777599 1 3 1 2
> 0.069818256450 1 4 1 5
> 0.069818256450 1 5 1 4
> 0.059500107090 1 7 1 2
> /EOF
>
>
> **********************************************************************************************************************************
> DATASETS * FILE NREC LENGTH (MB) RECORD NAMES
> 1 19 2.24 500 610 700
> 900 950 970 1000 129 960 1100
> VAR BASINP GEOM
> SYMINP ZMAT AOBASIS BASIS P2S ABASIS S
> 1400 1410 1200
> 1210 1080 1600 1650 1700 960(1)
> T V H0
> H01 AOSYM SMH MOLCAS OPER ABASIS
>
> 2 3 0.30 700 1000 2100
> GEOM BASIS RHF
>
> PROGRAMS * TOTAL FCI HF INT
> CPU TIMES * 0.28 0.02 0.01 0.04
> REAL TIME * 1.00 SEC
> DISK USED * 14.05 MB
> SF USED * 0.12 MB
> GA USED * 0.00 MB (max) 0.00 MB (current)
> **********************************************************************************************************************************
>
> 1PROGRAM * MULTI (Direct Multiconfiguration SCF) Authors: P.J.
> Knowles, H.-J. Werner (1984) S.T. Elbert (1988)
>
>
> Number of active orbitals: 8 ( 8 )
> Number of external orbitals: 0 ( 0 )
>
> State symmetry 1
>
> Number of electrons: 4 Spin symmetry=Singlet Space symmetry=1
> Number of states: 1
> Number of CSFs: 336 (784 determinants, 784 intermediate
> states)
>
> Molecular orbitals read from record 2100.2 Type=RHF/CANONICAL
> (state 1.1)
>
> Wavefunction dump at record 2140.2
>
> Convergence thresholds 0.10E-01 (gradient) 0.10E-05 (energy)
> 0.10E-02 (step length)
>
> Number of orbital rotations: 0 ( 0 Core/Active 0
> Core/Virtual 0 Active/Active 0 Active/Virtual)
> Total number of variables: 784
>
>
> ITER. MIC NCI NEG ENERGY(VAR) ENERGY(PROJ) ENERGY CHANGE
> GRAD(0) GRAD(ORB) GRAD(CI) STEP TIME
>
> 1 6 13 0 -1.13054659 -1.13054659 0.00000000
> 0.00000000 0.00000000 0.00000001 0.00E+00 0.04
>
> ** WVFN **** CONVERGENCE REACHED, FINAL GRADIENT: 0.00E+00
>
>
> First order charge density matrix for state 1.1 saved on record
> 2140.2 (density set 1)
>
> Results for state 1.1
> =====================
>
> !MCSCF STATE 1.1 Energy -1.130546590250
> Nuclear energy 5.73015684
> Kinetic energy 3.55743771
> One electron energy -10.16319936
> Two electron energy 3.30249592
> Virial ratio 1.31779800
>
> !MCSCF STATE 1.1 Dipole moment 0.00000000 0.00000000
> 0.00000000
> Dipole moment /Debye 0.00000000 0.00000000
> 0.00000000
>
>
> Natural orbital dump at molpro section 2140.2
> (Orbital set 2)
>
>
>
> **********************************************************************************************************************************
> DATASETS * FILE NREC LENGTH (MB) RECORD NAMES
> 1 20 2.27 500 610 700
> 900 950 970 1000 129 960 1100
> VAR BASINP GEOM
> SYMINP ZMAT AOBASIS BASIS P2S ABASIS S
> 1400 1410 1200
> 1210 1080 1600 1650 1700 960(1) 1380
> T V H0
> H01 AOSYM SMH MOLCAS OPER ABASIS JKOP
>
> 2 4 0.34 700 1000 2100
> 2140
> GEOM BASIS RHF
> MCSCF
>
> PROGRAMS * TOTAL MULTI FCI HF INT
> CPU TIMES * 0.34 0.05 0.02 0.01 0.04
> REAL TIME * 1.61 SEC
> DISK USED * 14.05 MB
> SF USED * 3.21 MB
> GA USED * 0.00 MB (max) 0.00 MB (current)
> **********************************************************************************************************************************
>
> MULTI FCI HF-SCF
> -1.13054659 -1.11030064 -1.06088680
> **********************************************************************************************************************************
> Variable memory released
> _______________________________________________
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> Molpro-user at molpro.net
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--
Prof. Peter J. Knowles
School of Chemistry, Cardiff University, Main Building, Park Place,
Cardiff CF10 3AT, UK
Email KnowlesPJ at Cardiff.ac.uk
WWW http://www.cardiff.ac.uk/chemy/contactsandpeople/academicstaff/knowles.html
Secretary: Alison Thompson, ThompsonAF at Cardiff.ac.uk Telephone +44 29
208 74805
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