[molpro-user] Why the MCSCF energy is lower than Full-CI?

cong.wang cong.wang at helsinki.fi
Sat Feb 13 15:28:05 GMT 2010


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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