# [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  ***
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

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

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

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

```