6 Data for Conventional Table-CI Selection

Data for the configuration selection module is initiated with the SELECT directive, followed by those directives characterising the symmetry of the state(s) of interest and reference configurations (CNTRL, SPIN, SYMMETRY, CONF etc.) and terminated by data (ROOTS, THRESH) controlling the process of selection.

6.1 SELECT

The SELECT directive is used to control the configuration selection module, and comprises a single data line read to the variables TEXT, TEXTF and TEXTB using format (3A).

• TEXT should be set to the character string SELECT.
• TEXTF is an optional parameter that may be used to control the quantity of printed output produced by the module. Valid settings include the strings,
  • NOPRINT, to suppress the major part of the output from the module, in particular all details of the perturbative energy lowerings associated with the initial set of configurations;
  • IPRINT, to produce an intermediate level of output;
  • FPRINT, to produce output suitable for debugging purposes. This includes the energy lowerings associated with the complete configuration list.
• TEXTB is an optional parameter that should be set to the string BYPASS if the user wishes to bypass SELECT processing. Such usage is typically associated with restarting Table-CI calculations.

6.2 CNTRL

This directive consists of one line read to variables TEXT, NELEC using format (A,I).

• TEXT should be set to the character string CNTRL.
• NELEC is used to specify the total number of `active' electrons in the CI calculation. Note that any inner shell electrons frozen out under control of the TRAN directive should not be included.

The CNTRL directive may be omitted, when the program will set NELEC to the value characterising the SCF process implicit within the RUNTYPE CI processing, subtracting out those electrons nominated through the CORE parameter of the TRAN data.

6.3 SPIN

This directive consists of one line read to variables TEXT, NSPIN using format (A,I).

• TEXT should be set to the character string SPIN.
• NSPIN is used to specify the spin degeneracy of the CI wavefunction of the electronic eigenstate(s) of interest, using the values 1,2,3 etc. for singlet, doublet, triplet states etc. respectively. It is also possible to use one of the character strings SINGLET, DOUBLET, TRIPLET, QUARTET and QUINTET to specify NSPIN.

The SPIN directive may be omitted, when the program will set NSPIN to the value specified on the MULTIPLICITY directive (see section 4.6.2)

Example

          SPIN 3

          SPIN TRIPLET

are equivalent; the wavefunction will be three-fold spin degenerate.

6.4 SYMMETRY

This directive consists of one line read to variables TEXT, NSYM using format (A,I).

• TEXT should be set to the character string SYMMETRY.
• NSYM is an integer parameter used to specify the spatial symmetry of the CI wavefunction, and is set to the appropriate sequence number of the required irreducible representation (see Table 1).

The SYMMETRY directive may be omitted, when the program will set NSYM to 1 i.e., the totally symmetric representation. (see section 4.6.2)

Example

In a system of C_2v symmetry, the data line

          SYMMETRY 3

would be required when performing calculations on states of B₂ symmetry. Failure to present the directive in such cases will lead to the default A₁ symmetry.

6.5 SINGLES

This directive consists of one line read to variables TEXT, NREF using format (A,I).

• TEXT should be set to the character string SINGLES.
• NREF is an integer parameter used to nominate a particular configuration within the set of reference functions. The selection module will then retain in the final CI all single excitations with respect to the nominated function regardless of their computed energy lowerings.

The SINGLES directive may be omitted, when the program will use the energy lowerings as the sole criteria for including configurations in the final CI.

Example

Presenting the data line

          SINGLES 1

in a Table-CI calculation of a closed-shell system, where the SCF configuration is the first in the CONF list, will lead to the inclusion of all single excitations with respect to the SCF function in the final CI. Such inclusion leads, of course, to a marked improvement in the quality of one-electron properties computed from the CI wavefunction.

Table: Resolution of the C _$\infty$v Species into the C_2v Species

Orbital		IRrep
C $\infty$v	C2v	Sequence No.
$\sigma$	a1	1
$\delta_{{x2-y2}}^{}$
$\pi_{{x}}^{}$	b1	2
$\pi_{{y}}^{}$	b2	3
$\delta_{{xy}}^{}$	a2	4

Table: Resolution of the D _$\infty$h Species into the D_2h Species

Orbital		IRrep
D $\infty$h	D2h	Sequence No.
$\sigma_{{g}}^{}$	ag	1
$\delta_{{g,x2-y2}}^{}$
$\pi_{{u,x}}^{}$	b3u	2
$\pi_{{u,y}}^{}$	b2u	3
$\delta_{{g,xy}}^{}$	b1g	4
$\sigma_{{u}}^{}$	b1u	5
$\delta_{{u,x2-y2}}^{}$
$\pi_{{g,x}}^{}$	b2g	6
$\pi_{{g,y}}^{}$	b3g	7
$\delta_{{u,xy}}^{}$	au	8

6.6 CONF

The CONF directive is used to specify the reference CSFs for the CI expansion. The first line of the CONF directive is set to the character string CONF. Each subsequent line defines a reference CSF by specifying the sequence numbers of the component active orbitals in I-format. A given reference CSF is defined by

1. the number of open-shell orbitals (NOPEN). NOPEN includes any unpaired orbitals together with those non-identical spin-coupled pairs open to substitution.
2. NOPEN integers specifying the sequence numbers of these orbitals
3. the (NELEC-NOPEN)/2 sequence numbers of the doubly-occupied orbitals i.e., the identically spin-coupled orbitals

where the sequence-numbers refers to the symmetry ordered orbitals performed at the outset of processing. Within the set of open- and doubly-occupied orbitals, the MOs are presented in groups of common IRrep, with the groups presented in order of increasing IRrep sequence number. Note that all reference function nominated by CONF must be of the same symmetry as that nominated on the SYMMETRY directive. A few examples will help clarify this order of presentation.

Example 1

Consider performing a valence-CI calculation on the PH₃ molecule using a 6-31G(*) basis. While the molecular symmetry is C_3v, the symmetry adaptation and subsequent CI will be conducted in the C_s point group. An examination of the SCF output reveals the following orbital analysis.

           =============================
           IRREP  NO. OF SYMMETRY ADAPTED
                  BASIS FUNCTIONS
           =============================
             1          18
             2           7
           =============================

and the following orbital assignments characterising the closed-shell SCF configuration:

1a₁²2a₁²1e⁴3a₁²4a₁²2e⁴5a₁² (1)

or, in the C_s symmetry representation:

1a'²2a'²1a''²3a'²4a'²5a'²6a'²2a''²7a'² (2)

          ===============================================
           M.O. IRREP  ORBITAL ENERGY   ORBITAL OCCUPANCY
          ===============================================
             1     1    -79.93661395           2.0000000
             2     1     -7.48916431           2.0000000
             3     1     -5.38319410           2.0000000
             4     2     -5.38319405           2.0000000
             5     1     -5.38149104           2.0000000
             6     1     -0.85610769           2.0000000
             7     1     -0.52191424           2.0000000
             8     2     -0.52191424           2.0000000
             9     1     -0.38579686           2.0000000
            10     1      0.16819544           0.0000000
            11     2      0.16819544           0.0000000
            12     1      0.26587776           0.0000000
            13     1      0.46072690           0.0000000
            14     2      0.46072690           0.0000000
            15     1      0.47871033           0.0000000
            16     1      0.56106989           0.0000000
            17     1      0.89229884           0.0000000
            18     2      0.89229885           0.0000000
            19     2      0.91131383           0.0000000
            20     1      0.91131383           0.0000000
            21     1      0.93118300           0.0000000
            22     1      1.17900613           0.0000000
            23     2      1.45058658           0.0000000
            24     1      1.45058658           0.0000000
            25     1      3.78674557           0.0000000
          ===============================================

Based on the above output, the CONF data lines may be deduced from the following table, where we assume that we wish to freeze the five inner shell orbitals:

1a'²2a'²1a''²3a'²4a'² (3)

IRrep	IRrep	No. of Basis	Frozen	Active	Sequence
	No.	Functions	MOs	MOs	Nos.
a'	1	18	4	14	1-14
a''	2	7	1	6	15-20

To perform an 8-electron valence-CI calculation, involving the SCF configuration and two degenerate (1e)' to (2e)' doubly-excited configurations

5a'²8a'²2a''²7a'² (4)

and

5a'²6a'²3a''²7a'² (5)

would require the following CONF data:

          CONF
          0 1 2 3 15
          0 1 3 4 15
          0 1 2 3 16

The complete data file for performing the SCF and subsequent CI would then be as follows:

          TITLE
          PH3 * 6-31G*  VALENCE-CI 3M/1R
          SUPER OFF NOSYM
          ZMAT 
          P
          H 1 RPH
          H 1 RPH 2 THETA
          H 1 RPH 2 THETA 3 THETA  1
          VARIABLES
          RPH 2.685   
          THETA 93.83  
          END
          BASIS 6-31G*
          RUNTYPE CI
          MRDCI
          TRAN CORE
          4 1
          1 TO 4 1
          SELECT
          SINGLES 1
          CONF
          0 1 2 3 15
          0 1 3 4 15
          0 1 2 3 16
          NATORB
          ENTER

Example 2

In this example we wish to perform a valence-CI calculation on the CuCl molecule using a 3-21G basis. While the molecular symmetry is C _$\infty$v, the symmetry adaptation and subsequent CI will be conducted in the C_2v point group. The resolution of the C _$\infty$v into the C_2v orbital species is given in Table 2. An examination of the SCF output reveals the following orbital analysis.

           =============================
           IRREP  NO. OF SYMMETRY ADAPTED
                  BASIS FUNCTIONS
           =============================
             1          22
             2           9
             3           9
             4           2
           =============================

and the following orbital assignments from the converged closed shell SCF:

           ===============================================
            M.O. IRREP  ORBITAL ENERGY   ORBITAL OCCUPANCY
           ===============================================
              1     1   -326.84723972           2.0000000
              2     1   -104.02836336           2.0000000
              3     1    -40.71695637           2.0000000
              4     1    -35.46377378           2.0000000
              5     3    -35.45608069           2.0000000
              6     2    -35.45608068           2.0000000
              7     1    -10.42193940           2.0000000
              8     1     -7.88512031           2.0000000
              9     2     -7.88222844           2.0000000
             10     3     -7.88222844           2.0000000
             11     1     -5.07729175           2.0000000
             12     1     -3.38247056           2.0000000
             13     3     -3.35978308           2.0000000
             14     2     -3.35978307           2.0000000
             15     1     -1.01099628           2.0000000
             16     3     -0.53702948           2.0000000
             17     2     -0.53702947           2.0000000
             18     4     -0.49640067           2.0000000
             19     1     -0.49640067           2.0000000
             20     1     -0.44715317           2.0000000
             21     3     -0.39988537           2.0000000
             22     2     -0.39988537           2.0000000
             23     1     -0.35127248           2.0000000
             24     1      0.00023285           0.0000000
             25     3      0.06300102           0.0000000
             26     2      0.06300102           0.0000000
             27     1      0.12855448           0.0000000
             28     1      0.19287013           0.0000000
             29     3      0.25729975           0.0000000
             30     2      0.25729975           0.0000000
             31     1      0.39720201           0.0000000
             32     1      0.86197727           0.0000000
             33     2      0.88942618           0.0000000
             34     3      0.88942618           0.0000000
             35     1      1.01877167           0.0000000
             36     1      2.16694989           0.0000000
             37     3      3.96181512           0.0000000
             38     2      3.96181512           0.0000000
             39     4      3.98212497           0.0000000
             40     1      3.98212497           0.0000000
             41     1      4.08851360           0.0000000
             42     1     24.51368240           0.0000000
           ===============================================

Based on the above output, the CONF data lines may be deduced from the following table, where we assume that we wish to freeze the first 14 inner shell orbitals:

$$\sigma^{{2}}_{} \sigma^{{2}}_{} \sigma^{{2}}_{} \sigma^{{2}}_{} \pi^{{4}}_{} \sigma^{{2}}_{} \sigma^{{2}}_{} \pi^{{4}}_{} \sigma^{{2}}_{} \sigma^{{2}}_{} \pi^{{4}}_{}$$ (6)

IRrep	IRrep	No. of Basis	Frozen	Active	Sequence
	No.	Functions	MOs	MOs	Nos.
a1	1	22	8	14	1-14
b1	2	9	3	6	15-20
b2	3	9	3	6	21-26
a2	4	2	0	2	27-28

To perform an 18-electron valence-CI calculation, based on the SCF configuration

$$\sigma^{{2}}_{} \pi^{{4}}_{} \delta^{{4}}_{} \sigma^{{2}}_{} \pi^{{4}}_{} \sigma^{{2}}_{}$$ (7)

would require the following CONF data:

          CONF
          0 1 2 3 4  15 16  21 22  27

The complete data file for performing the SCF and subsequent CI would then be as follows:

          TITLE\CUCL .. 3-21G
          ZMAT ANGSTROM\CU\CL 1 CUCL\
          VARIABLES\CUCL 2.093 \END 
          BASIS 3-21G
          RUNTYPE CI
          MRDCI
          TRAN CORE
          8 3 3 0
          1 TO 8  1 TO 3  1 TO 3
          SELECT 
          SINGLES 1
          CONF
          0 1 2 3 4  15 16  21 22  27
          NATORB
          ENTER

The inclusion of a second reference configuration corresponding to the doubly excited configuration

$$\sigma^{{2}}_{} \pi^{{4}}_{} \delta^{{4}}_{} \sigma^{{2}}_{} \pi^{{4}}_{} \sigma^{{2}}_{}$$ (8)

would require the following CONF data;

          CONF
          0 1 2 3 4  15 16  21 22  27
          0 1 2 3 5  15 16  21 22  27

Example 3

Consider performing a valence-CI calculation on the SiH₄ molecule using a 6-31G(*) basis. While the molecular symmetry is T_d, the symmetry adaptation and subsequent CI will be conducted in the C_2v point group. An examination of the SCF output reveals the following orbital analysis.

           =============================
           IRREP  NO. OF SYMMETRY ADAPTED
                  BASIS FUNCTIONS
           =============================
             1           9
             2           6
             3           6
             4           6
           =============================

and the following orbital assignments from the converged closed shell SCF:

          ===============================================
          M.O.  IRREP  ORBITAL ENERGY   ORBITAL OCCUPANCY
          ===============================================
            1     1    -68.77130710           2.0000000
            2     1     -6.12943325           2.0000000
            3     2     -4.23503117           2.0000000
            4     3     -4.23503117           2.0000000
            5     4     -4.23503117           2.0000000
            6     1     -0.73046864           2.0000000
            7     4     -0.48480821           2.0000000
            8     3     -0.48480821           2.0000000
            9     2     -0.48480821           2.0000000
           10     2      0.16291387           0.0000000
           11     3      0.16291387           0.0000000
           12     4      0.16291387           0.0000000
           13     1      0.25681257           0.0000000
           14     1      0.33606346           0.0000000
           15     3      0.37087856           0.0000000
           16     2      0.37087856           0.0000000
           17     4      0.37087856           0.0000000
           18     1      0.79946861           0.0000000
           19     1      0.79946861           0.0000000
           20     4      0.86232544           0.0000000
           21     3      0.86232544           0.0000000
           22     2      0.86232544           0.0000000
           23     1      1.23833149           0.0000000
           24     4      1.44033091           0.0000000
           25     3      1.44033091           0.0000000
           26     2      1.44033091           0.0000000
           27     1      3.13181655           0.0000000
          ===============================================

Based on the above output, the CONF data lines may be deduced from the following table, where we assume that we wish to freeze the first 5 silicon inner shell orbitals:

IRrep	IRrep	No. of Basis	Frozen	Active	Sequence
	No.	Functions	MOs	MOs	Nos.
a1	1	9	2	7	1-7
b1	2	6	1	5	8-12
b2	3	6	1	5	13-17
a2	4	6	1	5	18-22

To perform a 8-electron valence-CI calculation, based on the SCF configuration would require the following CONF data:

          CONF
          0 1 8 13 18

The complete data file for performing the SCF and subsequent CI would then be as follows:

          TITLE
          SIH4 * 6-31G* MRDCI VALENCE-CI 1M/1R
          ZMAT 
          SI
          H 1 SIH
          H 1 SIH 2 109.471
          H 1 SIH 2 109.471 3 120.0
          H 1 SIH 2 109.471 4 120.0
          VARIABLES
          SIH 2.80   
          END
          BASIS 6-31G*
          RUNTYPE CI
          MRDCI
          TRAN CORE
          2 1 1 1
          1 2 1 1 1
          SELECT
          CONF
          0 1 8 13 18
          SINGLES 1
          NATORB
          ENTER

Example 4

In this example we wish to perform a valence-CI calculation on the N₂ molecule using a 4-31G(*) basis. While the molecular symmetry is D _$\infty$h, the symmetry adaptation and subsequent CI will be conducted in the D_2h point group. The resolution of the D _$\infty$h into the D_2h orbital species is given in Table 2. An examination of the SCF output reveals the following orbital analysis.

           =============================
           IRREP  NO. OF SYMMETRY ADAPTED
                  BASIS FUNCTIONS
           =============================
             1           8
             2           3
             3           3
             4           1
             5           8
             6           3
             7           3
             8           1
           =============================

and the following orbital assignments from the converged closed shell SCF:

          ===============================================
          M.O.  IRREP  ORBITAL ENERGY   ORBITAL OCCUPANCY
          ===============================================
            1     1    -15.65951533           2.0000000
            2     5    -15.65474750           2.0000000
            3     1     -1.50615941           2.0000000
            4     5     -0.75782277           2.0000000
            5     1     -0.63244925           2.0000000
            6     3     -0.63135826           2.0000000
            7     2     -0.63135826           2.0000000
            8     6      0.20154861           0.0000000
            9     7      0.20154861           0.0000000
           10     5      0.63883097           0.0000000
           11     1      0.82491489           0.0000000
           12     3      0.89634343           0.0000000
           13     2      0.89634343           0.0000000
           14     1      0.91812387           0.0000000
           15     7      1.10036132           0.0000000
           16     6      1.10036132           0.0000000
           17     5      1.17625689           0.0000000
           18     5      1.66995008           0.0000000
           19     4      1.70518236           0.0000000
           20     1      1.70518236           0.0000000
           21     3      1.91001614           0.0000000
           22     2      1.91001614           0.0000000
           23     8      2.29436539           0.0000000
           24     5      2.29436539           0.0000000
           25     1      2.84356916           0.0000000
           26     7      3.00847817           0.0000000
           27     6      3.00847817           0.0000000
           28     5      3.37447679           0.0000000
           29     1      3.71753400           0.0000000
           30     5      4.09917273           0.0000000
          ===============================================

Based on the above output, the CONF data lines may be deduced from the following table, where we assume that we wish to freeze the two N1s inner shell orbitals:

IRrep	IRrep	No. of Basis	Frozen	Active	Sequence
	No.	Functions	MOs	MOs	Nos.
$\sigma_{{g}}^{}$	1	8	1	7	1-7
$\pi_{{u,x}}^{}$	2	3	0	3	8-10
$\pi_{{u,y}}^{}$	3	3	0	3	11-13
$\delta_{{g,xy}}^{}$	4	1	0	1	14
$\sigma_{{u}}^{}$	5	8	1	7	15-21
$\pi_{{g,x}}^{}$	6	3	0	3	22-24
$\pi_{{g,y}}^{}$	7	3	0	3	25-27
$\delta_{{u,xy}}^{}$	8	1	0	1	28

To perform a 10-electron valence-CI calculation, based on the SCF configuration

$$\sigma_{g}^{{2}} \sigma_{u}^{{2}} \sigma_{g}^{2} \pi_{u}^{{4}}$$ (9)

and associated $\pi$ to $\pi^{{*}}_{}$ excitations

$$\sigma_{g}^{{2}} \sigma_{u}^{{2}} \sigma_{g}^{2} \pi_{{u,y}}^{2} \pi_{{u,x}}^{2}$$ (10)

$$\sigma_{g}^{{2}} \sigma_{u}^{{2}} \sigma_{g}^{2} \pi_{{u,x}}^{2} \pi_{{u,y}}^{2}$$ (11)

$$\sigma_{g}^{{2}} \sigma_{u}^{{2}} \sigma_{g}^{2} \pi_{{u,x}}^{} \pi_{{u,x}}^{} \pi_{{u,y}}^{} \pi_{{u,y}}^{}$$ (12)

would require the following CONF data:

          CONF
          0 1 2 8 11 15
          0 1 2 11 15 22
          0 1 2 8 15 25
          4 8 11 22 25  1 2 15

The complete data file for performing the SCF and subsequent CI would then be as follows:

          TITLE\N2 .. 4-31G*
          SUPER OFF NOSYM
          ZMAT ANGS\N\N 1 NN
          VARIABLES\NN 1.05 \END
          BASIS 4-31G*
          RUNTYPE CI
          MRDCI
          TRAN CORE
          1 0 0 0 1 0 0 0
          1  1 
          SELECT 
          SINGLES 1
          CONF
          0 1 2 8 11 15
          0 1 2 11 15 22
          0 1 2 8 15 25
          4 8 11 22 25  1 2 15
          NATORB IPRIN
          ENTER

Now consider the corresponding calculation performed in a smaller 3-21G basis. An examination of the SCF output reveals the following orbital analysis.

           =============================
           IRREP  NO. OF SYMMETRY ADAPTED
                  BASIS FUNCTIONS
           =============================
             1           5
             2           2
             3           2
             5           5
             6           2
             7           2
           =============================

and the following orbital assignments from the converged closed shell SCF:

          ===============================================
          M.O.  IRREP  ORBITAL ENERGY   ORBITAL OCCUPANCY
          ===============================================
            1     1    -15.59983859           2.0000000
            2     5    -15.59796932           2.0000000
            3     1     -1.54485796           2.0000000
            4     5     -0.74550130           2.0000000
            5     2     -0.63373069           2.0000000
            6     3     -0.63373069           2.0000000
            7     1     -0.62012170           2.0000000
            8     6      0.20546760           0.0000000
            9     7      0.20546760           0.0000000
           10     5      0.79186362           0.0000000
           11     1      1.16445455           0.0000000
           12     2      1.26826720           0.0000000
           13     3      1.26826720           0.0000000
           14     7      1.43237859           0.0000000
           15     6      1.43237859           0.0000000
           16     5      1.55279124           0.0000000
           17     1      1.83635478           0.0000000
           18     5      2.63677794           0.0000000
          ===============================================

Note that there are now no MOs of IRREP 4 or 8. Based on the above output, the CONF data lines may be deduced from the following table, where we again assume that we wish to freeze the two N1s inner shell orbitals:

IRrep	IRrep	No. of Basis	Frozen	Active	Sequence
	No.	Functions	MOs	MOs	Nos.
$\sigma_{{g}}^{}$	1	5	1	4	1-4
$\pi_{{u,x}}^{}$	2	2	0	2	5-6
$\pi_{{u,y}}^{}$	3	2	0	2	7-8
$\sigma_{{u}}^{}$	5	5	1	4	9-12
$\pi_{{g,x}}^{}$	6	2	0	2	13-14
$\pi_{{g,y}}^{}$	7	2	0	2	15-16

To perform an 10-electron valence-CI calculation, based on the SCF configuration would require the following CONF data:

          CONF
          0 1 2 5 7  9

The complete data file for performing the SCF and subsequent CI would then be as follows:

          TITLE\N2 .. 3-21G
          SUPER OFF NOSYM
          ZMAT ANGS\N\N 1 NN
          VARIABLES\NN 1.05 \END
          BASIS 3-21G
          RUNTYPE CI
          MRDCI
          TRAN CORE
          1 0 0 1 0 0 
          1     1 
          SELECT 
          SINGLES 1
          CONF
          0 1 2 5 7  9
          NATORB IPRIN
          ENTER

Example 5

In this example we wish to perform a valence-CI calculation on the CaH₂ molecule using a 3-21G basis. While the molecular symmetry is D _$\infty$h, the symmetry adaptation and subsequent CI will be conducted in the D_2h point group. An examination of the SCF output reveals the following orbital analysis.

           =============================
           IRREP  NO. OF SYMMETRY ADAPTED
                  BASIS FUNCTIONS
           =============================
             1           7
             2           4
             3           4
             5           6
           =============================

and the following orbital assignments from the converged closed shell SCF:

          ===============================================
          M.O.  IRREP  ORBITAL ENERGY   ORBITAL OCCUPANCY
          ===============================================
            1     1   -148.37173884           2.0000000
            2     1    -16.76521275           2.0000000
            3     3    -13.55586861           2.0000000
            4     2    -13.55586861           2.0000000
            5     5    -13.55460610           2.0000000
            6     1     -2.26357685           2.0000000
            7     3     -1.36160958           2.0000000
            8     2     -1.36160958           2.0000000
            9     5     -1.35089927           2.0000000
           10     1     -0.34923025           2.0000000
           11     5     -0.31649941           2.0000000
           12     2      0.02334207           0.0000000
           13     3      0.02334207           0.0000000
           14     1      0.04980631           0.0000000
           15     5      0.09478404           0.0000000
           16     1      0.12395484           0.0000000
           17     3      0.13549605           0.0000000
           18     2      0.13549605           0.0000000
           19     5      0.28345574           0.0000000
           20     1      1.32404002           0.0000000
           21     5      1.45900204           0.0000000
          ===============================================

Based on the above output, the CONF data lines may be deduced from the following table, where we assume that we wish to freeze the nine Ca inner shell orbitals:

IRrep	IRrep	No. of Basis	Frozen	Active	Sequence
	No.	Functions	MOs	MOs	Nos.
$\sigma_{{g}}^{}$	1	7	3	4	1-4
$\pi_{{u,x}}^{}$	2	4	2	2	5-6
$\pi_{{u,y}}^{}$	3	4	2	2	7-8
$\sigma_{{u}}^{}$	5	6	2	4	9-12

To perform an 4-electron valence-CI calculation, based on the SCF configuration would require the following CONF data:

          CONF
          0 1 9

The complete data file for performing the SCF and subsequent CI would then be as follows:

          TITLE\CAH2 .. 3-21G
          SUPER OFF NOSYM
          ZMAT ANGS\CA\X 1 1.0\ H 1 CAH 2 90.0\H 1 CAH 2 90.0 3 THETA
          VARIABLES\CAH 2.148 \THETA 180.0 \END
          BASIS 3-21G
          RUNTYPE CI
          MRDCI
          TRAN CORE
          3 2 2  2 
          1 2 3  1 2  1 2  1 2
          SELECT 
          SINGLES 1
          CONF
          0 1 9
          NATORB IPRIN
          ENTER

6.7 ROOTS

The ROOTS directive is used to specify those eigenvectors of the `root' secular problem to be used in the process of selection, with the energy contributions of the configurations computed with respect to the nominated vectors. The directive consists of a single data line with the character string ROOTS in the first data field. Subsequent data comprises integer variables used to specify the number of root eigenstates (NROOT) and the sequence numbers of these vectors within the matrix of zero-order eigenvectors, (IROOT(I),I=1,NROOT). Two formats may be used in this specification:

1. If the lowest NROOT vectors are to be used, then the data line is read to the variables TEXT, NROOT using format (A,I);
   • TEXT is set to the character string ROOTS;
   • NROOT is an integer specifying the number of roots to be used, where the sequence numbers of the roots will be 1-NROOT.
2. If the NROOT vectors to be used are not the lowest in the root eigenvector matrix, then the sequence numbers within this matrix must be specified. The data line is then read to the variables TEXT, NROOT, (IROOT(I), I=1,NROOT), using format (A, (NROOT+1) I):
   • TEXT and NROOT are defined as above;
   • NROOT integers are read to the array IROOT defining the vectors of the zero-order matrix to be used in selection.

We now provide some further notes on the directive:

• the ROOTS directive may be omitted, when the energy contributions are calculated with reference to the lowest eigenstate of the root problem only. Omission of the directive is thus equivalent to presenting the data line

              ROOTS 1
  

• The number of root eigenstates to be specified will depend on the number of states required in the final CI. Thus if NVEC roots of the final CI matrix are to be subsequently generated in DIAG processing, the user should ideally perform selection with respect to at least the corresponding NVEC roots of the root secular problem to ensure a consistent treatment of each of the required states. The choice of the reference set will clearly prove crucial and should be such as to ensure a one to one correspondence between each of the final CI vectors and a certain vector of the root problem. Indeed the whole process of extrapolation to zero threshold is meaningless if this condition is not obeyed.

6.8 THRESH

This directive defines the threshold factors to be used in the process of configuration selection, and consists of a single line read to variables TEXT, TMIN, TINC using format (A,2F).

• TEXT should be set to the character string THRESH.
• TMIN should be set to the minimum threshold factor (in units of micro-hartree, $\mu$H) to be used in selection. Any CSF with a computed energy lowering greater than TMIN will be retained in the final list of selected configurations.
• TINC should be set to the threshold increment to be used in the process of extrapolation. This process involves solution of the final secular problem at a range of increasing thresholds defined by TMIN, TMIN + TINC, TMIN + 2 x TINC, ...., TMIN + (NEXTRP-1) x TINC , TMIN + NEXTRP x TINC where NEXTRP is the number of extrapolation passes requested under control of the EXTRAP directive (see the DIAG directives).

The THRESH directive may be omitted, when TMIN will be set to 30.0 and TINC to 10.0. With the default EXTRAP setting, this would lead to the solution of the T=50, 40 and 30 $\mu$H secular problem.

Example

          THRESH 5.0 5.0

          THRESH 5 5

are equivalent, causing T_min and T_inc to be set to 5 microhartree.