The Atlas ATMOL Manual is no longer available. This version of the Manual dates from 1982 after ATMOL was ported to the Cyber 205 at UMRCC.
The ATMOL Direct-CI program is a general multi-reference singles and doubles configuration interaction (CI) program. The method (direct or integral driven) used in the package is described in [1]. To invoke the Direct-CI program on the Cyber-205 at UMRCC, use the following JCL:
PATTACH,ATMOL.
DIRECT.
In default the program will request 3 large pages of main memory, although this can be increased by use of one of the pre-directives LPAGE or MEMORY [2]. For optimal running the main memory allocation should be at least 3 times longer than the number of configuration state functions (CSFs) in the CI expansion. The program will tolerate the allocation of less memory, but at the cost of increased disc input/output, and higher overall job cost. The default memory allocation will usually handle CI expansions of up to 50,000 CSFs, and we recommend that at least 6 large pages of memory be allocated for larger cases. If the PSORT or SORT directives are used to increase the blocking factor of the PSORTFILE or SORTFILE respectively (see below), we recommend the use of 6 large pages of memory even for small cases.
Data input and printed output are on FORTRAN streams 5 and 6 respectively. There is normally no need to mention these streams in the JCL.
The following datasets will be used by the program, and should be mentioned in the JCL, in REQUEST, ATTACH, MFLINK or GETFEP commands:
PSORTFILE: A dataset normally assigned using the VSOS local file name (LFN) PSORT will be used as a scratchfile in a pre-sort of the transformed molecular integrals. The VSOS LFN for the PSORTFILE can be altered with the PSORT directive (see below). The space requirement of the PSORTFILE are about 1.5 times that of the FINAL MAINFILE of transformed 2-electron integrals produced by the transformation program [3].
SORTFILE: A dataset normally assigned with the VSOS LFN SORT will be used as a scratchfile in a post-sort of the transformed molecular integrals. The VSOS LFN for the SORTFILE can be altered with the SORT directive (see below). The maximum space requirements of the SORTFILE are about twice that of the FINAL MAINFILE of transformed 2-electron integrals produced by the transformation program [3], although this will be much reduced in high symmetry, by an inverse factor approaching the order of the point group involved.
FINAL MAINFILE: Transformed 2-electron integrals over the molecular orbitals (MOs) will be read from this file. The user may direct that this dataset be read from any ATMOL file except ED7 or MT7 by means of the FFILE directive (see below). The default is to use ED6.
DUMPFILE: The file used by the transformation program [3] for the output of 1-electron integrals over the MOs may be assigned as any ATMOL file except ED7 or MT7 with the ONELEC directive (see below). The program may also output space and spin natural orbitals (NOs) of the CI wavefunction to this file if so desired (see the NATORB directive below). In the absence of a ONELEC directive the DUMPFILE will be assumed to reside on ED3.
CI-VECTOR FILE: The ATMOL file ED7 is used to accommodate the partial Hamiltonian matrix elements. ED7 is also used to store the update vectors created by the Davidson diagonalization procedure [4] . Twice the CI expansion length will be added at each iterative cycle. The EMIN, VMIN and LOCK directives (see below) may be used to reduce the maximum size of the Davidson sub-space, thus limiting the ultimate size of ED7, possibly at the expense of an inferior rate of convergence. If it is thought possible that the diagonalization procedure may not converge in one job, ED7 must be retained to allow for restarts.
OVERFLOW FILE: During the construction of the partial matrix elements a scratchfile allocated as ATMOL file MT7 may be required. This is particularly likely to occur if a large number of reference CSFs are specified, while its likelihood is decreased if a large main memory allocation is used. MT7 is usually of the order 1000 to 4000 blocks long if it is required.
All pre-directives [2] are applicable and should be presented before the program specific directives described below.
We strongly recommend that the CNTRL directive be presented first. It is read to TEXT,NELEC,NINT,NEXT in format (A,3I).
TEXT should be set to the character string CNTRL.
NELEC specifies the number of electrons in the CI calculation. Notice that any inner shell electrons frozen out with the FROZEN directive of the transformation program [3] should not be included.
NINT specifies the number of internal MOs. These will be used to construct reference CSFs. If a MO is not occupied in any reference CSF it should not ordinarily be classified as internal, unless high levels of internal excitation are contemplated (see EXCIT directive below). The internal MOs normally correspond to that set capable of producing a qualitatively correct wavefunction. Notice that NINT*2 must be greater than or equal to NELEC.
NEXT specifies the number of external MOs. Such MOs will be unoccupied in all reference CSF. Single and double excitations from the internal to the external MOs cause the latter to contribute to the CI expansion.
Notice that NINT+NEXT must be less than or equal to the number of active MOs as specified to the transformation program [3]. If less than, then some active MOs will not take part in the CI, and in the absence of a REORDER directive (see below), these will be the highest indexed active MOs.
The remainder of the directives may be presented in any order, with the exception of RESTORE or ENTER, one of which must come last. In several cases directives are inter-related and care should be taken when presenting them, since the order in which the directives are presented is in such cases often significant; this is particularly the case for the EXCIT, CONF and REFGEN directives. Not all directives will be required in the same job.
Allows the user to define an 80 character title for the run, and extends over two lines. The first line consists of the character string TITLE in the first data field, the second line the user defined title.
Example:
TITLE
PROPANE DIRECT-CI
This directive is read to TEXT,C,K in format (A,F,I).
TEXT should be set to the character string THRESH.
C,K The diagonalisation is converged to a threshold (T) such that T=C/(10**K). If K is not set, it will be given the value 0. The lowest value to which T may be set is 1E-8, and this minimum will be selected if the user attempts to set a smaller T value. The THRESH directive may be omitted, when T will be set to 3E-4.
Example:
THRESH 2 5
THRESH 2E-5
THRESH 0.00002
are equivalent, causing T to be set to 2E-5.
This directive is read to TEXT,MAXC in format (A,I).
TEXT should be set to the character string MAXCYC.
MAXC specifies the maximum number of iterative cycles to be carried out by the Davidson [4] diagonalizer.
The directive may omitted, when MAXC will take the default value 50. The program currently does not monitor time remaining for the job, so in large cases which are not expected to converge in one run, the MAXCYC directive provides a means of ensuring that the program will not fail 'TIME-UP', giving the user the opportunity to ensure the safety of ED7, which will be required in a restart job.
This directive is read to TEXT,SHIF in format (A,F).
TEXT should be set to the character string SHIFT.
SHIF should be set to the value of the level shifter for the CI diagonalization phase. If the SHIFT directive is omitted, the default SHIF=0.0 will be taken.
For ground states small values (between 0.0 and 0.2) provide an optimal rate of convergence, and usually there is little point in using the SHIFT directive. For excited states, the rate of convergence may sometimes be markedly improved by using a SHIF value of between 0.3 and 0.5, particularly if the ALTERNAT directive (see below) is used.
This directive consists of one line which should contain the character string ALTERNAT in the first data field. If presented, the directive causes the sign of the SHIF parameter (see the SHIFT directive above) to be altered at each iterative cycle of the CI diagonalization, and this may improve the convergence rate for excited states. We do not recommend use of ALTERNAT except in cases where severe convergence problems are encountered.
These directives are read to TEXT,NDAVID in format (2A,I).
These directives may be omitted, when the defaults ATEXT=EMIN and NDAVID=40 will be taken.
Example:
VMIN 40
VMIN
are all equivalent, causing the variance minimization option to be selected, with a maximum sub-space of 40.
This directive may be used to define the trial CI wavefunction as a linear combination of CSFs. There are 2 ways to do this.
1) Enter specify the coefficients of the CSFs in the input file.
In this case the first line should only contain the literal string
TRIAL
There may be up to 20 lines following this directive initiator, each being read to ICSF,CCSF in format (I,F).
Example:
TRIAL
1 0.5
2 -0.5
The trial wafunction will consist of a linear combination of the first and second CSF in the CI expansion, with coefficients 0.5 and -0.5 respectively. It will be subsequently normalized by the program.
2) Select a subspace of CSFs and compute the eigenvector of the matrix corresponding to the subspace.
In this case the syntax is:
TEXT TEXTA SUBDIR [ SUBDIR [ .. ] ]
where
Example:
TRIAL DIAG SELECT 25
This will cause the program to select the 25 CSFs with the lowest eigenvalues. The matrix in this basis is solved for the eigenvector to obtain the trial vector.
The TRIAL directive may be omitted, when the trial wavefunction will be taken to be the first CSF in the CI list multiplied by a CCSF factor of 1.0.
The DIIS directive turns on the diis acceleration of the 2*2 Davidson diagonalisation [9]. The syntax of this directive is:
DIIS CRITERION NITERATIONS [ IFIX ENERGY ]
where
Note that the diis process starts only if both the tester and the number of iterations satisfy CRITERION and NITERATIONS.
The JACDAV directive sets the controls of the Jacobi-Davidson preconditioning method. The syntax of this directive is
JACDAV SUBDIR [ SUBDIR [ .. ] ]
where
NOTE: Because the default threshold is determined from the CI threshold at time of calling JACDAV interchanging the order of the THRESH directive and the JACDAV directive may lead to different convergence behaviour.
Entering the CHECKD directive specifies that the energy and the variance of the wavefunction should be recalculated upon convergence of the Davidson diagonalisation. This directive may be used when high accuracy is required.
The syntax of the directive is:
CHECKD [ ICRIT ]
where "CHECKD" is a literal string. ICRIT specifies the criterion after which the check should be performed according to the expression
criterion = 0.1d0 ** ICRIT
If the CHECKD directive is omitted then the criterion is set to 0.9d-06. Otherwise, if ICRIT is omitted then the criterion is set to 1.0d0 which means that in practise the check will be performed always.
The Davidson diagonalisation method builds a subspace in which it searches for the optimal approximation of the eigenvector. The vectors that form the basis of this subspace have to be stored as well as the vectors that are obtained by multiplying the basis vectors with the Hamiltonian matrix. These vectors may be stored either on disc or in core memory.
The MEMDAV directive provides a means to specify the amount of core memory that should be used to store the subspace vectors. The directive has the following syntax:
MEMDAV MEMSIZE
where "MEMDAV" is a literal string and MEMSIZE is an integer specifying the required amount of memory in words (real*8).
If the MEMDAV directive is not entered MEMSIZE will be set to 2 Mword. The Davidson diagonalisation routine may be forced to store the vectors on disc by setting MEMSIZE to 0.
The OUTSTORE directive forces the matrix-vector multiplicator that is central to the direct-CI procedure to operate in "outstore" mode. This means that the integral information the multiplicator uses will be kept on disc as much as possible, thus saving as much memory as possible. This may be useful in large calculations where memory limitations cause problems.
The directive has syntax:
OUTSTORE
By default the program will attempt to operate in "instore" mode.
This directive is read to TEXT,NPR,TPR,ATEXT,BTEXT,CTEXT in format (A,I,F,3A), and is used to control printing of the CI wavefunction.
TEXT should be set to the character string VPRINT.
NPR specifies the maximum number of CI coefficients to be printed.
TPR CI coefficients less than TPR in absolute magnitude will not be printed.
ATEXT,BTEXT,CTEXT may each be set to one of the character strings VAC, N-1, or N-2. If VAC is specified, CI coefficients of all the vacuum states (those with no electrons in the external MO space) will be printed, irrespective of the values of NPR and TPR. Similarly the parameters N-1 and N-2 control printing of those CSFs with one or two electrons in the external space respectively.
This directive may be omitted, when the defaults NPR=100 and TPR=1E-7 will be taken.
Example:
VPRINT 50 0.02 VAC
will cause all vacuum state coefficients to be printed. All coefficients greater in absolute magnitude than 0.02 will be printed, unless there are more than 50 of these, in which case only the largest 50 will be printed.
This directive is read to TEXT,NSPIN in format (A,I).
TEXT should be set to the character string SPIN.
NSPIN is used to specify the spin degeneracy of the CI wavefunction, using the values 1,2,3 etc for singlet, doublet, triplet etc states respectively. It is also possible to use one of the character strings SINGLET, DOUBLET, TRIPLET, QUARTET, QUINTET, SEXTET, SEPTET, OCTET and NONET to specify NSPIN.
The SPIN directive may be omitted, when the program will set NSPIN to 1 or 2 if NELEC is even or odd respectively.
Example:
SPIN 4
SPIN QUARTET
are equivalent; the wavefunction will be four-fold spin degenerate.
The PSORT directive is read to TEXT,KSIZE,ATEXT in format (A,I,A).
TEXT should be set to the character string PSORT.
KSIZE specifies the blocking factor (in units of ATMOL blocks) to be used in data transfers involving the PSORTFILE. The maximum blocking factor is 24 (12K words), and if the user specifies greater than this, the program adjusts the value back to the maximum. If insufficient main memory is allocated to allow successful use of a given blocking factor, the latter will be reduced to the maximum compatible with the given main memory allocation. The larger the blocking factor, the more efficiently will the pre-sort phase of the program operate. It is recommended that at least 6 large pages of memory be allocated if the maximum blocking factor is to be used.
ATEXT may be used to specify the VSOS LFN of the PSORTFILE; if omitted, the program will assume the LFN is PSORT.
The PSORT directive may be omitted, when the defaults KSIZE=12 and ATEXT=PSORT will be taken.
The SORT directive is read to TEXT,KSIZE,ATEXT in format (A,I,A).
TEXT should be set to the character string SORT.
KSIZE specifies the blocking factor (in units of ATMOL blocks) to be used in data transfers involving the SORTFILE. The maximum blocking factor is 24 (12K words), and if the user specifies greater than this, the program adjusts the value back to the maximum. If insufficient main memory is allocated to allow successful use of a given blocking factor, the latter will be reduced to the maximum compatible with the given main memory allocation. The larger the blocking factor, the more efficiently will the post-sort phase of the program operate. It is recommended that at least 6 large pages of memory be allocated if the maximum blocking factor is to be used.
ATEXT may be used to specify the VSOS LFN of the SORTFILE; if omitted, the program will assume the LFN is SORT.
The SORT directive may be omitted, when the defaults KSIZE=12 and ATEXT=SORT will be taken.
This directive is used to define the location of the FINAL MAINFILE of transformed 2-electron integrals. The syntax has been described elsewhere [3].
Example:
FFILE
ED2
1
0
Valid ATMOL file names are ED0 to ED6 and MT0 to MT6. The FFILE directive may be omitted, when the FINAL MAINFILE will be assumed to reside on ED6, commencing at block 1 and terminating with an ENDFILE block. Omission is equivalent to:
FFILE
ED6
1
0
The NATORB directive is read to TEXT,KSPACE,KSPIN,ATEXT in format (A,2I,A).
TEXT should be set to the character string NATORB.
KSPACE is an integer (between 0 and 190 inclusive) specifying the section number of the DUMPFILE where the space NOs are to be placed. If KSPACE=0, space NOs will not be routed to the DUMPFILE.
KSPIN is an integer (between 0 and 190 inclusive) specifying the section number of the DUMPFILE where the spin NOs are to be placed. If KSPIN=0, spin NOs will not be routed to the DUMPFILE. Notice that spin NOs will not be produced for singlet wavefunctions (see SPIN directive above) because they have an occupation number of zero in this case.
ATEXT may be set to the character string PRINT, when the NOs will be printed. If ATEXT is omitted, the NOs will not be sent to the lineprinter.
Example:
NATORB 12 14 PRINT
The space and spin NOs are output to sections 12 and 14 respectively of the DUMPFILE, and routed to the lineprinter.
The ONELEC directive allows the user to specify the location of the DUMPFILE and the transformed 1-electron integrals placed thereon by the transformation program [3], and is read to TEXT,DDNAM,IBLK,ISECT in format (2A,2I).
TEXT should be set to the character string ONELEC.
DDNAM specifies the ATMOL file name assigned to the DUMPFILE. Valid names are ED0 to ED6 and MT0 to MT6.
IBLK specifies the starting block of the DUMPFILE.
ISECT specifies the section number of the transformed 1-electron integrals on the DUMPFILE. If ISECT is omitted, the transformed 1-electron integrals will be assumed to be in section 198, which is the default section number used by the transformation program [3].
The ONELEC directive may be omitted, when the defaults DDNAM=ED3, IBLK=1 and ISECT=198 will be taken.
This directive is used to give the symmetry point group and irreducible representation (irrep) of the required CI vector. The first data line is read to TEXT,TPOINT,TIRREP in format (3A).
TEXT should be set to the character string SYMMETRY.
TPOINT should be set to the required point group. Valid point groups are C1,CS,CI,C2,D2,C2V,C2H and D2H. TPOINT should be set to one of these character strings.
TIRREP may be set to the irrep of the CI wavefunction, as required by the user. If TIRREP is not set, the program will user the irrep of the first reference CSF (see the CONF directive below). The order and names of the irreps are as outlined in standard group theory, as shown below.
POINT GROUP
___________
C1 CS CI C2 D2 C2V C2H D2H
_______________________________________________
A A' AG A A A1 AG AG
I A'' AU B B1 A2 BG B1G
R B2 B1 AU B2G
R B3 B2 BU B3G
E AU
P B1U
B2U
B3U
Note that the double prime appearing in the A'' irrep of the CS point group should be typed as two single 'quotes', not as the single character 'double quote'. The point group and irrep names should be typed exactly as shown, with upper case letters.
After the first line follows one line for each irrep, each being read to NIRO,NERO in format (2I).
NIRO specifies the number of internal MOs of a given irrep.
NERO specifies the number of external MOs of a given irrep.
Note that these lines must be in the order of irreps indicated in the table, and that the sum of the NIRO and NERO parameters must equal the NINT and NEXT parameters respectively, see the CNTRL directive above.
Example:
SYMMETRY C2V A1
2 6
0 1
1 3
1 2
The molecule has the point group C2V and the required irrep of the wavefunction is A1. There are to be 2,0,1 and 1 internal MOs of A1,A2,B1 and B2 irrep respectively, and 6,1,3 and 2 external MOs of A1,A2,B1 and B2 irrep respectively. Note that if there are no internal and external MOs of a given irrep, the user must indicate this explicitly. The above example but without the A2 MOs would look like:
SYMMETRY C2V A1
2 6
0 0
1 3
1 2
If the SYMMETRY and SYMDET (see below) directives are both omitted, the program will take the point group to be C1. If the SYMDET directive is used the SYMMETRY directive must be omitted, and vice-versa.
This directive provides a more automatic way of specifying the symmetry data. The syntax is
SYMDET [ TPOINT TIRREP ] [ TIRREP1 [ TIRREP2 [ ... ] ] ] [ CRIT ICRIT ]
SYMDET is a literal string (it invokes the directive).
TPOINT is a text string that specifies the point group of the molecule. If this subdirective is not specified SYMDET will try to determine the point group automatically. If specified the TPOINT should be set to one of C1, CS, CI, C2, D2, C2V, C2H and D2H.
TIRREP is a text string that specifies the irreducible representation (irrep) of the CI wavefunction. The order and names of the irreps are as outlined in standard group theory, as shown at the SYMMETRY directive. Alternatively, TIRREP may be set to the literal string REF. In this case the program will use the irrep of the first reference CSF. Normally it is preferable to set TIRREP to REF, and this parameter should only be changed if the program has been run once on the problem, so that the user knows the group multiplication table generated by the program, and also understands to which irreps the labels correspond.
TIRREP1, TIRREP2, .... are text strings specifying the names of the few representations on the integral file. If these are not specified the program will automatically assign names to the representations. However, as the SYMDET directive does not use the molecular geometry but assigns names according to the properties of the integrals, these names may look a bit strange.
CRIT ICRIT is the literal string CRIT followed by the integer value ICRIT. The integer ICRIT specifies the accuracy in the symmetry determination. Molecular integrals of absolute magnitude less than 10**(-ICRIT) will be ignored. By default ICRIT is set to 5.
Examples:
SYMDET C2V REF A1 B1 CRIT 5
SYMDET CRIT 9
SYMDET D2H REF CRIT 10
This directive is used to renumber the internal and external MOs so that they are in the order required if the SYMMETRY directive (see above) is used. This ordering is such that:
The first data line should be set to the character string REORDER. Subsequent lines should define NINT+NEXT integers, these defining the MOs in the order required. The maximum value of these integers is the size of the active MO space as defined to the transformation program [3].
Example:
Consider the example quoted under the SYMMETRY directive, and suppose the symmetry assignments of the active MOs used in the transformation program [3] were as follows:
INTERNAL A1: 1 3
B1: 4
B2: 2
EXTERNAL A1: 5 6 7 10 11 16
A2: 12
B1: 8 13 14
B2: 9 15
an appropriate REORDER directive would look like:
REORDER
1 3 4 2
5 6 7 10 11 16 12 8 13 14 9 15
The REORDER directive can span as many lines as required, so that the above sequence can be presented as:
REORDER
1 3
4
2
5 6 7 10 11 16
12
8 13 14
9 15
The character string TO may be used to string together a consecutive sequence of MO numbers. Thus our example can also be presented as:
REORDER
1 3
4
2
5 TO 7 10 11 16
12
8 13 14
9 15
Note that any active MOs defined during integral transformation but not present in the REORDER list will not take part in the CI calculation. It is also possible to use the ACTIVE directive of the transformation program [3] to obtain the desired ordering of the MOs.
This directive is used to define the excitation pattern allowed for a set of reference CSFs defined with the CONF directive (see below). The EXCIT directive may be used more than once in the data input to allow the user to specify different excitation patterns for different reference CSFs, and normally consists of a single dataline, in which the first data field should contain the character string EXCIT.
The second data field may also be read in A format, and if so used should be set to one of the character strings OCTAL or BINARY. If this second A format field is omitted, the program takes OCTAL as default.
Subsequent data fields are read in I-format, and should contain either octal numbers (valid range 0 to 7) or binary numbers (valid range 0 to 1), according to the character string contained in the second data field. The octal or binary integers may be continued onto subsequent lines if necessary.
We now explain the significance of these integers if OCTAL input mode is selected.
The first octal integer specifies the external excitation pattern for the reference CSFs, (where no internal excitations have been applied). This octal number should be translated into a binary format, such that:
OCTAL NUMBER BINARY NUMBER
____________ _____________
0 = 0 0 0
1 = 0 0 1
2 = 0 1 0
3 = 0 1 1
4 = 1 0 0
5 = 1 0 1
6 = 1 1 0
7 = 1 1 1
The left-most binary integer defines a double external excitation, where two electrons are promoted from the internal to the external space. If it is 0 or 1 the process is forbidden or allowed respectively. The middle binary integer defines the single external excitation process. If this is set to 1, the process is allowed, if it is 0, single external excitations are forbidden. The right-most binary integer corresponds to a no external excitation process, the reference CSFs being left as they are. If set to 0 or 1 the reference CSFs will be eliminated from or retained in the final list of CSFs for the CI. Note that CSFs may also be eliminated from the CI list because they are of the wrong spin/space symmetry.
Example 1:
EXCIT OCTAL 7
This excitation mask will cause the reference CSFs and the single and double external excitations generated from them to be included in the final CI list of CSFs.
Example 2:
EXCIT OCTAL 5
Will cause all the reference CSFs and all double external excitations generated therefrom to be added to the list of CSFs for the CI.
Example 3:
EXCIT OCTAL 4
Will cause the double external excitations of the reference states to appear in the final list of CSFs. Note the reference and single external excited CSFs are excluded from the CI list.
If a second octal integer is defined, the reference CSFs have undergone a single internal excitation process. That is, a transfer of an electron from one internal MO to another. This second integer defines the external excitation mask on these newly constructed internal CSFs. A third octal integer defines the external excitation pattern after a double internal excitation. Additional octal integers may be presented, up to a maximum to 21 integers. Thus it is possible to define a state which is up to 20 fold internally excited and up to doubly externally excited.
Example 4:
EXCIT OCTAL 7 3 1
corresponds to a CI list containing the reference CSFs plus all single and double excitations (internally and externally).
If the BINARY option is chosen, then the full binary patterns of each equivalent octal integer must be given.
Example 5:
EXCIT OCTAL 7 3 1
EXCIT BINARY 1 1 1 0 1 1 0 0 1
are equivalent.
It is possible to give different excitation patterns to different reference CSFs.
Example 6:
EXCIT OCTAL 7 3 1
CONF
.
.
.
.
EXCIT OCTAL 5 0 1
CONF
.
.
.
The first set of reference CSFs are associated with the excitation pattern 7 3 1, while the second set have an excitation pattern 5 0 1.
If the EXCIT directive is not invoked the excitation pattern will default to the setting 7 3 1, corresponding to all single and double excitations. An EXCIT directive presented without parameters will cause restoration of the 7 3 1 default.
The CONF directive is used to specify the reference CSFs for the CI expansion. CONF may be presented more than once in the data input, usually in conjunction with a different excitation pattern (see the EXCIT directive above) acting on the reference CSFs. The first line of the CONF directive is set to the character string CONF. Each subsequent line specifies a reference CSF by giving the number of electrons (0,1 or 2) in each internal MO. Thus each reference CSF is defined by NINT numbers, the ordering of which should conform to the order of the internal MOs as specified by the REORDER directive (see above) if the latter is presented. If necessary, CSF defining data may be carried over to further lines.
Example 1:
Consider the example quoted under the SYMMETRY directive above, where we have 2 A1,1 B1, and 1 B2 internal MO. To define a fully occupied pattern use:
CONF
2 2 2 2
Example 2:
The situation is as in example 1, except that we wish to define a 7-electron reference CSF, with the B1 MO singly occupied. We assume that the REORDER directive has been used to get the MOs properly ordered. The data would look like:
CONF
2 2 1 2
Example 3:
The situation is as in example 2 except that SYMDET has been used to determine the irreps, so that the user has not needed to use a REORDER directive. Remembering that the original ordering of the internal MOs was A1 B2 A1 B1, appropriate data to define the 7 electron B1 state would look like:
CONF
2 2 2 1
Example 4:
CONF
2 2 1 2
1 2 2 2
Multiple reference CSFs are allowed; thus the above data defines two 7-electron reference CSFs of A1 symmetry, assuming that SYMDET was used. If however the SYMMETRY and REORDER directives were used, the first reference CSF will be of B1 symmetry, while the second will be A1.
The CONF directive directive may be omitted, when a single reference CSF will be generated by the program, where the first NEL/2 internal MOs will be populated with 2 electrons, and if NEL is odd, 1 further electron will be added to the next internal MO. Note however that this default reference CSF will not be generated until all the data has been processed, and so will be unavailable for use by the REFGEN directive described below.
Alternatively the CONF directive may be used to specify the complete configuration space. The syntax for this use of the CONF directive is:
CONF
VACUUM
[ conf1 [ ... ]]
N-1
[ conf2 [ ... ]]
N-2
[ conf3 [ ... ]]
Note that
Example:
For a calculation on a Lithium atom where the 1S and 2S are the active orbitals the following configuration space may be specified:
CONF
VACUUM
2 1
1 2
N-1
2 0
1 1
0 2
N-2
1 0
0 1
The first line should consist of the character string REFGEN in the first data field. Subsequent lines are read in I-format, to paired integers IA and IC. As many such lines as required may be presented.
IA and IC define annihilation and creation operators respectively, which will be allowed to operate on the set of reference CSFs in existence at the time when REFGEN is called. Thus at least one CONF directive must have been presented before using REFGEN, and the IA,IC integers refer to internal MOs. The result of the annihilation/creation process will be further reference CSFs, whose excitation mask will be that of the most recently issued EXCIT directive.
Example 1:
EXCIT OCTAL 7 3 1
CONF
2 2 0 0
EXCIT OCTAL 5
REFGEN
1 3
2 4
will result in a further two reference states, to give three in all, of the form:
CSFS EXCITATION MASK ORIGIN
____ _______________ ______
2 2 0 0 7 3 1 CONF directive
1 2 1 0 5 REFGEN directive
2 1 0 1 5 REFGEN directive
Example 2:
EXCIT OCTAL 7 3 1
CONF
2 2 0 0
EXCIT OCTAL 5
REFGEN
1 3 2 4
is equivalent to example 1; more than one IA/IC pair may be given on a single line.
Example 3:
EXCIT OCTAL 7 3 1
CONF
2 2 0 0
EXCIT OCTAL 5
REFGEN
1 3
EXCIT OCTAL 3
REFGEN
2 4
will produce 4 reference CSFs, of the form:
CSFS EXCITATION MASK ORIGIN
____ _______________ ______
2 2 0 0 7 3 1 CONF directive
1 2 1 0 5 First REFGEN directive
2 1 0 1 3 Second REFGEN directive
1 1 1 1 3 Second REFGEN directive
Example 4:
EXCIT 7 3 1
CONF
2 2 0 0
REFGEN
1 3 1 4 2 3 2 4
REFGEN
1 3 1 4 2 3 2 4
REFGEN
1 3 1 4 2 3 2 4
REFGEN
1 3 1 4 2 3 2 4
will produce a reference space consisting of all possible CSFs that can be generated by distributing 4 electrons in 4 MOs.
The CASGEN directive is meant for generating CAS or full-CI wavefunctions. If one or more reference configuration was specified please read the documentation on the EXCIT subdirective. This directive consists of one line
TEXT OPTION1 [ OPTION2 ] [ OPTION3 ] ...
TEXT should be set to the string CASGEN.
The options may be any of the following (the text between quotes is the literal keyword specifying the option):
This directive consists of one line whose first data field should contain the character string SCREEN. If this directive is presented all reference configurations will be checked to see if they are of the same spin/space symmetry as that of the required CI wavefunction. If they are not, they will be eliminated from the reference space, and will take no part in the excitation process. Normally, this directive may only be required if a REFGEN directive is presented, since reference states of undesired properties will not usually be presented under control of the CONF directive.
This directive provides a means of selectively eliminating CSFs from the CI expansion by specifying a minimum and maximum number of electrons which user specified sets of internal MOs may carry. The first line should contain the character string RESTRICT in the first data field. Subsequent lines are read to TEXT,MIN,MAX,(IORBS(i),i=1,m), in format (A,2I,mI).
TEXT should be set to one of the character strings REF, VAC, N-1 or N-2. If REF is chosen the restrictions will apply to the reference CSFs; should such a state fail to comply with the restriction applied it will take no part in the excitation process used to generate the CI list, and will most probably be used when REFGEN directives are used. The character strings VAC, N-1 and N-2 refer to CSFs with 0,1 or 2 electrons in the external space respectively.
MIN,MAX specify the minimum and maximum number of electrons to be allowed to populate the internal MOs defined by the IORBS parameters.
IORBS A sequence of internal MO indices terminated by the integer 0. This data may be carried over to subsequent lines if necessary, and the character string TO may be used to shorten the data if desired. These parameters refer to the reordered MO list if a REORDER directive (see above) has been presented.
Example:
RESTRICT
VAC 7 8 1 TO 4 0
N-1 7 8 1 TO 4 0
N-2 7 8 1 TO 4 0
Internal MOs 1 to 4 inclusive are allowed to carry either 7 or 8 electrons in vacuum,N-1 and N-2 CSFs.
This directive is meant to limit the amount of output produced in printing occupation patterns. For example, in situations were many reference CSFs are specified one will want to withhold the program from printing all occupation patterns.
The directive is read to TEXT,IPR in format (A,I).
TEXT should be set to the character string PRCONF.
IPR specifies that every IPR'th occupation pattern generated by the configuration generator is to be printed. If IPR=0, no occupation patterns will be printed.
The directive may be omitted, then all occupation patterns generated by the configuration generator will be printed.
This directive allows the user to introduce comments in his input data, and consists of one line, with a * character in column 1, followed by a space character, followed by up to 78 characters comprising the comment. The comment will be sent to the lineprinter output, but will otherwise have no effect. Any number of * directives can be placed in the input data.
Example:
* THIS IS AN EXAMPLE OF A COMMENT CARD
The CEPA directive allows the user to perform a CI calculation corrected for unlinked cluster contributions. The CEPA approach is more accurate than the Davidson correction. Activating the CEPA option forces the diagonaliser to work in Out-of-Store mode. Currently single reference and multi reference CEPA options are available, although some approaches may only work in single reference calculations.
The syntax of the CEPA directive is
"CEPA" [ MODE ] [ SUBDIR ] [ ... ]
The literal string CEPA may be followed by an optional parameter
The defaults are equivalent to the following example:
Example:
CEPA 1 SIN IT 3 CRIT 0.01d0
The MP directive allows the user to perform internally contracted (multi reference) MP 2 / 3 calculations. The current implementation allows the usage of the MP vector as a start for a (MR)CI or (MR)CEPA calculation.
The syntax of the MP directive is
"MP" [ IORDER ] [ SUBDIR ] [ ... ]
IORDER
This parameter selects the order of perturbation-theory that will be calculated. Currently IORDER may be set to 2 or 3. By default IORDER is set to 2. After this parameter any of the following subdirectives may be used
"MODEL" IMODEL
This subdirective selects the zeroth-order Hamiltonian for the calculation. In the case of a multi-configurational (MC) reference function the reference wavefunction is not necessarily an eigenfunction of the Fock operator. To obtain a zeroth-order Hamiltonian from the Fock operator that has the MC reference function as eigenfunction it suffices to split the into a part working on the reference function and a part working on the remainder of the configuration space (i.e. the singles and doubles). For this purpose the projection operators |P0>, |P1> |P2> and |P1+2> are used. These operators project onto the reference space, the space of the singly excited states, the space of the doubly excited states, and the space of the singly and doubly excited states respectively.
Using the projection operators the following zeroth order Hamiltonians have been implemented
The desired zeroth Hamiltonian may be selected by setting IMODEL to the appropriate value. By default IMODEL is set to 1.
"PRINT" IPRINT
This subdirective sets the output level of the MP routines. The higher the value of IPRINT the more output will be generated. By default IPRINT is set to 1, the highest value of IPRINT currently is 10001.
"CRIT" RCRIT ICRIT
This subdirective sets the convergence criterion for the linear system solver in the MP calculation. Here RCRIT is a real value and ICRIT is an integer value, the convergence criterion is calculated as MPCRIT = RCRIT * 10 ** (- ICRIT). By default the criterion is set to 1.0D-6.
"SCHMIDT" RSCHM ISCHM
Sets the convergence criterion for the schmidt orthogonormalisation procedure. Here RSCHM is a value and ISCHM is an integer, the convergence criterion is set to SCRIT = RSCHM * 10 ** (- ISCHM). By default the criterion is set to 1.0D-7. By default the Schmidt orthonormalisation is used.
"QR" RQR IQR
Sets the convergence criterion for the QR orthogonormalisation procedure. The QR orthonormalisation procedure is an more accurate alternative to the Schmidt orthonormalisation (although it is called QR it is not certain that it really is a QR). Basically the overlap matrix is diagonalized to find the transformation to orthogonal vectors, the zero-eigenvalues are removed to eliminate linear dependencies. Although this procedure is more accurate that modified Gramm-Schmidt it is also more expensive. Here RQR is a value and IQR is an integer, the convergence criterion is set to SCRIT = RQR * 10 ** (- IQR). By default the criterion is set to 1.0D-7. If this directive is not specified the Schmidt orthonormalisation is used.
"LEVEL" RLEVEL1 [ ICYC RLEVEL2 ]
This subdirective sets the level shifter for the linear system solver in the MP calculation. The first ICYC iterations level shifter RLEVEL1 will be used. After ICYC iterations level shifter RLEVEL2 will be used. ICYC may be set to any integer in the range from 1 to 9. By default RLEVEL1 is set to 0.0D0, ICYC is set to 0, and RLEVEL2 is set to 0.0D0.
"MAXCYC" MCYC
This subdirective sets the maximum number of iterations for the linear system solver in the MP calculation. By default MCYC is 50.
"FIGNORE" RIGNORE IIGNORE
This subdirective sets a threshold for the calculations of the FOCK-matrix elements. The threshold is calculated as MPIGNORE = RIGNORE * 10 ** (- IIGNORE). All matrix elements that are smaller in absolute value than MPIGNORE are ignored. By default MPIGNORE is 1.0D-8.
"FOCK" DUMPFILE IBLOCK ISECTION
This subdirective specifies the dumpfile, the number of the starting block on the dumpfile and the section number at which the FOCK-integrals should be stored. By default DUMPFILE is set to "ed3" and the values of IBLOCK and ISECTION are calculated by the program.
"NODOC"
This directive instructs the program to treat doubly occupied orbitals as virtual orbitals. This directive should be used for debugging purposes only.
"NODIAG"
This directive instructs the program to assume the external FOCK-integral-matrix to be non-diagonal. This directive should be used for debugging purposes only. Because of the default settings the two input lines in the following example are equivalent
Example:
MP
MP 2 MODEL 1 PRINT 1 CRIT 1.0 6 SCHMIDT 1.0 7 LEVEL 0.0 0 0.0 MAXCYC 50 FIGNORE 1.0 6
NOTE: The MP directive has a few side effects. Although these side effects are very reasonable you may want to get around them. The side effects are
The CCI directive allows the user to perform internally contracted multi reference CI calculations. The syntax of the directive is
"CCI" [ SUBDIR ] [ ... ]
The subdirectives may be any of the following
"PRINT" IPRINT
This subdirective allows the printing of additional information. In particular it switches on the printing of the contracted CI-vector. The integer value IPRINT determines the amount of extra information printed. More information is printed if the number is enlarged (up to a maximum of 2000). By default printing is off.
"NODOC"
This subdirective forces the program to behave as if all internal orbitals are active orbitals. This means the program believes that there are no doubly occupied orbitals. This option is meant for debugging purposes.
The CCEPA directive allows the user to perform internally contracted multi reference CEPA calculations. The syntax of the directive is
"CCEPA" [ SUBDIR ] [ ... ]
The subdirectives may be any of the following
"SIN" / "NOSIN"
The strings SIN and NOSIN select and deselect the single excitation shift option respectively. The default is SIN.
"IT" ITCEPA
This subdirective indicates after what iteration the CEPA mode may start. The integer parameter ITCEPA is the iteration number after which the CEPA mode may be switched on. By default ITCEPA is set to 3.
"CRIT" FCRIT
This subdirective indicates that the CEPA mode should be invoked at a particular threshold determined by the TESTER in the diagonalisation phase of the CI calculation. The threshold FCRIT should be set to a floating point value. By default FCRIT is set to 0.01.
"PRINT" IPRINT
This subdirective allows the printing of additional information. In particular it switches on the printing of the contracted CI-vector. The integer value IPRINT determines the amount of extra information printed. More information is printed if the number is enlarged (up to a maximum of 2000). By default printing is off.
"MICRO" IMICRO FMICRO
This subdirective controls the micro iteration proces. The integer IMICRO is the maximum number of micro interactions that may be performed each iteration. The micro iteration process may terminate in less than IMICRO iterations if a threshold becomes less than the floating point number FMICRO. The default is MICRO 3 0.01d0.
"NODOC"
This subdirective forces the program to behave as if all internal orbitals are active orbitals. This means the program believes that there are no doubly occupied orbitals. This option is meant for debugging purposes.
This should be the last directive presented, and consists of the character string ENTER or FINISH in the first data field. The program collates all the previous data and checks it for obvious errors, and commences the CI calculation.
This is an alternative to the ENTER directive described above, and should be the last line presented. It consists of the character string RESTORE in the first data field.
If a RESTORE directive is used then ED7 must be saved from the preceeding job and then used in the RESTORE run, to provide a source of trial CI vector.
Near the of the direct-CI output at tabel with core usage diagnostics is printed. These diagnostics may be used to trim the core usage of the program for optimal performance. A typical example of a core usage diagnostics tabel is:
**************************************************** ***** max core used 110572 words ***** ***** input 48 ***** ***** sort 110572 ***** ***** hbill 44 ***** ***** mp 615 ***** ***** genz 1226 ***** ***** jacdav 1226 ***** ***** contract 333 ***** ***** natorb 1540 ***** ****************************************************
Each heading in the tabel defines a phase in the calculation. The amount in words following a heading gives the maximum total memory usage during that phase. In this example the maximum memory usage while performing the matrix-vector multiplication in "genz" is 1226 words.
Notes per heading:
It may be necessary for the user to understand the nature and order of spin functions associated with a given occupation pattern. The program makes use of Yamanouchi-Kotani geneological spin functions, the coupling order being such that higher indexed MOs are coupled before lower indexed MOs. The ordering of the MOs is as defined with the ACTIVE directive of the transformation program [3], or the REORDER directive (see above), or as assigned by the program if the SYMDET directive (see above) was presented.
Use the digits 0 and 1 to denote down and up spin coupling respectively. Proceeding from the highest to the lowest indexed singly occupied MO, write down the digitized representation of the possible spin functions, the digits being written from left to right. The resultant binary number defines the lexical ordering of the members of the spin canonical set, the higher the number, the higher the lexical index.
Example:
Consider 5 doubly occupied MOs coupled to a doublet. The possible spin functions in digitized representation are, in order of increasing lexical index:
10101 - Spin function 1
10110 - Spin function 2
11001 - Spin function 3
11010 - Spin function 4
11100 - Spin function 5
A brief explanation of the possible ATMOL error codes is given below:
Error Code Explanation
__________ ___________
16 Directive unknown.
20 Occupation number in CONF directive should be 0,1, or 2.
42 File name in ONELEC or FFILE directive not known.
50 Invalid parameter in WIDTH pre-directive.
61 Index block of DUMPFILE not in correct format.
62 ATMOL block with invalid checksum has been read,
or input/output error on ATMOL file. If the
latter, a finite VSOS error code will be given
whose explanation will be found in [7].
63 A DUMPFILE Section number outside the allowed range of
1 to 190 has been specified.
64 The section used to hold the transformed 1-electron
integrals on the DUMPFILE is not defined. Check
that the transformation program ran to completion.
65 A DUMPFILE Section is of the wrong TYPE.
67 Illegal search of an ATMOL file.
68 Illegal character found in F-format data field.
69 Illegal character found in I-format data field.
71 The program has attempted to expand the DUMPFILE
beyond its maximum size. This may occur when NOs
are written to the DUMPFILE.
72 An attempt has been made to overwrite a section on
the DUMPFILE with a section of greater length. This
may occur when NOs are written to the DUMPFILE.
213 SYMDET unable to determine point group.
444 The user has attempted to use ED7 or MT7 as
DUMPFILE or FINAL MAINFILE.
446 Illegal parameter in the REORDER directive.
447 Same parameter twice in REORDER directive.
448 Invalid number of MO labels in REORDER directive.
There should be NINT+NEXT MO labels.
666 End of file condition detected on FORTRAN
stream 5. The program expects more data.
771 The sum of the NIRO or NERO parameters in the
SYMMETRY directive do not equal the NINT or NEXT
parameters of the CNTRL directive respectively.
772 A SYMMETRY directive appears after a SYMDET directive.
773 A SYMDET directive appears after a SYMMETRY directive.
774 The SYMMETRY directive has been presented twice.
777 The SCREEN directive can find no reference
configurations of the required symmetry.
778 Invalid value for NSPIN in the SPIN directive. NSPIN
should be odd or even as NELEC is even or odd respectively.
999 Insufficient main memory for the program to continue.
1232 Invalid number of electrons in a reference CSF.
1410 The wavefunction generated by the TRIAL directive cannot
be normalized. Probably all CCSF parameters are zero.
1411 Invalid ICSF parameter in TRIAL directive.
1412 Too many parameters in TRIAL directive. The maximum
number of CSFs that can be included is 20.
1505 TPOINT parameter in the SYMMETRY directive is unknown.
1516 A CSF with more than 16 singly occupied MOs
has been detected in the CI list.
1517 Too many spin functions associated with a given occupation
pattern in a CSF. The maximum is 50, although a special
version of the program is available capable of handling
spin canonical sets of dimension up to 130.
1631 The value of NINT in the CNTRL directive is invalid.
It should be greater than 0 and less than 63.
1632 The sum of the NINT and NEXT parameters of the CNTRL
directive is invalid. Should be greater than 0 and less
than 201. This diagnostic may be produced if CNTRL is not
presented first.
1633 Illegal value for NELEC parameter in the CNTRL directive.
Should be greater than 0 and less than or equal to NINT*2.
1711 Illegal CSFTYPE parameter in RESTRICT directive.
1712 Too many restrictions imposed by the the RESTRICT
directive. The maximum number is 10.
1713 Invalid MO label in RESTRICT directive. Should be
greater than 0 and less than or equal to NINT.
1888 No CSFs in final CI list. This may be because a RESTRICT
directive prevents the construction of any CSFs.
1903 Non-empty orbitals encountered while building reference
configuration in CASGEN.
1904 Number of electrons too small to doubly occupy all internal
orbitals in CASGEN.
2210 REFGEN directive appears before the first CONF directive.
2211 Invalid annihilator or creator label in REFGEN directive.
Should be greater than 0 and less than or equal to NINT.
3333 AFN not recognized in the FILE pre-directive.
3801 Conditions for running CEPA not acceptable. There
should be only one closed-shell reference CSF, with
a maximum number of internal MOs of 15.
3810 Parameter on CEPA directive unknown.
3811 The CASGEN directive has been used more than 3 times.
However, 3 times is the maximum.
The following examples do not illustrate all the features of Direct-CI program, only a guide is intended.
This example illustrates a CI calculation on the H2O monomer, where maximum use is made of the program defaults. The transformed 1- and 2-electron integrals were taken from the H2O monomer example shown as specimen job 1 of [3]. A single root closed shell CI calculation is shown, such that the internal MO space consists of the occupied Hartree-Fock MOs (not including the oxygen 1s inner shell MO and it's associated two electrons, which have been factored from the CI problem with the FROZEN directive of the transformation program [3]). The external space consists of all the Hartree-Fock virtual MOs. Automatic MO symmetry analysis is invoked by means of the SYMDET directive. The default diagonalization mode is EMIN, so the program will seek out the ground state.
/*JOB JOBNAME,ACCOUNT,ST=(C20,LP=1,WS=400),PW=PASSWORD,TI=9,C=B
REQUEST,SORT.
REQUEST,PSORT.
REQUEST,ED7,RT=U.
ATTACH,ED3V,ED6V,ACC=RW.
PATTACH,ATMOL.
DIRECT.
####S
LPAGE 1
FILE ED3 ED3V ED6 ED6V
CNTRL 8 4 20
TITLE
H2O DEFAULT EXAMPLE
SYMDET
ENTER
####S
As in the previous example, except that explicit use is made of the directives, with parameters corresponding to the program defaults. MO symmetry assignment is by means of the SYMMETRY and REORDER directives.
/*JOB JOBNAME,ACCOUNT,ST=(C20,LP=1,WS=400),PW=PASSWORD,TI=9,C=B
REQUEST,PSORT.
REQUEST,SORT.
REQUEST,ED7,RT=U.
ATTACH,ED3V,ED6V,ACC=RW.
PATTACH,ATMOL.
DIRECT.
####S
LPAGE 1
FILE ED3 ED3V ED6 ED6V
CNTRL 8 4 20
TITLE
H2O WITH ALL DIRECTIVES EXPLICITLY STATED
THRESH 3E-4
MAXCYC 50
SHIFT 0.0
EMIN 50
TRIAL
1 1.0
VPRINT 100 1E-7
SPIN SINGLET
ONELEC ED3 1
SYMMETRY C2V A1
2 9
0 2
1 3
1 6
PSORT 12
SORT 12
REORDER
1 3 4 2
5 8 10 12 14 16 21 22 24 13 20 7 15 19 6 9 11 17 18 23
EXCIT OCTAL 7 3 1
CONF
2 2 2 2
MAXCYC 50
ENTER
####S
This example is based on the H2O dimer. User attention is drawn to the specific routing of the large PSORT, SORT and ED7 data sets to PACK01 and PACK04, which are the scratch discs on the UMRCC Cyber-205 system. The transformed 1- and 2-electron integrals were taken from the H2O dimer example shown as specimen job 2 in [3]. There are 8 and 72 MOs in the internal and external spaces respectively. Note that 4 electrons from the two oxygen 1s MOs have been factored from the CI problem with the FROZEN directive of the transformation program [3]. MO symmetry assignment is through the SYMMETRY and REORDER directives.
/*JOB JOBNAME,ACCOUNT,ST=(C20,LP=6,WS=900),PW=PASSWORD,TI=320,C=C
REQUEST,SORT,PACK=PACK04.
REQUEST,PSORT,PACK=PACK04.
REQUEST,ED7,PACK=PACK01,RT=U.
ATTACH,DIMED3,DIMED6,ACC=RW.
PATTACH,ATMOL.
DIRECT.
####S
LPAGE 6
FILE ED6 DIMED6 ED3 DIMED3
TITLE
(H2O)2 1 ROOT EXTERNAL:72 ORBITALS:PSORT:24:SORT:24
CNTRL 16 8 72
PSORT 24
SORT 24
VMIN 40
SHIFT 0.10
REORDER
1 2 4 5 6 7
3 8
9 10 12 13 15 16 17 19 20 22 23 25 27 28 31 32 34 35 36 38 39
40 43 44 46 47 48 50 52 53 54 59 61 62 63 64 65 67 68 69 70 73
74 76 77 78 80
11 14 18 21 24 26 29 30 33 37 41 42 45 49 51 55 56 57 58 60 66
71 72 75 79
EXCIT OCTAL 7 3 1
CONF
2 2 2 2 2 2 2 2
MAXCYC 10
SYMMETRY CS A'
6 47
2 25
SPIN SINGLET
ENTER
####S
[1] V.R. Saunders and J.H. van Lenthe, Mol. Phys., 48, 923, (1983).
[2] D.Moncrieff and V.R. Saunders, ATMOL-Introductory Notes.
[3] D.Moncrieff and V.R. Saunders, ATMOL-Transformation Program.
[4] E.R. Davidson, J. Comp. Phys., 17, 87, (1975); J. Weber, R. Lacroix and G. Wanner, Computers and Chemistry, 4, 55, (1980).
[5] W. Butscher and W.E. Kammer, J. Comp. Phys., 20, 313, (1976).
[6] C. Zirz and R. Ahlrichs, in 'Electron Correlation: Proceedings of the Daresbury Study Weekend', eds. M.F. Guest and S. Wilson, (Daresbury Laboratory Report DL/SCI/R14), 83, (1980).
[7] CDC VSOS Manual, Form 60459410, Control Data Corporation; VSOS Reference Manual, NAT 208, University of Manchester Regional Computer Centre, (1985).
[8] P.J.A. Ruttink, J.H. van Lenthe, R. Zwaans, and G.C. Groenenboom, J. Chem. Phys., 94, 11, 1991
[9]"A Space-Saving Modification of Davidson's Eigenvector Algorithm", Johan H. van Lenthe, Peter Pulay, J. Comput. Chem., 11, 1164-1168, (1990)