2 Closed-Shell SCF Calculation

We wish to perform an SCF calculation at the geometry r(C-H)=1.099 A, r(C-O)=1.203 A and angle HCO=121.8^o. The geometry is specified through use of the z-matrix [2,3], where each line of the ZMATRIX directive is responsible for specifying the nature and location of a given nucleus in terms of the position of those nuclei defined by previous lines. Note at the outset that the z-matrix TAGs used to characterise the component nuclei of the system play a vital role in characterising the system. They act, for example, to define the charge of the component nuclei and are used in establishing the effective point group symmetry of the system. The program incorporates a number of `built-in' basis sets, with the split-valence 3-21G basis due to Pople et al [4] as the default. The following data sequence would be required in performing the SCF calculation using this default basis:

          TITLE
          H2CO - 3-21G DEFAULT BASIS - CLOSED SHELL SCF
          ZMATRIX ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          ENTER

Note that this data sequence assumes a number of default specifications; the corresponding sequence specifying these defaults in-line would be as follows;

          (*) DUMPFILE ED3 1
          (*) MAINFILE ED2
          (*) MINBLOCK ED2 1
          (*) MAXBLOCK ED2 99999
          (*) ADAPT ON
              TITLE
              H2CO - FULL DATA SPECIFICATION
          (*) CHARGE 0
          (*) MULT 1
          (*) SUPER ON
              ZMATRIX ANGSTROM
              C
              O 1 1.203
              H 1 1.099 2 121.8
              H 1 1.099 2 121.8 3 180.0
              END
          (*) BASIS SV 3-21G
          (*) RUNTYPE SCF
          (*) SCFTYPE RHF
          (*) LEVEL 1.0 5 0.3
          (*) DIIS ON
          (*) VECTORS ATOMS
          (*) ENTER 1

where the default specifications which apply in the present closed-shell single point geometry calculation are indicated by a (*). In particular

DUMPFILE, MAINFILE, MINBLOCK and MAXBLOCK specify the file attributes. Dumpfile output is routed to ED3 commencing at block 1, while Mainfile output is to ED2 commencing at block 1.
CHARGE and MULT specify the charge and spin multiplicity of the system, with the default referencing a closed-shell neutral system.
The ADAPT directive specifies that the SCF computation is to be performed in a symmetry adapted basis.

The SUPER directive specifies the format to be used in generation of the two-electron integral file. The program incorporates three options, namely

P-Supermatrix (2J-K)
separate J- and K-Supermatrices (in practice 2J-K and K)
conventional 2-electron integral format

In default efficiency considerations are used in deciding the appropriate format based on the particular computation to be undertaken (as defined by the SCFTYPE directive). Considerable Caution must be exercised when considering usage of the Mainfile produced in one phase of the computation in some subsequent phase, and specification of the SUPER directive provides some control over this usage. The default and available integral options are summarised in Table 2, where the specified defaults are those appropriate to RUNTYPE SCF.

**Table:** GAMESS-UK Integral Options as a function of SCFTYPE
SCFTYPE	Default	Available
Closed-shell SCF	P	P,J+K,2-electron integral
UHF	J+K	J+K,2-electron integral
Open-shell RHF	J+K	J+K,2-electron integral
GVB	J+K	J+K,2-electron integral
MP2	2-electron integral	2-electron integral
MP3	2-electron integral	2-electron integral
CASSCF	2-electron integral	2-electron integral
MCSCF	2-electron integral	2-electron integral

Thus, for example, attempting to use the integral file produced in default during a closed-shell SCF calculation (P-supermatrix) in a subsequent open-shell computation must be considered an invalid operation, and will lead to an error condition.

RUNTYPE and SCFTYPE define the computation to be carried out. RUNTYPE defines the particular task to be undertaken, while SCFTYPE specifies the form of wavefunction calculation to be employed throughout the task. RUNTYPE options are given in Table 3, while the categories of wavefunction that may be requested under control of the SCFTYPE directive are shown in Table 4.

**Table:** RUNTYPE Options Within GAMESS-UK
RUNTYPE INTEGRAL	Single point integral calculation
RUNTYPE SCF	Single point integral plus SCF calculation
RUNTYPE OPTIMIZE	Geometry optimisation (internal coordinates)
RUNTYPE OPTXYZ	Geometry optimisation (cartesian coordinates)
RUNTYPE SADDLE	Saddle point location
RUNTYPE FORCE	Force constant evaluation
RUNTYPE HESSIAN	Analytic Force constant evaluation
RUNTYPE POLARISABILITY	Polarisability calculation
RUNTYPE HYPER	Hyperpolarisability calculation
RUNTYPE MAGNET	Magnetisability calculation
RUNTYPE RAMAN	Calculation of Raman Intensities
RUNTYPE INFRARED	Calculation of IR intensities
RUNTYPE ANALYSE	Wavefunction analysis
RUNTYPE TRANSFORM	Integral transformation
RUNTYPE CI	CI calculation
RUNTYPE GF	Green's Function OVGF calculation
RUNTYPE TDA	Green's Function 2ph-TDA calculation
RUNTYPE RESPONSE	Response calculations of Excitation Energies

**Table:** SCFTYPE Specification within GAMESS-UK
SCFTYPE RHF	Restricted Hartree-Fock
SCFTYPE DIRECT	Direct-SCF
SCFTYPE UHF	Unrestricted Hartree-Fock
SCFTYPE DIRECT UHF	Direct-UHF
SCFTYPE GVB	Generalised Valence Bond
SCFTYPE DIRECT GVB	Direct-GVB
SCFTYPE MP2	2nd order Møller Plesset
SCFTYPE MP3	3nd order Møller Plesset
SCFTYPE CASSCF	Complete Active Space SCF
SCFTYPE MCSCF	2nd order MCSCF

Note that additional directives may be required in further characterising the SCFTYPE specification. The default program options are

          RUNTYPE SCF
          SCFTYPE RHF

i.e. single point restricted Hartree-Fock SCF computation.

LEVEL and DIIS define the convergence aids to apply throughout the computation. Note that the format of the LEVEL directive i.e. the number of level shifters to be specified, is dependent on the SCFTYPE setting.
The VECTORS directive determines the method to be used in generating a trial set of eigenvectors for the SCF calculation. The program incorporates many options; in default trial vectors are generated via the ATOMS option, involving the superposition of atomic SCF densities.
In default, the final set of converged vectors will be written to Section 1 of the Dumpfile, the default section for housing closed-shell SCF vectors (see Table 1). This could equally be achieved by explicit section specification (i.e. ENTER 1).

The following data sequence would be required in performing a minimal basis set (STO-3G) calculation at the above nuclear geometry. Note that the BASIS directive is now used to specify STO3G, while in the absence of the VECTORS directive the default ATOMS option is again used in generating a trial set of vectors.

          TITLE
          H2CO - MINIMAL STO3G BASIS - CLOSED SHELL SCF
          ZMATRIX ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS STO3G
          ENTER

The corresponding data for performing an extended, triple-zeta plus polarisation (TZVP) basis is shown below.

          TITLE
          H2CO - EXTENDED TZVP BASIS - CLOSED SHELL SCF
          ZMATRIX ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          ENTER

2.1 Spherical Harmonic Basis Sets

The default Cartesian angular functions (6 d, 10 f, 15 g) used throughout GAMESS-UK may now be overridden under control of the HARMONIC directive. This provides the option of using spherical-harmonic (5 d, 7 f, 9g) angular functions. Note that such usage is implemented internally through appropriate transformations, and not by computing integrals or derivative integrals over the spherical functions.

Typical usage will involve just presenting the string HARMONIC. Thus the data for performing an extended, triple-zeta plus polarisation (TZVP) spherical harmonic basis is shown below.

          TITLE
          H2CO - EXTENDED TZVP SPHERICAL HARMONIC BASIS - CLOSED SHELL SCF
          HARMONIC
          ZMATRIX ANGSTROM
          C
          O 1 1.203
          H 1 1.099 2 121.8
          H 1 1.099 2 121.8 3 180.0
          END
          BASIS TZVP
          ENTER

The following points should be noted:

The HARMONIC directive, if present, should appear before the BASIS directive.
A primary use of spherical functions is to help to eliminate problems with linear dependence.
It is not possible in the present release of the code to employ the HARMONIC option in Table-CI calculations.

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