The EXGEM program

1. General information

(1) MPP platform.

The program is implemented on parallel computers using MPI (message passing interface ) as communication tool between processors. In the present implementation, at least TWO processors must be attributed to a run.

(2) Implemented constraints.

Two executable versions of the EXGEM program is available. Each version has separate constraints with respect to memory and parameter limits.

xexgem672:

Maximum number of basis functions: 672

Maximum angular momentum quantum number l: 6 ( i-type functions)

Maximum number of fragments or subsystems: 3

Maximum number of nuclei in a fragment: 6

Maximum number of doubly occupied orbitals in a fragment: 21

Maximum number of natural orbitals in FCI calculations: 92

xexgem1344:

Maximum number of basis functions: 1344

Maximum angular momentum quantum number l: 6 ( i-type functions)

Maximum number of fragments or subsystems: 3

Maximum number of nuclei in a fragment: 12

Maximum number of doubly occupied orbitals in a fragment: 27

Maximum number of natural orbitals in FCI calculations: 92

(3) Cholesky decomposition.

Two-electron integrals are expressed in terms of integral tables generated by the Cholesky decomposition of the two-electron matrix:

When m is the number of basis functions, the theoretical value of t $_{\max }$ is m(m+1)/2. In practice, due to numerical redundancy in the two-electron matrix, the value of t $_{\max \text{ }}$ is considerably smaller. If the threshold for defining the numerical redundancy $\delta ^{Cholesky}$ is set equal to $10^{-p}$ , then typically

The integral tables , one table for each t, are distributed among the processors. With 2Gbyte memory allocated to integral tables, the minimum numbers of processors are roughly:

and

for exgem672 and exgem1344, respectively. However, it should be noted that the program with a chosen number of processors, runs even if not all the tables which are required for satisfying the Cholesky redundancy criterion are calculated. But the calculation has a lower accuracy.

As a rule of the thumb, the error in the total energy, due to the integral approximation defined by the Cholesky decomposition, is .

(4) Family basis sets.

Due to computaional reasons, i.e. feasibility in the computation of the two-electron integral tables, family type basis sets are adopted in the EXGEM program. A family type basis is characterized by one single set of exponents, i.e. the exponents of the different subsets are all taken from this single set of exponents. Consider the following example:

(14s9p5d3f1g ) uncontracted GTF ( Gaussian type functions ) family basis set.

Exponent s-type p-type d-type f-type g-type

$\zeta _{1}$ x

$\zeta _{2}$ x

$\zeta _{3}$ x

$\zeta _{4}$ x

$\zeta _{5}$ x

$\zeta _{6}$ x x

$\zeta _{7}$ x x

$\zeta _{8}$ x x

$\zeta _{9}$ x x x

$\zeta _{10}$ x x x x

$\zeta _{11}$ x x x x x

$\zeta _{12}$ x x x x

$\zeta _{13}$ x x x

$\zeta _{14}$ x x

This set corresponds to:

1 g-type family with exponent $\zeta _{11}$

2 f-type families with exponents

2 d-type families with exponents

4 p-type families with exponents

5 s-type families with exponents

No contraction of basis functions in the conventional sens is adopted in this program. Uncontracted functions are most convenient in the construction of two-electron integral tables. However, when dealing with FCI corrections, natural orbitals are utilized. This is somewhat similar to an extensive AMO type contraction.

2. The EXGEM input file.

The input file defines the calculation. The following information must be supplied:

Integral input:

(1) Integral tables on disk or in core?

(2) The number of different type of atoms and the number of atoms of each type.

(3) Charge of each atom type.

(4) Name and coordinates of nuclei.

(5) Number of family types and number of families of each type located on each type of atom.

(6) Orbital exponents of the family sets

(7) Cholesky threshold.

Fragment input:

(1) The number of fragments (molecules/atoms).

(2) The number of nuclei in each fragment and the sequential number of the nuclei as defined by the integral input.

(3) The number of doubly occupied orbitals in each fragment.

(4) The number of frozen doubly occupied orbitals in correlation calculation, i.e. the number of innermost orbitals not included in the correlation treatment.

(5) The number of correlation orbitals, i.e. natural orbitals, used in the FCI calculations of single and double pair corrections.

(6) The type of localization adopted for the isolated subsystems.

(7) Type of approximation adopted for double pair corrections.

Two-body input:

(1) The number of two-body, i.e. two-fragment, clusters for which one computes inter-fragment correlation terms.

(2) Specification of the two-body clusters in terms of sequence numbers of the fragments.

Convergence criteria:

(1) Energy threshold.

(2) Maximum number of iterative solutions of eigenvalue equations.

The form of the input file is given by some representative input files. In the input files extensive comment lines are given in order to describe the relevant input parameters. These comment lines are part of the input and is read by the program.

3. Access to the EXGEM program.

There is read permission on the catalog

/usr/local/chemistry/exgem

on the computer

nana.uit.no

at the HPC center, University of Tromsø. The following files exit on this catalog:

(1) The executable versions xexgem672 and xexgem1344 of the EXGEM program.

(2) The input files exgem.inp_h2lih and exgem.inp_h2ohf for the systems $H_{2}+LiH$ and $H_{2}O+HF$ , respectively.

(3) Result files res_h2lih and res_h2ohf, corresponding to EXGEM calculations on the systems defined in (2).

(4) Two jobscripts job4.h2lih and job8.h2ohf for running a 4- and 8-processor job on nana.uit.no, respectively.

(5) A short library for family type basis sets: family_basis.dat.

This file contains family basis sets for the atoms He to Ar.

At the HPC center, University of Oslo, the same type of information is given on the catalog

/site/share/chemistry/exgem

pico.uio.no

A Technology Transfer Project funded by NOTUR