PROGRAM SUMMARY
Title of program:
mcci
Catalogue identifier:
ADMY
Ref. in CPC:
131(2000)142
Distribution format: tar gzip file
Operating system: UNIX (HP-UX, IRIX, SOLARIS)/LINUX
High speed store required:
32MK words
Number of bits in a word:
32
Number of lines in distributed program, including test data, etc:
24608
Keywords:
Molecular physics, Structure, Configuration interaction,
Correlation energy, Electronic spectra, Quantum many body problems,
Variational wavefunction, Davidson algorithm, Exact spin coupling.
Programming language used: Fortran
Computer:
HP ,
Sun (SPARC) ,
Sun (ULTRA SPARC) ,
Convex ,
Hitachi ,
SGI ,
Pentium-PC .
Nature of physical problem:
The mcci program is a configuration interaction program and is suitable
for generating highly accurate solutions to quantum-many body problems;
there is no inherent limit set on the number of fermions, but typical
calculations to date have considered molecules with up to 20 correlated
electrons. With reasonable sized basis set expansions, 99 per cent of
the correlation energy has been obtained for small molecular systems.
In principle, there is no limit to the accuracy of the calculations
outside of memory and CPU time constraints. Selective convergence on
excited states is possible with the program. The program calculates
energy matrix elements from one- and two-body integrals, which are
read-in externally. The program is independent of the operators used in
these expectation values, and hence is equally valid for any spin
independent Hamiltonian composed of one- and two-body operators.
Accurate calculations of atomic and molecular spectra have been
demonstrated with the program. Calculation of the spectra of point
defects in solids is currently being investigated, and the electronic
states for simplified models of quantum dots are also being studied with
use of the program for electronic applications. Treatment of spin
states is exact within the program allowing for calculation of
simultaneous eigenfunctions of the energy H^ and spin S^z, S^**2
operators.
Method of solution
Within a CI calculation, the wavefunction of a system is represented as
a linear expansion
| Psi > = Sigma c | Psi > (1)
A A A
where the PsiA are a suitable complete set of many particle functions
and the cA are expansion coefficients. The energy is varied relative to
the coefficients leading to a matrix eigenvalue problem
-> ->
Hc = ESc (2)
with the elements of H given by
H =< Psi | H^ | Psi > (3)
AB A B
where H^ is the Hamiltonian operator for the system under consideration,
and S is the overlap matrix formed from the expansion functions
S = < Psi |Psi > (4)
AB A B
Solution of the variational problem is equivalent to solution of the
generalized eigenvalue problem eq. (2). The matrix diagonalization step
is solved using Davidson's modification of the Lanczos method [1,2].
The Monte Carlo nature of the calculation arises by randomly choosing
new expansion functions |PsiA > and adding these to a trial vector.
WIth the trial vector a diagonalization of the CI matrix is performed.
Unimportant expansion functions are discarded and the procedure is
repeated until convergence is achieved.
Restrictions on the complexity of the problem
The program is written to allow for an arbitrary number of fermions and
arbitrary basis set size. The program is thus capable of providing
exact solutions, within a given basis set Ansatz, to any quantum-many
body problem for fermions with one- and two-body spin-independent
interactions. Practical limitations are due to the random nature of the
configuration generation procedure as well as the amount of memory
required for storage of the Hamiltonian matrix elements and arrays of
one- and two-electron integrals. Computational time scales non-linearly
in proportion to the amount of the correlation energy to be obtained
from a calculation; convergence issues have been discussed previously
[3,4]. Computational time may be reduced through consideration of
spatial symmetry, however, only the point group D2h and its sub-groups
may be used.
Typical running time
For the Ne test run presented, on a SUN ULTRA60 SPARC workstation, the
time needed was about 1 minute, with 26 MB of core storage used.