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Manuscript Title: A Monte Carlo configuration generation computer program for the calculation of electronic states of atoms, molecules, and quantum dots.
Authors: L. Tong, M. Nolan, T. Cheng, J.C. Greer
Program title: mcci
Catalogue identifier: ADMY_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 131(2000)142
Programming language: Fortran.
Computer: HP, Sun (SPARC), Sun (ULTRA SPARC), Convex, Hitachi, SGI, Pentium-PC.
Operating system: UNIX (HP-UX/IRIX/SOLARIS), LINUX.
RAM: 32M words
Word size: 32
Keywords: Molecular physics, Structure, Configuration interaction, Correlation energy, Electronic spectra, Quantum many body problems, Variational wavefunction, Davidson algorithm, Exact spin coupling.
Classification: 16.1.

Nature of 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.

Solution method:
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:
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.

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.

References:
[1] C. Lanczos, J. Res. Nat. Bur. Stand. 45 (1950) 255.
[2] E.R. Davidson, J. Comput. Phys. 19 (1975) 87.
[3] J.C. Greer, J. Comput. Phys. 181 (1998) 146.
[4] J.C. Greer, Chem. Phys. Lett. 306 (1999) 197.