Efficient hybrid-symbolic methods for quantum mechanical calculations

We present hybrid symbolic–numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantum mechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.Program summaryProgram title: EVANCatalogue identifier: AEVU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 99020No. of bytes in distributed program, including test data, etc.: 5388574Distribution format: tar.gzProgramming language: Maple[1], MATLAB, Scilab [2], FORTRAN.Computer: Ranging from laptop to CLUSTER system.Operating system: Linux system which supports Maple and MATLAB (or Scilab).RAM: 64 bytesClassification: 4, 5, 16.External routines: Macrofort[3,4], BLAS, LAPACK[5]Nature of problem: Develop and showcase general tools for analyzing and solving ab initio quantum chemistry problems, in particular an efficient means of generating an accurate and high performance optimized program for any specific problem.Solution method: Use a Computer Algebra system (CAS) to analyze any given problem, study its symmetries, explore basis sets that best match its natural properties, seek preliminary solutions and when needed, use hybrid symbolic–numerical tools to generate optimized code in MATLAB (or Scilab) or FORTRAN (or C), etc., code which is tailored to a specific problem combined with high-performance numerical routines for solving the given problem. Particular attention is spent on matrix elements for a resulting Hamiltonian and using accessible eigensolvers, as well as their accuracy and performance.Additional comments: Subroutines Generated by Maple or MacrofortRunning time: Variable depending on problem size and speed of processors but good algorithmic complexityReferences:[1] L. Bernardin, P. Chin, P. DeMarco, K. O. Geddes, D. E. G. Hare, K. M. Heal, G. Labahn, J. P May, J. McCarron, M. B. Monagan, D. Ohashi and S. M. Vorkoetter, Maple Programming Guide, Toronto: Maplesoft, a division of Waterloo Maple, Inc., 2012.[2] C. Gomez (Ed.), C. Bunks, J.-P Chancelier, M. Goursat, R. Nikoukhah and S. Steer, Engineering and Scientific Computing with Scilab, Birkhauser, 1999.[3] C. Gomez, Macrofort: a fortran code generator in maple, INRIA report 119, 1990.[4] P. Capolsini, C. Gomez, Macroc and Macrofort, C and FORTRAN code generation within Maple, MapleTech 3, no. 3, 1996.[5] J. Dongarra, LAPACK Linear Algebra Package, http://www.netlib.org/lapack