A new variational algorithm called adaptive vibrational configuration interaction (A-VCI) intended for the resolution of the vibrational Schrödinger equation was developed. The main advantage of this approach is to efficiently reduce the dimension of the active space generated into the configuration interaction (CI) process. Here, we assume that the Hamiltonian writes as a sum of products of operators. This adaptive algorithm was developed with the use of three correlated conditions, i.e., a suitable starting space, a criterion for convergence, and a procedure to expand the approximate space. The velocity of the algorithm was increased with the use of a posteriori error estimator (residue) to select the most relevant direction to increase the space. Two examples have been selected for benchmark. In the case of H2CO, we mainly study the performance of A-VCI algorithm: comparison with the variation-perturbation method, choice of the initial space, and residual contributions. For CH3CN, we compare the A-VCI results with a computed reference spectrum using the same potential energy surface and for an active space reduced by about 90%.
Here is presented an original program based on molecular Schrödinger equations. It is dedicated to target specific states of infrared vibrational spectrum in a very precise way with a minimal usage of memory. An eigensolver combined with a new probing technique accumulates information along the iterations so that desired eigenpairs rapidly tend towards the variational limit. Basis set is augmented from the maximal components of residual vectors that usually require the construction of a big matrix block that here is bypassed with a new factorisation of the Hamiltonian. The latest borrows the mathematical concept of duality and the second quantization formalism of quantum theory.Licensing provisions: GNU General Public License 3.Programming languages: C/C++/Fortran. Supplementary materials: 1. The sources of the code grouped in folder DualVCI.zip also available at https: // github. com/ 4Rom1/ DualVCI 2. The input files of examples treated in section 6.Nature of problem: High computational cost in vibration configuration interaction methods [1,2], coming from the necessity to solve a large eigenvalue problem to acquire a good precision. The dimension of the matrix exponentially increases with the size of the studied molecule.Solution method: The A k decomposition [3] completed by a meaningful error evaluation namely the residue ||HX´EX|| minimised along iterations for specific targets given in input. The approximation space is generated in the same time as the residual vectors computed on the fly thanks to an adapted choice of excitations shaped on the Hamiltonian operator.
We present here a Finite Element Method devoted to the simulation of 3D periodic structures of arbitrary geometry. The numerical method based on ARPACK and PARDISO libraries, is discussed with the aim of extracting the eigenmodes of periodical structures and thus establishing their frequency band gaps. Simulation parameters and the computational optimization are the focus. Resolution will be used to characterize EBG (Electromagnetic Band Gap) structures, such as plasma rods and metallic cubes.
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