ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation

doi:10.1016/j.cpc.2009.03.005

Computer Physics Communications

Volume 180, Issue 12, December 2009, Pages 2401-2409

https://doi.org/10.1016/j.cpc.2009.03.005 Get rights and content

Abstract

We describe a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom. While the field-free Hamiltonian and the dipole matrices may be generated using an arbitrary primitive basis, they are assumed to have been transformed to the eigenbasis of the problem before the solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. Probabilities for survival of the ground state, excitation, and single ionization can be extracted from the propagated wavefunction.

Program summary

Program title: ALTDSE

Catalogue identifier: AEDM_v1_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDM_v1_0.html

Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 2154

No. of bytes in distributed program, including test data, etc.: 30 827

Distribution format: tar.gz

Programming language: Fortran 95. [A Fortran 2003 call to “flush” is used to simplify monitoring the output file during execution. If this function is not available, these statements should be commented out.].

Computer: Shared-memory machines

Operating system: Linux, OpenMP

Has the code been vectorized or parallelized?: Yes

RAM: Several Gb, depending on matrix size and number of processors

Supplementary material: To facilitate the execution of the program, Hamiltonian field-free and dipole matrix files are provided.

Classification: 2.5

External routines: LAPACK, BLAS

Nature of problem: We describe a computer program for a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom [1,2]. The probabilities for survival of the initial state, excitation of discrete states, and single ionization due to multi-photon processes can be obtained.

Solution method: The solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. The field-free Hamiltonian and the dipole matrices, originally generated in an arbitrary basis (e.g., the flexible B-spline R-matrix (BSR) method with non-orthogonal orbitals [3]), must be provided in the eigenbasis of the problem as input.

Restrictions: The present program is restricted to a ¹S^e initial state and linearly polarized light. This is the most common situation experimentally, but a generalization is straightforward.

Running time: Several hours, depending on the number of threads used.

References: [1] X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76 (2007) 053411. [2] X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78 (2008) 053402. [3] O. Zatsarinny, Comput. Phys. Comm. 174 (2006) 273.

Introduction

We recently described [1], [2] a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or quasi-two-electron targets. The critical ingredients of our particular time-dependent B-spline R-matrix (TDBSR) approach are field-free Hamiltonian and dipole matrices, which are generated using a flexible B-spline R-matrix method [3], followed by propagating the solution of the TDSE using the Arnoldi–Lanczos method [4], [5], [6]. The latter propagation scheme avoids the diagonalization of any large matrices. The method was successfully applied to the multi-photon excitation and ionization of Ne [1] and Ar [2] atoms.

The ingredients of an appropriate theoretical and computational formulation require an accurate and efficient generation of the Hamiltonian and the electron–field interaction matrix elements, as well as an optimal approach to propagate the solution of the TDSE in real time. There have been numerous calculations for two-electron systems such as He and H₂. (A partial list of references can be found in Guan et al. [7].) While these investigations emphasize the important role of two-electron systems in studying electron–electron correlation in the presence of a strong laser field, in its presumably purest form, experiments with He atoms are difficult and other noble gases, such as Ne and Ar, are often favored by the experimental community.

Fully ab initio theoretical approaches, which are applicable to complex targets beyond (quasi) two-electron systems, are still rare. This is mostly due to the difficulties associated with the structure description of complex targets such as the heavy noble gases, as well as the “half-collision” of the ejected electron with the residual ion. For (infinitely) long interaction times, the R-matrix Floquet ansatz [8] has been highly successful. A critical ingredient of this method is the general atomic R-matrix method developed over many years by Burke and collaborators in Belfast. A modification of the method, allowing for relatively long though finite-length pulses was described by Plummer and Noble [9]. Recently, a time-dependent formulation [10] of this method was applied to short-pulse laser interactions with Ar [11].

In this paper, we provide a general computer program, which allows for the propagation of the initial state of a complex target that is affected by an intense laser pulse with a duration of a few optical cycles. While our field-free and dipole interaction matrices were generated using the BSR code [3], we assume that the matrices have been transformed to the eigenbasis of the problem before the propagation is started. Consequently, the Hamiltonian for the entire system has a block structure, in which the field-free blocks are diagonal for each partial wave symmetry with total orbital angular momentum L and given parity π. Furthermore, these blocks are coupled to symmetries $L^{'} = L \pm 1$ and opposite parity via the dipole matrices. The current program is restricted to an initial ¹S^e bound state, but the input matrices could have been generated by any other method.

After summarizing the basic equations in the next section, we will describe the computer code and then present the results of a test case. Unless specified otherwise, atomic units (a.u.) are used throughout this manuscript.

Section snippets

Numerical method

A detailed description of the time-dependent B-spline R-matrix (TDBSR) approach, was given by Guan et al. [1], [2]. Hence, we only summarize the basic equations here. We also illustrate, using the BSR matrices as an example, how the field-free and dipole matrices generated by any approach would need to be transformed in order to use the current time-propagation scheme.

Program description

The program ALTDSE is designed to solve the time-dependent Schrödinger equation describing an atom in a strong linearly polarized laser pulse. For the present version of the program, two assumptions are being made. Namely: (1) The matrices needed to describe the field-free partial-wave symmetries can be diagonalized with the available computational resources. (2) It is possible to store an entire field-free Hamiltonian or dipole matrix on a single processor core. In this circumstance it is

Test case: Application to argon

Our test case is part of the calculation performed for the recent paper by Guan et al. [2] for multi-photon ionization of argon. In that work, we employed a three-state close-coupling expansion to describe the scattering of the ejected electron from the residual Ar⁺ ion. Specifically, we included the ( $3 s^{2} 3 p^{5}$ )²P^o, ( $3 s 3 p^{6}$ )²S, and (3s²3p⁴3d)²S states of Ar⁺.

The radial wavefunctions of the outer electron were expanded in terms of a set of 561 B-splines of order eight, using a semi-exponential

Conclusions and outlook

We have presented a general computer code to propagate the solution of the TDSE for multi-photon processes of atoms in a strong laser pulse. As long as the field-free and dipole matrices are represented in the eigenbasis of the problem, the Arnoldi–Lanczos propagation scheme presented here was found to be both efficient and reliable for the cases that we studied to date [1], [2]. Note, however, that the computational demands increase rapidly with increasing wavelength of the laser. While we

Acknowledgements

This work was supported by the United States National Science Foundation under grants No. PHY-0757755 (X.G. and K.B.) and PHY-0555226 (C.J.N., O.Z., and K.B.). We gratefully acknowledge supercomputer resources provided by the U.S. Department of Energy through its National Energy Research Scientific Computer Center (NERSC) and the NSF through Teragrid allocations under TG-PHY090031.

References (11)

O. Zatsarinny
Comput. Phys. Comm.
(2006)
E.S. Smyth et al.
Comput. Phys. Comm.
(1998)
B.I. Schneider et al.
J. Non-Cryst. Solids
(2005)
X. Guan et al.
Phys. Rev. A
(2007)
X. Guan et al.
Phys. Rev. A
(2008)

There are more references available in the full text version of this article.

Cited by (33)

MP-CITDSE: A set of ab-initio programs for the simulation of hydrogenic and helium-like atom-laser interactions
2023, Computer Physics Communications
MP-CITDSE is a package of programs which solves the time-dependent Schrödinger equation for hydrogenic and helium-like atomic systems interacting with an ultra-short laser pulse (of attosecond or femtosecond duration). The output of the computations – with some minimal processing – may be used to calculate excited populations, single and double ionisation yields, kinetic, angular and radial electron distributions, and harmonic yields. For the Helium atom, a full account of the inter-electronic correlation effects is included via a configuration interaction approach; for the time propagation of the wavefunction a spectral basis expansion on the eigenstates of the field-free Hamiltonian is used; for this reason post-processing of the expansion coefficients just after the pulse lead to simple formulas for quantities of experimental interest.
Program Title: MP-CITDSE
CPC Library link to program files: https://doi.org/10.17632/gv4zxmfdx3.1
Developer's repository link: https://github.com/aforembs/MP-CITDSE
Licensing provisions: GPLv3
Programming language: C++
Nature of problem: The ultra-fast high-intensity laser pulses of modern experimental sources require an ab-initio theoretical treatment, as the characteristics of such pulses are generally incompatible with the established Lowest-order Perturbation Theory (LOPT) approximation. Such a treatment can be quite cumbersome to not only implement, but also describe in a clear, intuitive manner. Its inherent complexity ensures that even in its simplest form, an ab-initio TDSE solver can easily consist of several thousand lines of code. As with any project of such scope a significant amount of effort is required to keep the code up to date, running on several platforms, compilers and operating systems. As such, while the numerical problem tackled by MP-CITDSE is that of the simulation of hydrogenic and helium-like atom-laser interactions on a single node computer/workstation; its main challenges are longevity and expandability. By doing away with unnecessary abstractions within the code, using a modern standard of a widely used and performant language (C++ 17) and hosting the source code on a publicly available GitHub repository we hope that the programs provided herein prove themselves useful to many current and future AMO Physicists.
Solution method: The atomic systems are considered confined in a spherical box of finite size. In the one-electron case (hydrogen) the eigenstates are calculated in a spherical coordinate system by the direct diagonalisation of the field-free Hamiltonian matrix representation on a B-splines piecewise polynomial basis expansion of the radial part of the eigenfunctions; for the two-electron case (helium) the numerically calculated one-electron eigenstates are angularly coupled to form a zero-order (uncorrelated) two-electron numerical basis; then the latter basis is further coupled via a configuration-interaction approach to eventually calculate the helium's two-electron eigenstates.
Following these steps, for both systems (hydrogen and helium) the computation proceeds by expanding the time-dependent wavefunction on the corresponding field-free eigenstate basis; thus, we end up to a system of first-order ordinary differential equations (ODEs) in time for the expansion (time-dependent) coefficients; the dynamical parameters for the ODEs time propagation, namely the eigenenergies and dipole matrix elements are calculated only once prior to the ODEs propagation [2]. The structure of the propagating matrix is block tridiagonal.
Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the MP-CITDSE code. In this version we solve the ODEs using a Runge-Kutta-Felnberg (RKF) algorithm. Also we have restricted the code to treat hydrogen and helium but with very little effort (non-relativistic) hydrogenic and helium-like atomic systems can also be simulated. The programs are supplied with two methods of compilation, via make and cmake to ensure greater portability.
- [1]
  L.A.A. Nikolopoulos, A package for the ab-initio calculation of one- and two-photon cross sections of two-electron atoms, using a CI B-splines method, 150 (2003) 140.
- [2]
  L.A.A Nikolopoulos, P. Lambropoulos, Helium double ionisation signals under soft-x-ray coherent radiation, 39 (2006) 883.
QPC-TDSE: A parallel TDSE solver for atoms and small molecules in strong lasers
2023, Computer Physics Communications
The QPC-TDSE program serves as a general tool to study laser-driven dynamics of electrons in ideal isolated atoms and molecules by solving the full-dimensional non-relativistic time-dependent Schrödinger equation (TDSE) within single-active-electron approximation. It expands the full-dimensional electronic wavefunction in spherical coordinates by spherical harmonics and B-spline functions and employs a set of parallel Crank-Nicolson propagators combined with split-operator techniques to evolve the wavefunction in time, which support centrifugal and multi-polar static potentials to treat atomic and molecular scenarios and accepts arbitrary combinations of linearly or elliptically polarized lasers within the dipole approximation. The program is capable of extracting the photo-electron momentum distribution via t-SURFF approach or projection onto either the exact scattering states or the planewaves. Its applications in different scenarios are given as examples, e.g., above threshold ionization, attosecond clock, higher-order harmonic generation.
Program Title: QPC-TDSE
CPC Library link to program files: https://doi.org/10.17632/xjm3kfgv75.1
Licensing provisions: GPLv3
Programming language: C++
External libraries: HDF5, GSL, MKL
Nature of problem: Numerical solution of TDSE and extraction of various types of electron spectrum.
Solution method: The electronic wavefunction is expanded by B-spline functions and spherical harmonics whose range is chosen elaborately to reduce the total number of partial waves for non-linearly polarized lasers. The Crank-Nicolson approach combined with an operator-splitting scheme is used to propagate the wavefunction in time, either in velocity gauge or length gauge. Matrix inversions are solved via either dense or sparse linear algebra solvers according to their structures. The t-SURFF method and projections onto either the scattering states or planewaves are provided for the accurate extraction of the momentum distributions.
Additional comments including restrictions and unusual features: Only lasers within dipole approximation are supported. For the multi-polar potentials, only pure Coulombic ones are supported. Routines for solving exact scattering states have only been implemented for centrifugal potentials. The codes are written in C++17 and can only be compiled on the platforms that support the avx instruction sets. An extension for the propagation algorithm using the avx-512 intrinsics is provided as optional.
PCTDSE: A parallel Cartesian-grid-based TDSE solver for modeling laser–atom interactions
2017, Computer Physics Communications
Citation Excerpt :
The quantum-mechanical wave function contains all the information of the systems, compared with other approximately analytic models [5]. The numerical solutions of the TDSE give ab initio simulations of the electron dynamics, and have been extensively carried out for single- [6], two- [7], and many-electron atoms [8], for long-wavelength optical lasers [9] and short-wavelength X-ray lasers [10]. Different levels of approximates have been made for the mentioned situations.
We present a parallel Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for modeling laser–atom interactions. It can simulate the single-electron dynamics of atoms in arbitrary time-dependent vector potentials. We use a split-operator method combined with fast Fourier transforms (FFT), on a three-dimensional (3D) Cartesian grid. Parallelization is realized using a 2D decomposition strategy based on the Message Passing Interface (MPI) library, which results in a good parallel scaling on modern supercomputers. We give simple applications for the hydrogen atom using the benchmark problems coming from the references and obtain repeatable results. The extensions to other laser–atom systems are straightforward with minimal modifications of the source code.
Program title: PCTDSE
Catalogue identifier: AFBM_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBM_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: BSD 3 - Clause
No. of lines in distributed program, including test data, etc.: 398662
No. of bytes in distributed program, including test data, etc.: 6355779
Distribution format: tar.gz
Programming language: Fortran 2003.
Computer: Distributed memory machines.
Operating system: Unix-like system.
RAM: Depends on the size of the Cartesian grid
Classification: 2.1, 2.2, 2.5.
External routines: 2DECOMP&FFT; FFTW; MPI
Nature of problem:
Simulate the single-electron dynamics of atoms under the strong fields of modern lasers according to the time-dependent Schrödinger equation.
Solution method:
The package solves the TDSE in the FFT-split-operator method, employing the split-operator method to approximate the time evolution operator and fast Fourier transforms to calculate the spatial derivatives.
Restrictions:
The code is restricted to problems where the atoms are in the single-active-electron approximation and the lasers are in the dipole approximation. It is also limited by the CPU time and memory that one can afford.
Unusual features:
We adopt the parallel strategy where the Cartesian grid is distributed among processors using a 2D decomposition, which has no limitation for large-scale simulations.
Running time:
The running time depends on the size of the grid, the number of time step, the number of processors, and the choice of the processor grid, ranging from a few hours to several days.
Simple, accurate, and efficient implementation of 1-electron atomic time-dependent Schrödinger equation in spherical coordinates
2016, Computer Physics Communications
Citation Excerpt :
Results of one-electron TDSE simulations are routinely published in leading physics journals [2–6], contribute to the discovery of previously unsuspected phenomena [7,8], and cause intense controversies [9–12]. Despite the apparent simplicity of the problem, development of new, increasingly efficient numerical approaches for solving 1-electron TDSEs in central potentials remains an active area of research [13–26]. The pursuit of numerical efficiency is not entirely surprising: addressing some open research questions in high-harmonic generation (HHG) in optically-dense media and laser filamentation requires simultaneous propagation of 103–106 coupled atomic TDSEs [27–30].
Modelling atomic processes in intense laser fields often relies on solving the time-dependent Schrödinger equation (TDSE). For processes involving ionisation, such as above-threshold ionisation (ATI) and high-harmonic generation (HHG), this is a formidable task even if only one electron is active. Several powerful ideas for efficient implementation of atomic TDSE were introduced by H.G. Muller some time ago (Muller, 1999), including: separation of Hamiltonian terms into tri-diagonal parts; implicit representation of the spatial derivatives; and use of a rotating reference frame. Here, we extend these techniques to allow for non-uniform radial grids, arbitrary laser field polarisation, and non-Hermitian terms in the Hamiltonian due to the implicit form of the derivatives (previously neglected). We implement the resulting propagator in a parallel Fortran program, adapted for multi-core execution. Cost of TDSE propagation scales linearly with the problem size, enabling full-dimensional calculations of strong-field ATI and HHG spectra for arbitrary field polarisations on a standard desktop PC.
Program title: SCID-TDSE: Time-dependent solution of 1-electron atomic Schrödinger equation in strong laser fields.
Catalogue identifier: AEYM_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYM_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 334254
No. of bytes in distributed program, including test data, etc.: 20005596
Distribution format: tar.gz
Programming language: Fortran-2003 with OpenMP extensions.
Computer: Portable code. Tested on x86_64 Linux.
Operating system: Portable code. Tested on x86_64 Linux.
RAM: Memory requirements depend on the input parameters. Time propagation of a given initial state requires $O (32 * N_{R} * (L_{MAX} + 1) * (M_{MAX} - M_{MIN} + 1))$ bytes of memory (double precision), where $N_{R}$ is the number of the radial grid points; $L_{MAX}$ is the maximum desired angular momentum; $M_{MIN}$ and $M_{MAX}$ are respectively the smallest and largest desired angular momentum projections. Preparation of the initial atomic states and analysis of the final wavefunction in terms of the field-free atomic states may require $O (64 * N_{R}^{2} * N_{CPU})$ bytes of RAM (double precision), where $N_{CPU}$ is the number of processing threads used.
Classification: 2.5, 4.3.
External routines: BLAS and LAPACK (required); libhugetlbfs (optional), DGEFA and DGEDI (LINPACK); routines included with the code.
Nature of problem: Time propagation of non-relativistic 1-electron Schrödinger equation for a central potential, under the influence of a long-wavelength laser field treated in the velocity-gauge dipole approximation.
Solution method: The propagator is constructed by separating the Hamiltonian into a large number of non-commuting terms, where each term can be handled simply and computationally efficiently (linear scaling). Time-reversibility of the propagator is ensured by combining the individual terms symmetrically around time midpoint (See ref. [1] and the text). The numerical accuracy is achieved through implicit representation of derivatives (accurate to $O (d^{4})$ for a uniform grid), combined with variable grid spacing.
Restrictions: Ill-conditioned Hamiltonians can occur for some choices or radial grids. The propagator is only approximately norm-conserving; small time steps may be necessary to achieve stable propagation.
Unusual features: Due to the implicit representation of the spatial derivative operators, the overall Hamiltonian is not Hermitian. As the result, the left wavefunction is no longer given by a complex conjugate of the right wavefunction, and must be propagated explicitly.
The code makes no assumptions on the accuracy of numerical types, and can be built for any real or integer kinds supported by the compiler. Detailed instructions for building the code in single, double, and quadruple precision are included.
Running time: Running time is input dependent. Time propagation of the Schrödinger equation scales as $O (N_{R} * (L_{MAX} + 1) * (M_{MAX} - M_{MIN} + 1))$ per time step. Preparation of the initial atomic state and analysis of the results in terms of the field-free atomic states may require $O (N_{R}^{3})$ and $O (N_{R}^{3} * (L_{MAX} + 1))$ work, respectively. On a 3.6 GHz core i7 desktop with 4 CPU cores available, run times are from 2 s (probability of a perturbative bound- to-bound transition in hydrogen atom) to 1 h (high-harmonic spectrum of a hydrogen atom driven by intense elliptically-polarised IR field).
References:
- [1]
  H.G. Muller, Laser Physics 9 (1999), 138–148.
DMTDHF: A full dimensional time-dependent Hartree-Fock program for diatomic molecules in strong laser fields
2015, Computer Physics Communications
We present the DMTDHF package, which investigates the non-perturbative electronic dynamics of diatomic molecules subjected to strong external laser fields by the fully propagated time-dependent Hartree–Fock theory. The package uses the prolate spheroidal coordinates, together with the finite-element method and discrete-variable representation, while short iterative Lanczos algorithm is employed for the time propagation. This package can be applied to diatomic molecules with many electrons, and is implemented to allow easy extensions for additional capabilities.
Program title: DMTDHF
Catalogue identifier: AEWN_v1_0
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEWN_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 702996
No. of bytes in distributed program, including test data, etc.: 7336872
Distribution format: tar.gz
Programming language: Fortran 2003.
Computer: All computers with a Fortran compiler supporting at least Fortran 2003.
Operating system: All operating systems with such a compiler. The makefile depends on a Unix-like system and needs modification under Windows.
Has the code been vectorized or parallelized?: The program is able to run both in sequential and parallel mode. For parallel running, the number of processors can be arbitrary.
RAM: Several GBs, depends on the size of the molecules and the number of DVR basis functions.
Classification: 16.1, 16.2, 16.6.
External routines: BLAS, LAPACK, FFTW3, MPI
Nature of problem: The investigation of molecules interacting with intense laser pulses requires non-perturbative theoretical treatment. It has been evidenced that multiorbital and multipole effects come into play for strong-field physics, while the direct numerical integration of TDSE is computationally prohibitive for systems with more than two electrons. TDHF goes beyond the SAE approach and includes the response to the field of all electrons, which is helpful to resolve the multielectron effects from the collective response of electrons.
Solution method: The package uses the prolate spheroidal coordinates, together with the finite-elements method and discrete-variable representation, while short iterative Lanczos algorithm is employed for the time propagation.
Restrictions: Currently, the spin-restricted form of TDHF is implemented, which can be applied to closed-shell molecules. However, the extension to spin-unrestricted form is straight forward.
Unusual features: Due to the prolate spheroidal coordinates, the Coulomb potential is treated accurately. The calculations can converge with only a mild number of basis functions and are highly efficient due to the nature of DVR functions in calculation of the two-electron integrals.
Running time: The running time depends on the size of the molecules, the number of basis functions, the duration of laser pulses, and the number of processors used. Depending on these factors, it can vary between a few hours and weeks.
SLIMP: Strong laser interaction model package for atoms and molecules
2015, Computer Physics Communications
Citation Excerpt :
In the high intensity regime it is no longer possible to describe the interaction of the field with molecules with perturbation theory, and many strong-field phenomena are theoretically poorly understood. The direct numerical integration of the time-dependent Schrödinger equation has been successful in explaining many experimental results, but this method is computationally prohibitive for systems with more than two electrons [7–10]. The popular approximations include the time-dependent Hartree–Fock (TDHF) theory [11,12], the time-dependent density functional theory (TDDFT) [13–16] and the multiconfiguration TDHF (MCTDHF) theory [17–19].
We present the SLIMP package, which provides an efficient way for the calculation of strong-field ionization rate and high-order harmonic spectra based on the single active electron approximation. The initial states are taken as single-particle orbitals directly from output files of the general purpose quantum chemistry programs GAMESS, Firefly and Gaussian. For ionization, the molecular Ammosov–Delone–Krainov theory, and both the length gauge and velocity gauge Keldysh–Faisal–Reiss theories are implemented, while the Lewenstein model is used for harmonic spectra. Furthermore, it is also efficient for the evaluation of orbital coordinates wavefunction, momentum wavefunction, orbital dipole moment and calculation of orbital integrations. This package can be applied to quite large basis sets and complex molecules with many atoms, and is implemented to allow easy extensions for additional capabilities.
Program title: SLIMP
Catalogue identifier: AEWE_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWE_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 90277
No. of bytes in distributed program, including test data, etc.: 927942
Distribution format: tar.gz
Programming language: Fortran 90.
Computer: All computers with a Fortran compiler supporting at least Fortran 90.
Operating system: All operating systems with such a compiler. The makefile depends on a Unix-like system and needs modification under Windows.
RAM: Memory requirement depends on the size of the molecules and the number of basis functions. For instance, about 2.8MB RAM is required for $N_{2}$ molecules with the acc-pvqz basis set (210 basis functions). However, the ${SF}_{6}$ molecules require 22MB RAM with the same basis set (739 basis functions).
Classification: 16.1, 16.10, 2.7.
Nature of problem: In modeling of atoms and molecules subjected to intense laser pulses, there is a general need for the calculation of theoretical models. However, the application of these models requires the effective evaluation of orbital coordinates wavefunction, momentum wavefunction, orbital dipole moment or calculation of orbital integrations. This package provides an efficient way for these calculations directly from the output files of the widely used GAMESS, Firefly and Gaussian programs.
Solution method: The molecular orbital is constructed from a linear combination of atomic orbitals, which is further expanded with Cartesian gaussian type orbitals (GTO). The orbital momentum wavefunction and dipole moment can be constructed with the Fourier transformed GTOs. Orbital integrations rely on the elementary integrations of GTOs. These results are used directly as input in the subsequent models calculations.
Restrictions: Current implementation supports the S, P L, D, F and G types, of GTOs. Here L indicates the diffuse basis. However, the extension to higher order basis is straight-forward. This package supports the versions of GAMESS (US, 2013), Firefly (8.1), and Gaussian (both 09 and 03). For older versions, mild modifications on the reading formats may be necessary in the modules.
Running time: The running time depends on the size of the molecules, the number of basis functions, and most importantly, on the problem to which this package has been employed. Typically for a single-processor PC-type computer it can vary between a few seconds and days.

View all citing articles on Scopus

^☆: This paper and its associated computer program are available via the Computer Physics Communications homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655).

¹: Permanent address: Computational Science and Engineering Department, Daresbury Laboratory, Warrington WA4 4AD, UK.

View full text

40th Anniversary IssueALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation☆