title: Modified Ehrenfest Formalism for Efficient Large-Scale ab initio Molecular Dynamics.
abstract: We present in detail the recently derived ab initio molecular dynamics (AIMD) formalism [Alonso et al. Phys. Rev. Lett. 2008, 101, 096403], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work, we provide the formal details of the new method, describe its implementation, and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave function representation, making it suitable for inclusion in any AIMD software package.
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: Xavier
authors.initials: X
authors.lastname: Andrade
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: Alberto
authors.initials: A
authors.lastname: Castro
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: David
authors.initials: D
authors.lastname: Zueco
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: J L
authors.initials: JL
authors.lastname: Alonso
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: Pablo
authors.initials: P
authors.lastname: Echenique
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: Fernando
authors.initials: F
authors.lastname: Falceto
authors.affiliation: Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Mixto CSIC-UPV, and DIPC, Edificio Korta, Av. Tolosa 72, E-20018 San Sebastián, Spain, Institut für Theoretisch Physik, Freie Universität Berlin, Arnimallee, 14, Berlin 14195, Deutschland, Institut für Physik, Universität Augsburg, Universitätsstraβe 1, D-86135 Augsburg, Germany, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain, and Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
authors.forename: Ángel
authors.initials: Á
authors.lastname: Rubio