arXiv subjects

J. L. Alonso

Publications and source records attributed to J. L. Alonso.

At least 37 records · Page 2Linked to original sources

arXiv2013

Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" [J. Chem. Phys. 137, 22A530 (2012)]

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment.

physics.chem-ph↗

arXiv2012

Non-adiabatic effects within a single thermally-averaged potential energy surface: Thermal expansion and reaction rates of small molecules

At non-zero temperature and when a system has low-lying excited electronic states, the ground-state Born--Oppenheimer approximation breaks down and the low-lying electronic states are involved in any chemical process. In this work, we use a temperature-dependent effective potential for the nuclei which can accomodate the influence of an arbitrary number of electronic states in a simple way, while at the same time producing the correct Boltzmann equibrium distribution for the electronic part. With the help of this effective potential, we show that thermally-activated low-lying electronic states can have a significant effect in molecular properties for which electronic excitations are oftentimes ignored. We study the thermal expansion of the Manganese dimer, Mn$_2$, where we find that the average bond length experiences a change larger than the present experimental accuracy upon the inclusion of the excited states into the picture. We also show that, when these states are taken into account, reaction rate constants are modified. In particular, we study the opening of the ozone molecule, O$_3$, and show that in this case the rate is modified as much as a 20% with respect to the ground-state Born--Oppenheimer prediction.

physics.chem-ph↗

arXiv2012

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.

physics.chem-ph↗

arXiv2011

An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptide

physics.comp-ph↗

arXiv2011

Statistics and Nosé formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schrödinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nosé (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.

physics.chem-ph↗

arXiv2011

On the Combination of TDDFT with Molecular Dynamics: New Developments

In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we wish to look at (including dynamical properties or observables dependent on excited states) there is a corresponding functional of the ground-state density. Yet the unavailability of such magic functionals in many cases (the theorem is a non-constructive existence result) demands the development and use of the alternative exact reformulation of quantum mechanics provided by TDDFT. This theory defines a convenient route to electronic excitations and to the dynamics of a many-electron system subject to an arbitrary time-dependent perturbation. This is, in fact, the main purpose of inscribing TDDFT in a MD framework -the inclusion of the effect of electronic excited states in the dynamics. However, as we will show in this review, it may not be the only use of TDDFT in this context. In this manuscript, we review two recent proposals: In Section 1.2, we show how TDDFT can be used to design efficient gsBOMD algorithms -even if the electronic excited states are in this case not relevant. The work described in Section 1.3 addresses the problem of mixed quantum-classical systems at thermal equilibrium.

cond-mat.str-el↗

arXiv2010

Geometry and Statistics of Ehrenfest dynamics

Quantum dynamics (e.g., the Schrödinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the presence of extra structure in the quantum case, that leads to the appearance of the probabilistic nature of the measurements and the indetermination and superposition principles. In this paper we first show that the quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann's distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. This work provides the basis for extending stochastic methods to Ehrenfest dynamics.

quant-ph↗

arXiv2010

Ab Initio Molecular Dynamics on the Electronic Boltzmann Equilibrium Distribution

We prove that for a combined system of classical and quantum particles, it is possible to write a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In addition, these molecular dynamics do not need to assume that the electrons immediately follow the nuclear motion (in contrast to any adiabatic approach), and do not present problems in the presence of crossing points between different potential energy surfaces (conical intersections or spin-crossings). A practical application of this molecular dynamics to study the effect of temperature in molecular systems presenting (nearly) degenerate states - such as the avoided crossing in the ring-closure process of ozone - is presented.

cond-mat.other↗

arXiv2009

A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], 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.

cond-mat.mtrl-sci↗

arXiv2008

Efficient formalism for large scale ab initio molecular dynamics based on time-dependent density functional theory

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schroedinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations.

cond-mat.mtrl-sci↗

arXiv2007

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.

physics.chem-ph↗

arXiv2007

Efficient model chemistries for peptides. I. Split-valence Gaussian basis sets and the heterolevel approximation in RHF and MP2

We present an exhaustive study of more than 250 ab initio potential energy surfaces (PESs) of the model dipeptide HCO-L-Ala-NH2. The model chemistries (MCs) used are constructed as homo- and heterolevels involving possibly different RHF and MP2 calculations for the geometry and the energy. The basis sets used belong to a sample of 39 selected representants from Pople's split-valence families, ranging from the small 3-21G to the large 6-311++G(2df,2pd). The reference PES to which the rest are compared is the MP2/6-311++G(2df,2pd) homolevel, which, as far as we are aware, is the more accurate PES of a dipeptide in the literature. The aim of the study presented is twofold: On the one hand, the evaluation of the influence of polarization and diffuse functions in the basis set, distinguishing between those placed at 1st-row atoms and those placed at hydrogens, as well as the effect of different contraction and valence splitting schemes. On the other hand, the investigation of the heterolevel assumption, which is defined here to be that which states that heterolevel MCs are more efficient than homolevel MCs. The heterolevel approximation is very commonly used in the literature, but it is seldom checked. As far as we know, the only tests for peptides or related systems, have been performed using a small number of conformers, and this is the first time that this potentially very economical approximation is tested in full PESs. In order to achieve these goals, all data sets have been compared and analyzed in a way which captures the nearness concept in the space of MCs.

q-bio.QM↗

arXiv2006

Definition of Systematic, Approximately Separable and Modular Internal Coordinates (SASMIC) for macromolecular simulation

A set of rules is defined to systematically number the groups and the atoms of organic molecules and, particularly, of polypeptides in a modular manner. Supported by this numeration, a set of internal coordinates is defined. These coordinates (termed Systematic, Approximately Separable and Modular Internal Coordinates, SASMIC) are straightforwardly written in Z-matrix form and may be directly implemented in typical Quantum Chemistry packages. A number of Perl scripts that automatically generate the Z-matrix files for polypeptides are provided as supplementary material. The main difference with other Z-matrix-like coordinates normally used in the literature is that normal dihedral angles (``principal dihedrals'' in this work) are only used to fix the orientation of whole groups and a somewhat non-standard type of dihedrals, termed ``phase dihedrals'', are used to describe the covalent structure inside the groups. This physical approach allows to approximately separate soft and hard movements of the molecule using only topological information and to directly implement constraints. As an application, we use the coordinates defined and ab initio quantum mechanical calculations to assess the commonly assumed approximation of the free energy, obtained from ``integrating out'' the side chain degree of freedom chi, by the Potential Energy Surface (PES) in the protected dipeptide HCO-L-Ala-NH2. We also present a sub-box of the Hessian matrix in two different sets of coordinates to illustrate the approximate separation of soft and hard movements when the coordinates defined in this work are used.

q-bio.BM↗

arXiv2006

Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the Alanine dipeptide

If constraints are imposed on a macromolecule, two inequivalent classical models may be used: the stiff and the rigid one. This work studies the effects of such constraints on the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2 without any simplifying assumption. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of all the correcting terms to the naive CED based in the Potential Energy Surface (PES) that appear when the constraints are considered. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.

q-bio.QM↗

arXiv2006

Effects of constraints in general branched molecules: A quantitative ab initio study in HCO-L-Ala-NH2

A general approach to the design of accurate classical potentials for protein folding is described. It includes the introduction of a meaningful statistical measure of the differences between approximations of the same potential energy, the definition of a set of Systematic and Approximately Separable and Modular Internal Coordinates (SASMIC), much convenient for the simulation of general branched molecules, and the imposition of constraints on the most rapidly oscillating degrees of freedom. All these tools are used to study the effects of constraints in the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of the correcting terms to the naive CED based in the Potential Energy Surface (PES) without any simplifying assumption. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.

q-bio.BM↗

arXiv2005

A physically meaningful method for the comparison of potential energy functions

In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient r has no units and allows only semi-quantitative statements to be made. Those that do have units of energy and whose value may be compared to a physically relevant scale, such as the root mean square deviation (RMSD), the mean error of the energies (ER), the standard deviation of the error (SDER) or the mean absolute error (AER), overestimate the distance between potentials. Moreover, their precise statistical meaning is far from clear. In this article, a new measure of the distance between potential energy functions is defined which overcomes the aforementioned difficulties. In addition, its precise physical meaning is discussed, the important issue of its additivity is investigated and some possible applications are proposed. Finally, two of these applications are illustrated with practical examples: the study of the van der Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y) and the comparison of different levels of the theory in the ab initio study of the Ramachandran map of the model peptide HCO-L-Ala-NH2.

q-bio.QM↗

arXiv2004

Phase diagram of the (bosonic) Double-Exchange Model

The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

cond-mat.str-el↗

arXiv2002

Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.

gr-qc↗