Papers by Jhon Fredy Pérez Torres
In this work, we adopt a quantum mechanical approach based on time-dependent density functional t... more In this work, we adopt a quantum mechanical approach based on time-dependent density functional theory (TDDFT) to study the optical and electronic properties of alizarin supported on TiO 2 nano-crystallites, as a prototypical dye-sensitized solar cell. To ensure proper alignment of the donor (alizarin) and acceptor (TiO 2 nano-crystallite) levels, static optical excitation spectra are simulated using time-dependent density functional theory in response. The ultrafast photoelectron transfer from the dye to the cluster is simulated using an explicitly time-dependent, one-electron TDDFT ansatz. The model considers the δ-pulse excitation of a single active electron localized in the dye to the complete set of energetically accessible, delocalized molecular orbitals of the dye/nano-crystallite complex. A set of quantum mechanical tools derived from the transition electronic flux density is introduced to visualize and analyze the process in real time. The evolution of the created wave packet subject to absorbing boundary conditions at the borders of the cluster reveal that, while the electrons of the aromatic rings of alizarin are heavily involved in an ultrafast charge redistribution between the carbonyl groups of the dye molecule, they do not contribute positively to the electron injection and, overall, they delay the process.
The Journal of Physical Chemistry C, 2015
The electronic and structural details for the acetylene selective catalytic activation by one of ... more The electronic and structural details for the acetylene selective catalytic activation by one of the few small gold clusters whose experimental gas-phase initial geometry in neutral charge state is known, the gold heptamer, are investigated. Doing an exhaustive search of the acetylene-gold heptamer ZORA scalar relativistic PW91/TZ2P configurational space, we determine the main, secondary, and also the unimportant structures relative to the catalytic activation. We found that the leading mechanism of activation consists in the tendency to the disappearance of one of the acetylene π bonds at the expense of the formation of C-Au strong interactions, by the predominant dative interaction of s/d-like gold heptamer molecular orbitals toward a π* orbital of acetylene. This results in adducts having very diminished energy barriers toward processes such as, for example, the selective hydrogenation reaction to ethylene. This activation would occur with a considerable change of the participant species geometries and, with the formation of a frontier single occupied molecular orbital, very localized at carbon atoms region.
Computation of the Electronic Flux Density in the Born–Oppenheimer Approximation
The Journal of Physical Chemistry A, 2013
A molecule in the electronic ground state described in the Born–Oppenheimer approximation (BOA) b... more A molecule in the electronic ground state described in the Born–Oppenheimer approximation (BOA) by the wave function ΨBO = Φ0χ0 (where Φ0 is the time-independent electronic energy eigenfunction and χ0 is a time-dependent nuclear wave packet) exhibits a nonzero nuclear flux density, whereas it always displays zero electronic flux density (EFD), because the electrons are in a stationary state. A hierarchical approach to the computation of the EFD within the context of the BOA, which utilizes only standard techniques of quantum chemistry (to obtain Φ0) and quantum dynamics (to describe the evolution of χ0 on the ground-state potential energy surface), provides a resolution of this puzzling, nonintuitive result. The procedure is applied to H2(+) oriented parallel with the z-axis and vibrating in the ground state (2)Σg(+). First, Φ0 and χ0 are combined by the coupled-channels technique to give the normally dominant z-component of the EFD. Imposition of the constraints of electronic continuity, cylindrical symmetry of Φ0 and two boundary conditions on the EFD through a scaling procedure yields an improved z-component, which is then used to compute the complementary orthogonal ρ-component. The resulting EFD agrees with its highly accurate counterpart furnished by a non-BOA treatment of the system.
Photoionization of Oriented HD(1Σ+) Yields Vibrating HD+(2Σ+) with Charge Breathing and Small Charge Transfer
The Journal of Physical Chemistry A
Two Novel Approaches Based on the Thompson Theory and Shape Analysis for Determination of Equilibrium Structures of Nanoclusters: Cu8, Ag8 and Ag18 as study cases
Journal of Physics: Conference Series, 2019
Two new efficient methods for finding stable atomic clusters are introduced in this work. A purel... more Two new efficient methods for finding stable atomic clusters are introduced in this work. A purely algebraic and geometrical approach based on shape analysis provides a consistent set for optimization of structures which converge to local and global low-energy configurations. A second proposal based on the Thompson theory gives also candidate structures which became in equilibrium faster than the standard stochastic search models. The performance of the approaches is compared in three metal atomic clusters involving magic numbers. Both methods find the global and local low-energy structures reported in literature, but also obtain new structures. For Cu8, Ag8 and Ag18 the shape analysis method provides more structures than the approach based on Thompson theory.
Journal of Chemical Education, 2019
The aim of this article is to present a set of simple exercises that help the students of a secon... more The aim of this article is to present a set of simple exercises that help the students of a second course in quantum chemistry to understand that some molecular properties do not improve even when the molecular energy improves with an increasing number of basis functions in the expansion of the wavefunction. The essential idea is to create a dilemma for the students by showing that a wavefunction that gives a better energy (i.e., lower, according to the variational principle) may not yield a better value for another molecular property. The first exercise is to calculate the ground-state energy of the hydrogen atom for the contracted 1s STO-2G basis function; the second is to compute the ground-state energy for the STO-2G basis function reformulated as a linear variational function; the third is to calculate the expectation value of the electron-nuclear distance for the two approximate wavefunctions. Comparison of the approximate results with the exact one reveals starkly the dilemma of the "best wavefunction". The set of exercises presented here are interesting to any quantum mechanics course.
Physical Review A, 2017
We compute the entanglement between the electronic and vibrational motions in the simplest molecu... more We compute the entanglement between the electronic and vibrational motions in the simplest molecular system, the hydrogen molecular ion, considering the molecule as a bipartite system, electron and vibrational motion. For that purpose we compute an accurate total non-Born-Oppenheimer wave function in terms of a huge expansion using nonorthogonal B-spline basis sets that expand separately the electronic and nuclear wave functions. According to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, it is possible to find a much shorter but equivalent expansion in terms of the natural orbitals or Schmidt bases for the electronic and nuclear half spaces. Here we extend the Schmidt decomposition theorem to the case in which nonorthogonal bases are used to span the partitioned Hilbert spaces. This extension is first illustrated with two simple coupled systems, the former without an exact solution and the latter exactly solvable. In these model systems of distinguishable coupled particles it is shown that the entanglement content does not increase monotonically with the excitation energy, but only within the manifold of states that belong to an existing excitation mode, if any. In the hydrogen molecular ion the entanglement content for each non-Born-Oppenheimer vibronic state is quantified through the von Neumann and linear entropies and we show that entanglement serves as a witness to distinguish vibronic states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.
Multidirectional Angular Electronic Flux during Adiabatic Attosecond Charge Migration in Excited Benzene
The Journal of Physical Chemistry A, 2016
Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the f... more Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the first time, with application to the oriented iodoacetylene cation where AACM starts from the initial superposition of the ground state (φ0) and an electronic excited state (φ1). Here, we develop the theory for electronic fluxes during AACM in ring-shaped molecules, with application to oriented benzene prepared in the superposition of the ground and first excited singlet states. The initial state and its time evolution are analogous to coherent tunneling where φ0 and φ1 have different meanings; however, they denote the wave functions of the lowest tunneling doublet. This analogy suggests to transfer the theory of electronic fluxes during coherent tunneling to AACM, with suitable modifications which account for (i) the different time scales and (ii) the different electronic states, and which make use of (iii) the preparation of the initial state for AACM by a linearly polarized laser pulse. Application to benzene yields the multidirectional angular electronic flux with a pincer-motion type pattern during AACM: this unequivocal result confirms a previous working hypothesis. Moreover, the theory of AACM allows quantification of the electronic flux; that is, the maximum number of electrons (out of 42) which flow concertedly during AACM in benzene is 6 × 0.08 = 0.48.
Physical Chemistry Chemical Physics, 2015
Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B4.
Physical Review A, 2014
The presence of net circular dichroism in the photoionization of nonchiral homonuclear molecules ... more The presence of net circular dichroism in the photoionization of nonchiral homonuclear molecules has been put in evidence recently through the measurement of molecular-frame photoelectron angular distributions in dissociative photoionization of H 2 [Dowek et al., Phys. Rev. Lett. 104, 233003 (2010)]. In this work we present a detailed study of circular dichroism in the photoelectron angular distributions of H 2 and D 2 molecules, oriented perpendicularly to the propagation vector of the circularly polarized light, at different photon energies (20, 27, and 32.5 eV). Circular dichroism in the angular distributions at 20 and to a large extent 27 eV exhibits the usual pattern in which inversion symmetry is preserved. In contrast, at 32.5 eV, the inversion symmetry breaks down, which eventually leads to total circular dichroism after integration over the polar emission angle. Time-dependent ab initio calculations support and explain the observed results for H 2 in terms of quantum interferences between direct photoionization and delayed autoionization from the Q 1 and Q 2 doubly excited states into ionic states (1sσ g and 2pσ u ) of different inversion symmetry. Nevertheless, for D 2 at 32.5 eV, there is a particular case where theory and experiment disagree in the magnitude of the symmetry breaking: when D + ions are produced with an energy of around 5 eV. This reflects the subleties associated to such simple molecules when exposed to this fine scrutiny.
Molecules, 2015
In this work, we adopt a quantum mechanical approach based on time-dependent density functional t... more In this work, we adopt a quantum mechanical approach based on time-dependent density functional theory (TDDFT) to study the optical and electronic properties of alizarin supported on TiO 2 nano-crystallites, as a prototypical dye-sensitized solar cell. To ensure proper alignment of the donor (alizarin) and acceptor (TiO 2 nano-crystallite) levels, static optical excitation spectra are simulated using time-dependent density functional theory in response. The ultrafast photoelectron transfer from the dye to the cluster is simulated using an explicitly time-dependent, one-electron TDDFT ansatz. The model considers the δ-pulse excitation of a single active electron localized in the dye to the complete set of energetically accessible, delocalized molecular orbitals of the dye/nano-crystallite complex. A set of quantum mechanical tools derived from the transition electronic flux density is introduced to visualize and analyze the process in real time. The evolution of the created wave packet subject to absorbing boundary conditions at the borders of the cluster reveal that, while the electrons of the aromatic rings of alizarin are heavily involved in an ultrafast charge redistribution between the carbonyl groups of the dye molecule, they do not contribute positively to the electron injection and, overall, they delay the process.
The Journal of Physical Chemistry A, 2015
The nuclear and electronic probability and flux densities for a vibrating and dissociating H 2 + ... more The nuclear and electronic probability and flux densities for a vibrating and dissociating H 2 + molecular ion in the electronic and rotational ground state (corresponding to the quantum numbers 2 Σ g + ,JM = 00) are calculated. As a consequence of the isotropy of the scenario, the vibrating H 2 + appears as a pulsating quantum bubble, while the dissociating H 2 + appears as an exploding quantum bubble. The dissociating part is represented by a discretization of the continuum through use of 2 integrable B-spline basis set. It is shown that the vibrating part (the pulsating quantum bubble) interferes with the dissociating part (the exploding quantum bubble) and that the interference is much more noticeable in the probability density than in the flux density.
Physical Review A, 2015
Pump-probe spectroscopy has allowed the construction of the nuclear probabihty density p (R ,t) a... more Pump-probe spectroscopy has allowed the construction of the nuclear probabihty density p (R ,t) as a function of the internuclear bond distance (/?) and the time (/) in diatomic molecules and consequent deduction of the nuclear flux density j(R ,t). Thus, the two observables [p (R ,t),j(R ,t)] comprise a very detailed description of the nuclear motion in ultrafast molecular dynamics. Here a Fourier analysis of j( R .t) is proposed and compared with the already existing Fourier analysis of p(R ,t). It is shown that the two power spectra \p(R,u>\ T)\2 and | j{R,<D\ T )|2 provide the same information in the frequency domain a>, but entirely different information in the spatial domain (i.e., along the R coordinate).
Probing Electron Dynamics in Simple Molecules with Attosecond Pulses
Springer Series in Chemical Physics, 2012
Attosecond pulses are an ideal tool to explore electron and nuclear dynamics in atoms and molecul... more Attosecond pulses are an ideal tool to explore electron and nuclear dynamics in atoms and molecules. Either as single attosecond pulses (SAP), in attosecond pulse trains (APT), or in combination with infrared (IR) pulses, these pulses, with frequencies in the VUV-XUV regime, have been widely used to probe ionization, electron tunneling, or autoionization in atoms. More recently, similar processes have been studied in molecules. A correct theoretical description of such processes in molecules often requires a fully dimensional treatment due to the important role of nuclear motion and electron correlation. This restricts ab initio calculations to the simplest molecules. In this chapter, we discuss single ionization of hydrogen molecules (H2 and D2) induced by time-delayed SAP+IR and APT+IR schemes. Ab initio time-dependent theoretical calculations are compared with existing experiments.
Probing vibrational wave packets in molecular excited states
Theoretical Chemistry Accounts, 2010
A time-dependent theoretical method is used to describe a UV pump–UV probe strategy to trace, at ... more A time-dependent theoretical method is used to describe a UV pump–UV probe strategy to trace, at a femtosecond time scale, the motion of vibrational wave packets created in excited states of the hydrogen molecule by measuring single ionization probabilities. We use a spectral method to solve the time-dependent Schrödinger equation in full dimensionality, including correlation and all electronic and vibrational
Vibrating H2+(2Σg+, JM = 00) Ion as a Pulsating Quantum Bubble in the Laboratory Frame
The Journal of Physical Chemistry A, 2014
We present quantum dynamics simulations of the concerted nuclear and electronic densities and flu... more We present quantum dynamics simulations of the concerted nuclear and electronic densities and flux densities of the vibrating H2(+) ion with quantum numbers (2)Σg(+), JM = 00 corresponding to the electronic and rotational ground state, in the laboratory frame. The underlying theory is derived using the nonrelativistic and Born–Oppenheimer approximations. It is well-known that the nuclear density of the nonrotating ion (JM = 00) is isotropic. We show that the electronic density is isotropic as well, confirming intuition. As a consequence, the nuclear and electronic flux densities have radial symmetry. They are related to the corresponding densities by radial continuity equations with proper boundary conditions. The time evolutions of all four observables, i.e., the nuclear and electronic densities and flux densities, are illustrated by means of characteristic snapshots. As an example, we consider the scenario with initial condition corresponding to preparation of H2(+) by near-resonant weak field one-photon-photoionization of the H2 molecule in its ground state, (1)Σg(+), vJM = 000. Accordingly, the vibrating, nonrotating H2(+) ion appears as pulsating quantum bubble in the laboratory frame, quite different from traditional considerations of vibrating H2+ in the molecular frame, or of the familiar alternative scenario of aligned vibrating H2(+) in the laboratory frame.
Physical Review Letters, 2013
When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear f... more When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear flux density, was introduced by Schro ¨dinger in 1926, but until now, it has not been measured. Here the first experimental results are deduced from high-resolution pump-probe measurements of the time-dependent nuclear densities in a vibrating diatomic molecule or molecular ion. The nuclear densities are converted to flux densities by means of the continuity equation. The flux densities are much more sensitive to timedependent quantum effects than the densities. Applications to the sodium molecule and the deuterium molecular ion unravel four new effects; e.g., at the turns from bond stretch to compression, the flux of the nuclei exhibits multiple changes of directions, from small to large bond lengths, a phenomenon that we call the ''quantum accordion.''
Physical Review Letters, 2010
Circular dichroism is a consequence of chirality. However, nonchiral molecules can also exhibit i... more Circular dichroism is a consequence of chirality. However, nonchiral molecules can also exhibit it when the measurement itself introduces chirality, e.g., when measuring molecular-frame photoelectron angular distributions. The few such experiments performed on homonuclear diatomic molecules show that, as expected, circular dichroism vanishes when the molecular-frame photoelectron angular distributions are integrated over the polar electron emission angle. Here we show that this is not the case in resonant dissociative ionization of H 2 for photons of 30-35 eV, which is the consequence of the delayed ionization from molecular doubly excited states into ionic states of different inversion symmetry.
Physical Review A, 2010
Using a novel split-mirror set-up attached to a Reaction Microscope at the Free electron LASer in... more Using a novel split-mirror set-up attached to a Reaction Microscope at the Free electron LASer in Hamburg (FLASH) we demonstrate an XUV-pump -XUV-probe ) 38 ( eV = ω experiment by tracing the ultra-fast nuclear wave-packet motion in the D 2 + (1sσ g -state) with <10 fs time resolution. Comparison with time-dependent calculations yields excellent agreement with the measured vibrational period of 22±4 fs in D 2 + , points to the importance of the inter-nuclear distance dependent ionization probability and paves the way to control sequential and non-sequential two-photon double ionization contributions. COLCIENCIAS. The European COST Action "CUSPFEL" (CM0702) is also acknowledged. Computations were carried out at Mare Nostrum BSC and CCC-UAM.
Physical Review A, 2009
Photoelectron angular distributions from fixed-in-space H 2 molecules exposed to ultrashort xuv l... more Photoelectron angular distributions from fixed-in-space H 2 molecules exposed to ultrashort xuv laser pulses have been evaluated. The theoretical method is based on the solution of the time-dependent Schrödinger equation in a basis of stationary states that include all electronic and vibrational degrees of freedom. Asymmetric angular distributions are observed as a consequence of the delayed ionization from the H 2 doubly excited states, which induces interferences between gerade and ungerade ionization channels. The analysis of this asymmetry as a function of pulse duration can provide an estimate of the corresponding autoionization widths.
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Papers by Jhon Fredy Pérez Torres