First-order Couplings Research Articles

Analytical derivative couplings within the framework of time-dependent density functional theory coupled with conductor-like polarizable continuum model: Formalism, implementation, and applications.

The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost.

Quantum simulation of tunable and ultrastrong mixed-optomechanics.

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.

Dynamic positioning of ROV in the wave zone during launch and recovery from a small surface vessel

Dynamical positioning (DP) control of a remotely operated vehicle (ROV) using thrusters is investigated as a means to increase operability of its launch and recovery system (LARS) on relatively small surface vessels. The ROV uses its DP control system to dynamically track the wave-driven motion of the surface vessel that may also be under DP control. We consider the critical phase when the ROV position is very close to the LARS. In this phase, the ROV’s motion is strongly influenced by first-order surface waves and hydrodynamic couplings from the surface vessel motion. Hence, there is risk of collision between the ROV and the surface vessel and its LARS. We employ a time-domain dynamic system simulator that calculates the coupled motions of both the surface vessel and the ROV to analyse and optimize the operability of the system. It is based on coupled added mass, damping and wave force response amplitude operators (RAO) for both the surface vessel and the ROV, which can be calculated using WAMIT coupled hydrodynamic multi-body computations, accounting also for the moonpool water column dynamics. Simulation results show the positive effect of the ROV DP on the operability of the LARS using statistical environmental data from the North Sea.

Experimental signatures of a new dark matter WIMP

The WIMP proposed here yields the observed abundance of dark matter, and is consistent with the current limits from direct detection, indirect detection, and collider experiments, if its mass is GeV/c 2. It is also consistent with analyses of the gamma rays observed by Fermi-LAT from the Galactic center (and other sources), and of the antiprotons observed by AMS-02, in which the excesses are attributed to dark matter annihilation. These successes are shared by the inert doublet model (IDM), but the phenomenology is very different: the dark matter candidate of the IDM has first-order gauge couplings to other new particles, whereas the present candidate does not. In addition to indirect detection through annihilation products, it appears that the present particle can be observed in the most sensitive direct-detection and collider experiments currently being planned.

Investigation of spatio-temporal stretching in a duplex grating compressor.

We employ the modified 6×6 matrix formalism to describe a pulsed Gaussian beam diffracted by a grating with arbitrary orientation. The matrix treatment is used to analyze the evolution of a pulsed beam propagating in a duplex grating compressor (DGC). For chirped pulse incidence, the inclination angle required in DGC setups will introduce several kinds of first-order spatio-temporal couplings (STCs). We found that temporal stretching due to spatial chirp is suppressed with enlarged beam diameter. Pulse-front tilt and residual frequency chirp in the compressed pulse will be eliminated simultaneously. Pulse with the transform-limited duration can be expected in ultra-intense and ultra-short pulse laser systems employing DGC.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation.

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born-Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions. Our scheme is based on quadratic response theory and includes orbital relaxation terms neglected in previous approaches. Simultaneous computation of multiple derivative couplings and energy gradients enables efficient multistate nonadiabatic molecular dynamics simulations in conjunction with Tully's fewest switches surface hopping (SH) method. We benchmark the thus obtained multistate TDDFT-SH scheme by simulating ultrafast decay of UV-photoexcited thymine, for which accurate gas-phase data from ultrafast spectroscopy experiments are available. The calculations predict a fast 153 fs decay from the bright S2 to the dark S1 excited state, followed by a much slower 14 ps S1 deactivation to the ground state; statistical uncertainties were estimated using bootstrap sampling. These results agree well with the experimentally observed time constants of 100-200 fs and 5-7 ps, respectively, unlike previous multiconfigurational self-consistent field and second-order algebraic diagrammatic construction calculations. Furthermore, our results support the S1-trapping hypothesis [J. J. Szymczak et al., J. Phys. Chem. A, 2009, 113, 12686-12693]. For thymine, the computational cost of a single TDDFT-SH time-step including the lowest 3 states, all couplings and gradients, is ∼5 times larger than the cost of a single Born-Oppenheimer dynamics time step for the ground state in our implementation. Thus, ps nonadiabatic dynamics simulations using multistate hybrid TDDFT-SH for systems with up to ∼100 atoms are possible without drastic approximations on single workstation nodes. Our implementation will be made available through Turbomole.

First-order nonadiabatic couplings in extended systems by time-dependent density functional theory.

We propose an ab initio formulation that enables a rigorous calculation of the first-order nonadiabatic couplings (NAC) between electronic states based on time-dependent density functional theory in conjunction with planewave bases, projector augmented-wave pseudopotentials, and hybrid exchange-correlation functionals. The linear and quadratic time-dependent response theory is used to derive analytic expressions for the NAC matrix elements. In contrast to the previous formulation in atomic basis sets, the present formulation eliminates explicit references to Kohn-Sham virtual orbitals. With the introduction of Lagrangian functionals, the present formulation circumvents expensive derivative calculations of Kohn-Sham orbitals with respect to ionic coordinates. As a validation of the formulation, the NAC matrix elements of small molecules LiH and HeH+ are calculated and compared to previous results with the atomic orbital basis. This development paves the way for accurate ab initio nonadiabatic molecular dynamics in extended systems.

Validity of the Born-Oppenheimer approximation in the indirect-dissociative-recombination process

An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of freedom. The two-dimensional $R$-matrix can be constructed simultaneously on the electronic and nuclear surfaces using all three forms developed previously for electron-atom and electron-molecule collisions. These are the eigenchannel $R$-matrix form, inversion technique of Nesbet and Robicheaux, and the Wigner-Eisenbud-type form using expansion over the poles of the symmetrized Hamiltonian. The 2D $R$-matrix method is employed to solve a simple model tailored to describe the dissociative recombination and the vibrational excitation of H$_2^+$ cation in the singlet ungerade symmetry $^1\Sigma_u$. These results then serve as a (near-exact) benchmark for the following calculation in which the $R$-matrix states are replaced by their Born-Oppenheimer approximations. The accuracy of this approach and its correction with the first-order nonadiabatic couplings are discussed.

Coupled Raman-Raman modes in the ionic Raman scattering process

We employ a lattice Hamiltonian to examine the dynamics of coupled normal modes excited through a nonlinear phononic process, extending the model beyond infrared and first-order Raman active mode couplings to include interactions between symmetry-allowed Raman active modes. We examine the strength of the interactions between two Raman active modes on the targeted driven-mode dynamics to confirm that all symmetry allowed Raman modes interact with each other. We apply the model to the correlated insulating ferromagnet YTiO3 and present the resulting renormalization effects on the driven-mode dynamics from the anharmonic interactions. Owing to the dependence of the displacive amplitude of the Raman active mode on such interactions, especially for those modes with small amplitude, we suggest that models of anharmonic phononic coupling in materials with electronic, ferroic, or superconducting properties derived from competing Raman-like distortions should include these low-order terms in the equations of motion describing the excited phonons to obtain accurate physical models.

On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections.

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

Visualizing spatiotemporal pulse propagation: first-order spatiotemporal couplings in laser pulses.

Even though a general theory of first-order spatiotemporal couplings exists in the literature, it is often difficult to visualize how these distortions affect laser pulses. In particular, it is difficult to show the spatiotemporal phase of pulses in a meaningful way. Here, we propose a general solution to plotting the electric fields of pulses in three-dimensional space that intuitively shows the effects of spatiotemporal phases. The temporal phase information is color-coded using spectrograms and color response functions, and the beam is propagated to show the spatial phase evolution. Using this plotting technique, we generate two- and three-dimensional images and movies that show the effects of spatiotemporal couplings.

First-order derivative couplings between excited states from adiabatic TDDFT response theory.

We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.

Comment on “Nonadiabatic couplings from the Kohn-Sham derivative matrix: Formulation by time-dependent density-functional theory and evaluation in the pseudopotential framework”

The issue of the ab initio evaluation of the first-order nonadiabatic couplings (NAC's) is re-examined. In particular, a recent derivation in Phys. Rev. A 82, 062508 (2010) of the NAC's is corrected by performing an extension of the derivation to the case of arbitrary values of the Kohn-Sham (KS) occupation factors. A single expression for the nonadiabatic couplings, valid both for integer and fractional values of the KS occupation factors, is provided.

一阶时空耦合高斯脉冲光束的传输特性研究

一阶时空耦合高斯脉冲光束的传输特性研究

Describing spatiotemporal couplings in ultrashort pulses using coupling coefficients

Three coupling coefficients are defined to describe spatiotemporal coupling in ultrashort pulses. With these coupling coefficients, the first-order spatiotemporal couplings of Gaussian pulse and beam are described analytically. Also, the first-order and the second-order spatiotemporal couplings caused by angular dispersion elements are studied using these coupling coefficients. It can be shown that these coupling coefficients are dimensionless and normalized, and readily indicate the severity of spatiotemporal coupling.

Diabatization Schemes for Generating Charge-Localized Electron-Proton Vibronic States in Proton-Coupled Electron Transfer Systems.

A scheme for the rigorous construction of charge-localized diabatic electron-proton vibronic states for proton-coupled electron transfer (PCET) reactions is presented. The diabatic electronic states are calculated using an adiabatic-to-diabatic transformation designed to ensure that the first-order nonadiabatic couplings with respect to a specified one-dimensional reaction coordinate vanish exactly. This scheme is applied to both symmetric and asymmetric PCET systems with several different one-dimensional reaction coordinates, including the hydrogen transfer coordinate, a normal mode coordinate, and the intrinsic reaction coordinate. This approach is also extended to describe the three-dimensional motion of the transferring hydrogen. The diabatic electronic states exhibit relatively invariant charge distributions along the reaction coordinate and are in excellent agreement with the analogous states obtained from the generalized Mulliken-Hush and Boys localization methods. Furthermore, these diabatic electronic states are combined with the associated proton vibrational wave functions to generate charge-localized electron-proton vibronic states that describe one- or three-dimensional hydrogen motion. These electron-proton vibronic states can be used to calculate the vibronic couplings, rate constants, and kinetic isotope effects of PCET reactions.

Proton-Coupled Electron Transfer versus Hydrogen Atom Transfer: Generation of Charge-Localized Diabatic States

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.

First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance

First-order nonadiabatic coupling matrix elements (NACMEs) are key for phenomena such as nonradiative transitions and excited-state decay, yet a consistent and practical first principles treatment has been elusive for molecules with more than a few heavy atoms. Here we present theory, implementation using Gaussian basis sets, and benchmarks of first-order NACMEs between ground and excited states in the framework of time-dependent hybrid density functional theory (TDDFT). A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined. In contrast to previous approaches, the present treatment produces exact analytical derivative couplings between time-dependent Kohn-Sham (TDKS) determinants in a finite atom-centered basis set. As in analytical gradient theory, derivative molecular orbital coefficients can be eliminated, making the computational cost independent of the number of nuclear degrees of freedom. Our expression reduces to the exact Chernyak-Mukamel formula for first-order NACMEs in the complete basis-set limit, but greatly improves basis-set convergence in finite atom-centered basis sets due to additional Pulay type terms. The Chernyak-Mukamel formula is shown to be equivalent to the Hellmann-Feynman contribution in analytical gradient theory. Our formalism may be implemented in TDDFT analytical excited-state gradient codes with minor modifications. Tests for systems with up to 147 atoms show that evaluation of first-order NACMEs causes total computation times to increase by an insignificant 10% on average. The resolution-of-the-identity approximation for the Coulomb energy (RI-J) reduces the computational cost by an order of magnitude for nonhybrid functionals, while errors are insignificant with standard auxiliary basis sets. We compare the computed NACMEs to full configuration interaction (FCI) in benchmark results for diatomic molecules; hybrid TDDFT and FCI are found to be in agreement for regions of the potential energy curve where the Kohn-Sham ground-state reference is stable and the character of the excitation is properly captured by the present functionals. With these developments, nonadiabatic molecular dynamics simulations of molecular systems in the 100 atoms regime are within reach.

Resolving the Structure of Ligands Bound to the Surface of Superparamagnetic Iron Oxide Nanoparticles by High-Resolution Magic-Angle Spinning NMR Spectroscopy

A major challenge in magnetic nanoparticle synthesis and (bio)functionalization concerns the precise characterization of the nanoparticle surface ligands. We report the first analytical NMR investigation of organic ligands stably anchored on the surface of superparamagnetic nanoparticles (MNPs) through the development of a new experimental application of high-resolution magic-angle spinning (HRMAS). The conceptual advance here is that the HRMAS technique, already being used for MAS NMR analysis of gels and semisolid matrixes, enables the fine-structure-resolved characterization of even complex organic molecules bound to paramagnetic nanocrystals, such as nanosized iron oxides, by strongly decreasing the effects of paramagnetic disturbances. This method led to detail-rich, well-resolved (1)H NMR spectra, often with highly structured first-order couplings, essential in the interpretation of the data. This HRMAS application was first evaluated and optimized using simple ligands widely used as surfactants in MNP synthesis and conjugation. Next, the methodology was assessed through the structure determination of complex molecular architectures, such as those involved in MNP3 and MNP4. The comparison with conventional probes evidences that HRMAS makes it possible to work with considerably higher concentrations, thus avoiding the loss of structural information. Consistent 2D homonuclear (1)H- (1)H and (1)H- (13)C heteronuclear single-quantum coherence correlation spectra were also obtained, providing reliable elements on proton signal assignments and carbon characterization and opening the way to (13)C NMR determination. Notably, combining the experimental evidence from HRMAS (1)H NMR and diffusion-ordered spectroscopy performed on the hybrid nanoparticle dispersion confirmed that the ligands were tightly bound to the particle surface when they were dispersed in a ligand-free solvent, while they rapidly exchanged when an excess of free ligand was present in solution. In addition to HRMAS NMR, matrix-assisted laser desorption ionization time-of-flight MS analysis of modified MNPs proved very valuable in ligand mass identification, thus giving a sound support to NMR characterization achievements.

The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams

We present a rigorous, but mathematically relatively simple and elegant, theory of first-order spatio-temporal distortions, that is, couplings between spatial (or spatial-frequency) and temporal (or frequency) coordinates, of Gaussian pulses and beams. These distortions include pulse-front tilt, spatial dispersion, angular dispersion, and a less well-known distortion that has been called "time vs. angle." We write pulses in four possible domains, xt, xomega, komega, and kt; and we identify the first-order couplings (distortions) in each domain. In addition to the above four "amplitude" couplings, we identify four new spatio-temporal "phase" couplings: "wave-front rotation," "wave-front-tilt dispersion," "angular temporal chirp," and "angular frequency chirp." While there are eight such couplings in all, only two independent couplings exist and are fundamental in each domain, and we derive simple expressions for each distortion in terms of the others. In addition, because the dimensions and magnitudes of these distortions are unintuitive, we provide normalized, dimensionless definitions for them, which range from -1 to 1. Finally, we discuss the definitions of such quantities as pulse length, bandwidth, angular divergence, and spot size in the presence of spatio-temporal distortions. We show that two separate definitions are required in each case, specifically, "local" and "global" quantities, which can differ significantly in the presence of spatio-temporal distortions.