Theoretical Shaping of Femtosecond Laser Pulses for Molecular Photodissociation with Control Techniques Based on Ehrenfest′s Dynamics and Time‐Dependent Density Functional Theory

The combination of nonadiabatic Ehrenfest‐path molecular dynamics (EMD) based on time‐dependent density functional theory (TDDFT) and quantum optimal control formalism (QOCT) was used to optimize the shape of ultra‐short laser pulses to achieve photodissociation of a hydrogen molecule and the trihydrogen cation H₃⁺. This work completes a previous one [A. Castro, ChemPhysChem, 2013 , 14, 1488–1495], in which the same objective was achieved by demonstrating the combination of QOCT and TDDFT for many‐electron systems on static nuclear potentials. The optimization model, therefore, did not include the nuclear movement and the obtained dissociation mechanism could only be sequential: fast laser‐assisted electronic excitation to nonbonding states (during which the nuclei are considered to be static), followed by field‐free dissociation. Here, in contrast, the optimization was performed with the QOCT constructed on top of the full dynamic model comprised of both electrons and nuclei, as described within EMD based on TDDFT. This is the first numerical demonstration of an optimal control formalism for a hybrid quantum–classical model, that is, a molecular dynamics method.     

Local Control Theory in Trajectory Surface Hopping Dynamics Applied to the Excited‐State Proton Transfer of 4‐Hydroxyacridine

The application of local control theory combined with nonadiabatic ab initio molecular dynamics to study the photoinduced intramolecular proton transfer reaction in 4‐hydroxyacridine was investigated. All calculations were performed within the framework of linear‐response time‐dependent density functional theory. The computed pulses revealed important information about the underlying excited‐state nuclear dynamics highlighting the involvement of collective vibrational modes that would normally be neglected in a study performed on model systems constrained to a subset of the full configuration space. This study emphasizes the strengths of local control theory for the design of pulses that can trigger chemical reactions associated with the population of a given molecular excited state. In addition, analysis of the generated pulses can help to shed new light on the photophysics and photochemistry of complex molecular systems.     

Nonadiabatic molecular theory and its application. II. Water molecule

We introduce a new molecular theory beyond the Born–Oppenheimer approximation, where both electrons and nuclei are treated quantum mechanically and equivalently. First, we develop the coupled mean-field theory (CMFT) for both the electronic and nuclear fields. Then, to take into account the dynamic correlation between these particles, we develop a new molecular theory using the generator coordinate method (GCM) based upon the CMFT, which enables us to calculate the molecular eigenstate and eigenvalue directly. Finally, we apply this method to a water molecule and analyze the isotope effect on the vibrational frequency and the particle density. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 629–637, 1998     

Molecular integrals by numerical quadrature. I. Radial integration

 This article presents a numerical quadrature intended primarily for evaluating integrals in quantum chemistry programs based on molecular orbital theory, in particular density functional methods. Typically, many integrals must be computed. They are divided up into different classes, on the basis of the required accuracy and spatial extent. Ideally, each batch should be integrated using the minimal set of integration points that at the same time guarantees the required precision. Currently used quadrature schemes are far from optimal in this sense, and we are now developing new algorithms. They are designed to be flexible, such that given the range of functions to be integrated, and the required precision, the integration is performed as economically as possible with error bounds within specification. A standard approach is to partition space into a set of regions, where each region is integrated using a spherically polar grid. This article presents a radial quadrature which allows error control, uniform error distribution and uniform error reduction with increased number of radial grid points. A relative error less than 10⁻¹⁴ for all s-type Gaussian integrands with an exponent range of 14 orders of magnitude is achieved with about 200 grid points. Higher angular l quantum numbers, lower precision or narrower exponent ranges require fewer points. The quadrature also allows controlled pruning of the angular grid in the vicinity of the nuclei. Received: 30 August 2000 / Accepted: 21 December 2000 / Published online: 3 April 2001     

Broadband excitation pulses for high‐field solid‐state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses (“hard pulses”) are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid‐state samples under magic‐angle‐spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting ¹³C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer. Copyright © 2012 John Wiley & Sons, Ltd.     

Crystal structure based design of signal enhancement schemes for solid-state NMR of insensitive half-integer quadrupolar nuclei

A combination of density functional and optimal control theory has been used to generate amplitude- and phase-modulated excitation pulses tailored specifically for the (33)S nuclei in taurine, based on one of several reported crystal structures. The pulses resulted in significant signal enhancement (stemming from population transfer from the satellite transitions) without the need for any experimental optimization. This allowed an accurate determination of the (33)S NMR interaction parameters at natural abundance and at a moderate magnetic field strength (11.7 T). The (33)S NMR parameters, along with those measured from (14)N using frequency-swept pulses, were then used to assess the accuracy of various proposed crystal structures.     

Formulation of N- and v-representable density functional theory. IV. Non-Born–Oppenheimer approach

Local-scaling transformations are employed in order to formulate a desity functional theory where both electrons and nuclei are treated quantum mechanically. Because of the properties of these transformations, the ensuing version of density functional theory is N- and v- representable. In particular, we study the effect of these transformations on both densities and generating wave functions, and as a result, a functional for the energy expressed in terms of the electronic and nuclear densities is constructed. Plausible physical approximations for simplifying this electronic-nuclear functional are considered, and upon variation of the fuctional with respect to the electronic and nuclear densities, a system of coupled Euler–Lagrange equations is obtained.     

Quantum control of vibrational excitations in a heteronuclear diatomic molecule

Optimal control theory is applied to obtain infrared laser pulses for selective vibrational excitation in a heteronuclear diatomic molecule. The problem of finding the optimized field is phrased as a maximization of a cost functional which depends on the laser field. A time dependent Gaussian factor is introduced in the field prior to evaluation of the cost functional for better field shape. Conjugate gradient method^21,24 is used for optimization of constructed cost functional. At each instant of time, the optimal electric field is calculated and used for the subsequent quantum dynamics, within the dipole approximation. The results are obtained using both Morse potential as well as potential energy obtained using ab initio calculations.     

Mixed quantum-classical dynamics in the adiabatic representation to simulate molecules driven by strong laser pulses

The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynamics can be simulated quite accurately by a semiclassical surface-hopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na(2) using the surface-hopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.     

Grid-free DFT implementation of local and gradient-corrected XC functionals

Following an approach to density functional theory calculations based on the matrix representation of operators, we implemented a scheme as an alternative to traditional grid-based methods. These techniques allow integrals over exchange-correlation operators to be evaluated through matrix manipulations. Both local and gradient-corrected functionals can be treated in a similar way. After deriving all the required expressions, selected examples with various functionals are given. Received: 7 March 1998 / Accepted: 21 May 1998 / Published on line: 6 August 1998     

最优化“调控”区间分离密度泛函理论的研究进展

发展精确、高效的交换-关联泛函一直是密度泛函理论工作者所追求的神圣目标。传统密度泛函被证实在计算原子或分子体系的某些基态和激发态性能时存在困难,而且预测不具有普适性;另一方面,一些高水平方法如耦合簇（CC）理论和基于格林函数（G）和屏蔽库仑作用（W）近似的多体微扰理论（MBPT）,尽管相对精确但往往需要消耗昂贵的计算成本,因而其研究体系的尺寸和实用性受到了很大的限制。近年来,“最优化”调控区间分离泛函的发展在一定程度上使得上述问题得到改善,尤其是在消耗较少的计算成本前提下能够达到与高水平方法相媲美的预测精度,引起了越来越多的关注。本文首先简要回顾了密度泛函领域的理论背景,在区间分离密度泛函理论的基础上,重点介绍了最优化“调控”的概念;并且结合近期的理论工作对其在实际计算时的表现进行评价;最后,就最优化“调控”方法的前景和应用进行了展望。     

Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime

Our concept for a quantum computational system is based on qubits encoded in vibrational normal modes of polyatomic molecules. The quantum gates are implemented by shaped femtosecond laser pulses. We adopt this concept to the new species manganese pentacarbonyl bromide [MnBr(CO)5] and show that it is a promising candidate in the mid-infrared (IR) frequency range to connect theory and experiment. As direct reference for the ab initio calculations we evaluated experimentally the absorption bands of MnBr(CO)5 in the mid-IR as well as the related transition dipole moments. The two-dimensional potential-energy surface spanned by the two strongest IR active modes and the dipole vector surfaces are calculated with density-functional theory. The vibrational eigenstates representing the qubit system are determined. Laser pulses are optimized by multitarget optimal control theory to form a set of global quantum gates: NOT, CNOT, Pi, and Hadamard. For all of them simply structured pulses with low pulse energies around 1 microJ could be obtained. Exemplarily for the CNOT gate we investigated the possible transfer to experimental shaping, based on the mask function for pulse shaping in the frequency regime as well as decomposition into a train of subpulses.     

Quantum embedding for material chemistry based on domain separation and open subsystems

This perspective considers two theories we recently proposed to perform quantum embedding calculations for chemical systems: domain-separated density functional theory (DS-DFT) and locally coupled open subsystems (LCOS). The development includes both the fundamentals of each theory as well as potential applications, some technical aspects, and related challenges. DS-DFT is suited to study intramolecular effects, where one can apply a high level of theory (based on DFT or wave function theory) to a region of interest inside a molecule or solid and lower level theory elsewhere, with smooth switching between the regions. LCOS, in contrast, is a fragment-based embedding, which offers computational advantages to study intermolecular behavior such as electron hopping, spin-environment interaction, and charge-transfer excitations. However, both theories can exchange roles when appropriate. In addition, these theories allow for control of computational scaling of their algorithms. We explore paths to determine the charge-transfer operator used in LCOS, and suggest an auxiliary energy minimization that can provide a practical estimate to this operator. We also briefly discuss how to implement density fitting techniques in domain separation, and how domain separation can be used for pure wave function-based embedding.     

密度泛函活性理论中的Rényi熵, Tsallis熵和Onicescu信息能

根据密度泛函理论,分子的电子密度确定了该体系基态下的所有性质,其中包括结构和反应活性.如何运用电子密度泛函有效地预测分子反应活性仍然是一个有待解决的难题.密度泛函活性理论(DFRT)倾力打造这样一个理论和概念架构,使得运用电子密度以及相关变量准确地预测分子的反应特性成为可能.信息理论方法的香农熵和费舍尔信息就是这样的密度泛函,研究表明,它们均可作为反应活性的有效描述符.本文将在DFRT框架中介绍和引进三个密切相关的描述符, Rényi熵、Tsallis熵和Onicescu信息能.我们准确地计算了它们在一些中性原子和分子中的数值并讨论了它们随电子数量和电子总能量的变化规律.此外,以第二阶Onicescu信息能为例,在分子和分子中的原子两个层面上,系统地考察了其随乙烷二面角旋转的变化模式.这些新慨念的引入将为我们深入洞察和预测分子的结构和反应活性提供额外的描述工具.     

用密度泛函活性理论和Hammett常数预测单双取代苯酚的酸性

用从头算和密度泛函理论准确预测分子的酸碱性仍然是一个悬而未决的理论和计算难题. 近年来运用密度泛函活性理论(DFRT)发展的分子静电势和价自然原子轨道等概念为该问题的解决提供了一个简单而有效的途径. 最近我们还提出用Hammett常数预测分子酸碱性, 并发现对苯甲酸衍生物其预测精度与DFRT方法一致. 本文将这两个新方法运用于苯酚衍生物体系以验证其普适性, 一共计算了83个体系. 发现二者均可以得到较好的预测精度, 且DFRT方法比Hammett常数结果稍好. 对进一步从局部和整体角度理解分子性质的起源以及这些性质的决定因素提供了有益启示. 该文同时还验证了Hammett常数求和规则的普适性.     

Influence of molecular orientation on the photodissociation process of LiH molecules

Regulation of photodissociation dynamics of oriented LiH molecules in different dissociation channels is proposed based on time dependent quantum wave packet theory. The enhancement of molecular orientation on the photodissociation of LiH is obvious with our theoretical scheme. The results show that the molecular orientation in the ground state has a great effect on the angular distributions of wave packets. By using the proper laser pulses and controlling the polarization direction of the laser pulses, the enhancement of the photodissociation could be realized. After the molecular orientation, an optimal dissociation channel is observed with an improved dissociation probability. Compared with the results without molecular orientation, the maximal dissociation probability is increased by 8.1% in the indirect dissociation channel and 30.7% in the direct dissociation channel. The enhancement effect is more obvious in the direct dissociation channel, which provides a possible method to manipulate the dissociation of LiH molecules experimentally. Additionally, the photodissociation process of LiH also relies on the electric intensity and delay time of two pump pulses.     

Controlling Molecular Conductance: Switching Off π Sites through Protonation

Conductance switching through chemical modification of a molecular bridge is a major goal in molecular electronics, with the potential to lead to molecule‐based functional devices. In terms of switching speed, mechanisms that rely on only minor rearrangements of molecular structures are particularly promising. We demonstrate, based on density functional theory calculations combined with a coherent tunneling approach, how protonation and deprotonation of amine‐substituted or amine‐bridged model molecular wires can switch off and on π‐sites and thus: a) remove or introduce interference features in the electron transmission, and b) decrease or increase coupling along a chain. This mechanism may also be relevant for interactions between molecular bridges and metal cations, for example, in sensor applications.     

Time‐dependent density functional theory study on direction‐dependent electron and hole transfer processes in molecular systems

We report on real‐time time‐dependent density functional theory calculations on direction‐dependent electron and hole transfer processes in molecular systems. As a model system, we focus on α‐sulfur. It is shown that time scale of the electron transfer process from a negatively charged S₈ molecule to a neighboring neutral monomer is comparable to that of a strong infrared‐active molecular vibrations of the dimer with one negatively charged monomer. This results in a strong coupling between the electrons and the nuclei motion which eventually leads to S₈ ring opening before the electron transfer process is completed. The open‐ring structure is found to be stable. The similar infrared‐active peak in the case of hole transfer, however, is shown to be very weak and hence no significant scattering by the nuclei is possible. The presented approach to study the charge transfer processes in sulfur has direct applications in the increasingly growing research field of charge transport in molecular systems. © 2017 Wiley Periodicals, Inc.     

Development of a new density functional program for all-electron calculation of proteins

In this article, we propose a new molecular orbital program for all-electron calculation of proteins which is based on density functional theory. To carry it out in a fully analytical way, we adopted the (pure-) analytical Xα method and modified it for saving a lot of memories for large-scale calculations. The recent software technology sophisticated in information science is inevitably applied to achieve calculations of large molecular systems. The program is coded by the object-oriented language C + +, its output is shown graphically, and the most of the procedures in this program are controlled through an efficient graphical user interface developed by ourselves. Such technology supports the safe construction of the huge software, the tidy representation of enormous data, and the ready control of complex calculations. Test calculations with various sizes of glycine polypeptides indicate that the computation time is proportional to the 1.7 powers of the number of residues. This result suggests that the all-electron calculations of proteins consisting of over 1000 atoms could be performed with distributed and/or massively parallel computers. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 245–256, 1997