The Influence of Dissipation on Vibrational Dynamics in a System of Two Interacting Electronic States

The vibrational dynamics of a nonadiabatic transition between two interacting electronic states in a molecular system in a thermal environment was considered. Two models were used. In one of these, both states, and in the other, only one state interacted with the environment. The electronic states were described by one-dimensional harmonic oscillators on the assumption that the interaction amplitude with the environment (bath) linearly depended on the coordinates of the bath and system. Model parameters typical of electron transfer in photosynthesis reaction centers were selected. The numerical solutions to the Redfield equations for the reduced density matrix were used to calculate the time characteristics of the system, including the mean vibrational energy, product population, and the degree of vibrational motion coherence. The influence of temperature and intensity of interactions with the bath on the time dependence of these values was studied. The character of vibrational dynamics had features common to both models, namely, (1) the vibrational energy monotonically decreased with the time, and this dependence was close to one-exponential in the majority of cases and (2) the time dependence of reaction yield, i.e., product population, was a step function, and the probability of the electron transition decreased as the temperature increased. It was found that there was a fundamental difference between the models under consideration: if only the reaction product interacted with the bath, vibrational coherence was retained for a long time (up to 2000 fs).     

Hybrid quantum/classical molecular dynamics for a proton transfer reaction coupled to a dissipative bath

A hybrid quantum/classical molecular dynamics approach is applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. In this approach, the proton is treated quantum mechanically and all bath modes are treated classically. The transition state theory rate constant is obtained from the potential of mean force, which is generated along a collective reaction coordinate with umbrella sampling techniques. The transmission coefficient, which accounts for dynamical recrossings of the dividing surface, is calculated with a reactive flux approach combined with the molecular dynamics with quantum transitions surface hopping method. The hybrid quantum/classical results agree well with numerically exact results in the spatial-diffusion-controlled regime, which is most relevant for proton transfer in proteins. This hybrid quantum/classical approach has already been shown to be computationally practical for studying proton transfer in large biological systems. These results have important implications for future applications to hydrogen transfer reactions in solution and proteins.     

An efficient molecular dynamics simulation method for calculating the diffusion-influenced reaction rates

We present a molecular dynamics (MD) simulation method for calculating the diffusion-influenced reaction rates in the limit of low reactant concentrations. To calculate the reaction rate coefficient, we use MD trajectories of a nonreactive equilibrium system that are initiated with a pair of reactant molecules in reactive configuration. Hence reaction systems involving complicated reactant molecules with geometrically restricted reactivities can be treated with comparable efficiency as the simple hard-sphere reaction system. Compared to the similar MD method proposed by Van Beijeren, Dong, and Bocquet [J. Chem. Phys. 114, 6265 (2001)], the present method has a couple of advantages. First, reactions involving more general sink functions can be treated. Second, more accurate results can be obtained when the reaction probability upon collision is less than unity. As an application, we investigate the effects of nondiffusive dynamics and hydrodynamic interaction of reactants on the reaction rate.     

甲酯化气相色谱法检测化妆品中防腐剂十一烯酸及其锌盐

采用硫酸催化甲酯化法检测了化妆品中的十一烯酸及其锌盐,并对甲酯化试剂、硫酸浓度、反应体系含水量、甲酯化温度、反应时间等条件进行了优化,发现反应体系的含水量对产率影响较明显。以5%硫酸甲醇溶液为甲酯化试剂,65℃水浴中反应1 h,正己烷为提取溶剂,采用GC/FID色谱法测定,外标法定量。十一烯酸甲酯产率达95%以上,该方法在0.05～1.0 mg范围内线性良好(r>0.999),检出限和定量下限分别为0.001 2%和0.004%。膏霜、乳液、化妆水和洗手液中十一烯酸的平均回收率为93%～104%,相对标准偏差为0.39%～5.1%。     

Stochastic surrogate Hamiltonian

The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath.     

Stereochemical studies—VIII Unequivocal determination of the absolute configuration in biaryl systems

According to the reaction sequences shown in Figs 1-5, the absolute configuration of optically active biaryl derivatives such as biphenyl, binaphthyl, bianthryl and bianthroaquinonyl have been clearly established, based on the standard compound (R)-(+)-I, in the binaphthyl system, whose absolute configuration was unequivocally determined by the anomalous X-ray diffraction method.     

离子色谱法测定蚀刻槽废氢氟酸中的六氟硅酸

建立了一种新的检测蚀刻槽废氢氟酸中六氟硅酸的离子色谱方法。色谱柱为Metrosep A Supp 7阴离子交换柱,流动相为3.2 mmol/L碳酸钠-1.0 mmol/L碳酸氢钠,流速为0.7 mL/min。六氟硅酸经过抑制型电导检测器后进行衍生化反应,在360 nm波长下用紫外检测器检测。六氟硅酸的线性范围为2.4~120 mg/L,相关系数r²大于0.999,定量限为0.24 mg/L,平均加标回收率为97.2%。本方法还可以同时利用电导检测器检测废氢氟酸中的氢氟酸、醋酸、盐酸、硝酸、磷酸和硫酸的含量。该方法快速、准确,适用于蚀刻槽液中六氟硅酸的检测。     

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.     

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths

The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.     

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.     

A self-consistent coulomb bath model using density fitting

A self-consistent Coulomb bath model is presented to provide an accurate and efficient way of performing calculations for interfragment electrostatic and polarization interactions. In this method, a condensed-phase system is partitioned into molecular fragment blocks. Each fragment is embedded in the Coulomb bath due to other fragments. Importantly, the present Coulomb bath is represented using a density fitting method in which the electron densities of molecular fragments are fitted using an atom-centered auxiliary basis set of Gaussian type. The Coulomb bath is incorporated into an effective Hamiltonian for each fragment, with which the electron density is optimized through an iterative double self-consistent field (DSCF) procedure to realize the mutual many-body polarization effects. In this work, the accuracy of interfragment interaction energies enumerated using the Coulomb bath is tested, showing a good agreement with the exact results from an energy decomposition analysis. The qualitative features of many-body polarization effects are visualized by electron density difference plots. It is also shown that the present DSCF method can yield fast and robust convergence with near-linear scaling in performance with increase in system size.     

Gas and liquid phases interaction at the FeO·Cr2O3 cathode of a direct-current arc discharge

The study of an arc discharge in argon has been made with the cathode of the discharge system in the form of molten chromite, FeO·Cr₂O₃. The partial pressure distributions of the elements Fe and Cr, as well as the temperature distributions, have been determined in the arc by spectroscopic methods. The data obtained were used, in conjunction with a mathematical model, for the determination of the oxygen species distribution in the same medium. The cathode bath surface was measured by means of the two-wavelength method. From a consideration of free energy of reaction values, it is concluded that the presence of elemental Fe and Cr in the cathode bath is mainly related to the migration of Fe⁺ and Cr⁺, present in the arc, toward the liquid cathode. The formation of these elements in the molten cathode is very unlikely.     

Reaction rate calculation with time-dependent invariant manifolds

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment.     

Effect of phase transfer chemistry, segmented fluid flow, and sonication on the synthesis of cinnamic esters

Wittig reaction under Phase Transfer conditions was performed in a flow reaction system. Different bases, aldehydes, phosphonium salts, and flow reaction parameters were investigated, in absence of a phase transfert catalyst. An improvement of the reaction outcome (yield and reaction time) was achieved through the immersion of the reactor into an ultrasound bath.     

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

The recently proposed mixed quantum-classical method is extended to applications at finite temperatures. The method is designed to treat complex systems consisting of a low-dimensional quantum part (the primary system) coupled to a dissipative bath described classically. The method is based on a formalism showing how to systematically correct the approximate zeroth-order evolution rule. The corrections are defined in terms of the total quantum Hamiltonian and are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary system is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on a standard model system describing proton transfer in a condensed-phase environment: a symmetric double-well potential bilinearly coupled to a bath of harmonic oscillators. Flux correlation functions and thermal rate constants have been calculated at two different temperatures for a range of coupling strengths. The results have been compared to the fully quantum simulations of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] with the real path integral method.     

Influence of Temperature on the Formation of Silver Nanoparticles by using a Seed‐Free Photochemical Method under Sodium‐Lamp Irradiation

Silver nanoparticles can be prepared by using a seed‐free photo‐assisted citrate reduction method under the irradiation of a sodium lamp. Under the same irradiation intensity, bath temperatures are crucial in influencing the reaction rate, morphologies of final products, and shape evolution of the silver nanostructures. For example, when the bath temperature is 80 °C, the product yields of silver nanoplates, nanorods, and nanodecahedra are 38±6 %, 35±10 %, and 12±8 %, respectively. However, when the bath temperature is 30 °C, the product yields of silver nanoplates, nanorods, and nanodecahedra are 6±3 %, 0 %, and 83±16 %, respectively. Time‐dependent UV/Vis spectra and TEM images show that silver nanoplates were formed at the earlier reaction stage and greatly decreased in amount at the later stage when the bath temperatures are less than or equal to 40 °C. This indicates that the silver nanoplates, which can be regarded as intermediates, are kinetically favored products. They are not thermodynamically favored products at these relatively low bath temperatures. The SERS spectra of crystal violet (CV) show that all the silver colloids synthesized at various temperatures exhibit good enhancement factors and that the colloids prepared at lower bath temperatures have a higher enhancement factor.     

A local coherent-state approximation to system-bath quantum dynamics

A novel quantum method to deal with typical system-bath dynamical problems is introduced. Subsystem discrete variable representation and bath coherent-state sets are used to write down a multiconfigurational expansion of the wave function of the whole system. With the help of the Dirac-Frenkel variational principle, simple equations of motion--a kind of Schrodinger-Langevin equation for the subsystem coupled to (pseudo) classical equations for the bath--are derived. True dissipative dynamics at all times is obtained by coupling the bath to a secondary, classical Ohmic bath, which is modeled by adding a friction coefficient in the derived pseudoclassical bath equations. The resulting equations are then solved for a number of model problems, ranging from tunneling to vibrational relaxation dynamics. Comparison of the results with those of exact, multiconfiguration time-dependent Hartree calculations in systems with up to 80 bath oscillators shows that the proposed method can be very accurate and might be of help in studying realistic problems with very large baths. To this end, its linear scaling behavior with respect to the number of bath degrees of freedom is shown in practice with model calculations using tens of thousands of bath oscillators.     

毛细管电泳-电化学检测法测定硫酸铜-维生素C反应体系中的羟基自由基和菊花的抗氧化活性

采用毛细管电泳-电化学检测方法,以对羟基苯甲酸为自由基捕捉剂,测定了硫酸铜-维生素C反应体系(pH 7.4)中生成的羟基自由基。研究了电极电位、运行液的pH值、电泳电压及进样时间对体系中反应物和产物分离的影响,得到了最优化的测定条件;讨论了体系中各反应物浓度和反应时间对产物浓度的影响。以直径为300 μm的碳圆盘电极为检测电极,工作电极电位为0.95 V(vs.SCE),目标产物3,4-二羟基苯甲酸在1.5×10-4~6.0×10-6 mol/L范围内线性关系良好,检测限（S/N=3）为1.5×10-6 mol/L。应用该方法,研究测定了不同品种菊花的抗氧化活性。