Experimental and Modeling Study on the Ignition Kinetics of Nitromethane behind Reflected Shock Waves.

Nitromethane (NM) is the simplest nitroalkane fuel and has demonstrated potential usage as propellant and fuel additive. Thus, understanding the combustion characteristics and chemistry of NM is critical to the development of hierarchical detailed kinetic models of nitro-containing energetic materials. Herein, to further investigate the ignition kinetics of NM and supplement the experimental database for kinetic mechanism development, an experimental and kinetic modeling analysis of the ignition delay times (IDTs) of NM behind reflected shock waves at high fuel concentrations is reported against previous studies. Specifically, the IDTs of NM are measured via a high-pressure shock tube within the temperature from 900 to 1150 K at pressures of 5 and 10 bar and equivalence ratios of 0.5, 1.0, and 2.0. Brute-force sensitivity analysis and chemical explosive mode analysis in combination with reaction path analysis are employed to reveal the fundamental ignition kinetics of NM. Finally, a skeletal mechanism for NM is derived via the combination of directed relation graph-based methods, which demonstrates good prediction accuracy of NM ignition and flame speeds. The present work should be valuable for understanding the combustion chemistry of NM and the development of the fundamental reaction mechanism of nitroalkane fuels.

Pentacyclic triterpene-amino acid derivatives induced apoptosis and autophagy in tumor cells, affected the JNK and PI3K/AKT/mTOR pathway.

A series of pentacyclic triterpene-amino acid derivatives were synthesized and tested for anti-proliferative activity. The results showed that most of the target compounds had good anti-proliferative activity. 2c did not contain protecting groups and hydrochloride, had excellent cytotoxicity, so it had been selected for further study in the mechanism of action in T24 cells. The data from transcriptome sequencing indicated that 2c was found to be closely related to apoptosis and autophagy. Observation of fluorescence staining and analysis from flow cytometry demonstrated that 2c induced apoptosis and cause cell cycle arrest in S/G2 phase in T24 cells. Molecular mechanism studies exhibited that 2c induced apoptosis in the intrinsic and extrinsic pathways. 2c also induced cellular autophagy in T24 cells. Results from Western Blotting showed that 2c could activate JNK pathway and inhibit PI3K/AKT/mTOR pathway. In conclusion, 2c was deserved further investigation in the field of anti-tumor.

Experimental and Kinetic Modeling Study on High-Temperature Autoignition of Cyclohexene.

Cyclohexene is an important intermediate during the oxidation of cycloalkanes, which comprise a significant portion of real fuels. Thus, experimental data sets and kinetic models of cyclohexene play an important role in the understanding of the combustion of cycloalkanes and real fuels. In this work, an experimental and kinetic modeling study of the high-temperature ignition of cyclohexene is performed. Ignition delay time (IDT) measurements are carried out in a high-pressure shock tube (HPST). The studied pressures are 5, 10, and 20 bar; the equivalence ratios are 0.5, 1.0, and 2.0; and the temperatures range from 980 to 1400 K for IDT in HPST. It is shown that the IDTs of cyclohexene exhibit Arrhenius behaviors as a function of temperature, and the IDTs decrease as the equivalence ratio and pressure increase. The experimental results are simulated using three previous detailed kinetic mechanisms and an updated detailed mechanism in this work. The updated detailed kinetic mechanism exhibits good agreement with experimental results. Reaction path analysis and sensitivity analysis are performed to provide insights into the chemical kinetics controlling the ignition of cyclohexene. The results demonstrate that different detailed kinetic mechanisms are significantly different, and there are still no unified conclusions about the major reaction path for cyclohexene oxidation. However, it is worth noting that the abstraction reaction by oxygen at the allylic site and the submechanism of cyclopentene are of significant importance for the accurate prediction of IDTs of cyclohexene. The present experimental data set and kinetic model should be valuable to improve our understanding of the combustion chemistry of cycloalkanes.

A Hierarchical Theoretical Study of the Hydrogen Abstraction Reactions of H2/C1-C4 Molecules by the Methyl Peroxy Radical and Implications for Kinetic Modeling.

The hydrogen atom abstraction by the methyl peroxy radical (CH3O2) is an important reaction class in detailed chemical kinetic modeling of the autoignition properties of hydrocarbon fuels. Systematic theoretical studies are performed on this reaction class for H2/C1-C4 fuels, which is critical in the development of a base model for large fuels. The molecules include hydrogen, alkanes, alkenes, and alkynes with a carbon number from 1 to 4. The B2PLYP-D3/cc-pVTZ level of theory is employed to optimize the geometries of all of the reactants, transition states, and products and also the treatments of hindered rotation for lower frequency modes. Accurate benchmark calculations for abstraction reactions of hydrogen, methane, and ethylene with CH3O2 are performed by using the coupled cluster method with explicit inclusion of single and double electron excitations and perturbative inclusion of triple electron excitations (CCSD(T)), the domain-based local pair-natural orbital coupled cluster method (DLPNO-CCSD(T)), and the explicitly correlated CCSD(T)-F12 method with large basis sets. Reaction rate constants are computed via conventional transition state theory with quantum tunneling corrections. The computed rate constants are compared with literature values and those employed in detailed chemical kinetic mechanisms. The calculated rate constants are implemented into the recently developed NUIGMECH1.1 base model for kinetic modeling of ignition properties.

Machine Learning Prediction of the Exfoliation Energies of Two-Dimension Materials via Data-Driven Approach.

Exfoliation energy is one of the fundamental parameters in the science and engineering of two-dimensional (2D) materials. Traditionally, it was obtained via indirect experimental measurement or first-principles calculations, which are very time- and resource-consuming. Herein, we provide an efficient machine learning (ML) method to accurately predict the exfoliation energies for 2D materials. Toward this end, a series of simple descriptors with explicit physical meanings are defined. Regression trees (RT), support vector machines (SVM), multiple linear regression (MLR), and ensemble trees (ET) are compared to develop the most suitable model for the prediction of exfoliation energies. It is shown that the ET model can efficiently predict the exfoliation energies through extensive validations and stability analysis. The influence of the defined features on the exfoliation energies is analyzed by sensitivity analysis to provide novel physical insight into the affecting factors of the exfoliation energies.

Data-driven machine learning model for the prediction of oxygen vacancy formation energy of metal oxide materials.

Metal oxides are widely used in the fields of chemistry, physics and materials science. Oxygen vacancy formation energy is a key parameter to describe the chemical, mechanical, and thermodynamic properties of metal oxides. How to acquire quickly and accurately oxygen vacancy formation energy remains a challenge for both experimental and theoretical researchers. Herein, we propose a machine learning model for the prediction of oxygen vacancy formation energy via data-driven analysis and the definition of simple descriptors. Starting with the database containing oxygen vacancy formation energies for 1750 metal oxides with enough structural diversity, new descriptors that effectively avoid the defects of molecular fingerprints, molecular graphic descriptors and site descriptors are defined. The descriptors have obvious physical meanings and wide practicability. Multiple linear regression analysis is then used to screen important features for machine learning model development, and two strongly associated features are obtained. The selected descriptors are used as input for the training of 21 machine learning models to select and develop the most accurate machine learning model. Finally, it is shown that the least squares support vector regression method exhibits the best performance for accurate prediction of the targeted oxygen vacancy formation energy through systematic error analysis, and the prediction accuracy is also verified by the external dataset. Our work establishes a novel and simple computational approach for accurate prediction of the oxygen vacancy formation energy of metal oxides and highlights the availability of data-driven analysis for metal oxide material research.

Single-Pulse Shock Tube Experimental and Kinetic Modeling Study on Pyrolysis of a Direct Coal Liquefaction-Derived Jet Fuel and Its Blends with the Traditional RP-3 Jet Fuel.

A basic understanding of the high-temperature pyrolysis process of jet fuels is not only valuable for the development of combustion kinetic models but also critical to the design of advanced aeroengines. The development and utilization of alternative jet fuels are of crucial importance in both military and civil aviation. A direct coal liquefaction (DCL) derived liquid fuel is an important alternative jet fuel, yet fundamental pyrolysis studies on this category of jet fuels are lacking. In the present work, high-temperature pyrolysis studies on a DCL-derived jet fuel and its blend with the traditional RP-3 jet fuel are carried out by using a single-pulse shock tube (SPST) facility. The SPST experiments are performed at averaged pressures of 5.0 and 10.0 bar in the temperature range around 900-1800 K for 0.05% fuel diluted by argon. Major intermediates are obtained and quantified using gas chromatography analysis. A flame-ionization detector and a thermal conductivity detector are used for species identification and quantification. Ethylene is the most abundant product for the two fuels in the pyrolysis process. Other important intermediates such as methane, ethane, propyne, acetylene, and 1,3-butadiene are also identified and quantified. The pyrolysis product distributions of the pure RP-3 jet fuel are also performed. Kinetic modeling is performed by using a modern detailed mechanism for the DCL-derived jet fuel and its blends with the RP-3 jet fuel. Rate-of-production analysis and sensitivity analysis are conducted to compare the differences of the chemical kinetics of the pyrolysis process of the two jet fuels. The present work is not only valuable for the validation and development of detailed combustion mechanisms for alternative jet fuels but also improves our understanding of the pyrolysis characteristics of alternative jet fuels.

Accelerating the optimization of enzyme-catalyzed synthesis conditions via machine learning and reactivity descriptors.

Enzyme-catalyzed synthesis reactions are of crucial importance for a wide range of applications. An accurate and rapid selection of optimal synthesis conditions is crucial and challenging for both human knowledge and computer predictions. In this work, a new scenario, which combines a data-driven machine learning (ML) model with reactivity descriptors, is developed to predict the optimal enzyme-catalyzed synthesis conditions and the reaction yield. Fourteen reactivity descriptors in total are constructed to describe 125 reactions (classified into five categories) included in different reaction mechanisms. Nineteen ML models are developed to train the dataset and the Quadratic support vector machine (SVM) model is found to exhibit the best performance. The Quadratic SVM model is then used to predict the optimal reaction conditions, which are subsequently used to obtain the highest yield among 109 200 reaction conditions with different molar ratios of substrates, solvents, water contents, enzyme concentrations and temperatures for each reaction. The proposed protocol should be generally applicable to a diverse range of chemical reactions and provides a black-box evaluation for optimizing the reaction conditions of organic synthesis reactions.

Single-Pulse Shock Tube Pyrolysis Study of RP-3 Jet Fuel and Kinetic Modeling.

A single-pulse shock tube study of the pyrolysis of two different concentrations of Chinese RP-3 jet fuel at 5 bar in the temperature range of 900-1800 K has been performed in this work. Major intermediates are obtained and quantified using gas chromatography analysis. A flame-ionization detector and a thermal conductivity detector are used for species identification and quantification. Ethylene is the most abundant product in the pyrolysis process. Other important intermediates such as methane, ethane, propyne, acetylene, butene, and benzene are also identified and quantified. Kinetic modeling is performed using several detailed, semidetailed, and lumped mechanisms. It is found that the predictions for the major species such as ethylene, propene, and methane are acceptable. However, current kinetic mechanisms still need refinement for some important species. Different kinetic mechanisms exhibit very different performance in the prediction of certain species during the pyrolysis process. The rate of production (ROP) is carried out to compare the differences among these mechanisms and to identify major reaction pathways to the formation and consumption of the important species, and the results indicate that further studies on the thermal decomposition of 1,3-butadiene are needed to optimize kinetic models. The experimental data are expected to contribute to a database for the validation of mechanisms under pyrolytic conditions for RP-3 jet fuel and should also be valuable to a better understanding of the combustion behavior of RP-3 jet fuel.

Benchmark calculations for bond dissociation energies and enthalpy of formation of chlorinated and brominated polycyclic aromatic hydrocarbons.

Thermodynamic properties, i.e., bond dissociation energies and enthalpy of formation, of chlorinated and brominated polycyclic aromatic hydrocarbons play a fundamental role in understanding their formation mechanisms and reactivity. Computational electronic structure calculations routinely used to predict thermodynamic properties of various species are limited for these compounds due to large computational cost to obtain accurate results by employing high-level wave function theory methods. In this work, a number of composite model chemistry methods (CBS-QB3, G3MP2, G3, and G4) are used to compute bond dissociation energies and enthalpies of formation of small to medium-size chlorinated and brominated polycyclic aromatic hydrocarbon compounds. The enthalpy of formation is derived via the atomization method and compared against the recommended values. Statistical analysis indicates that G4 is the best method. For comparison, three commonly used density functional theory (DFT) methods (M06-2X, ωB97X-D and B2PLYP-D3) with various basis sets including 6-311++G(d, p), cc-pVTZ, and cc-pVQZ in the prediction of bond dissociation energies and enthalpies of formation have been tested using the optimized geometries at the same M06-2X/6-311++G(d, p) level of theory. It is found that ωB97X-D/6-311++G(d, p) shows the best performance in computing the bond dissociation energies, while ωB97X-D/cc-pVTZ exhibits the best prediction in enthalpy of formation of the studied reaction systems. The structural effect on the bond dissociation energies and enthalpy of formation of chlorinated and brominated polycyclic aromatic hydrocarbons are then systematically analyzed. Based on comparisons of the various methods, reliable DFT methods are recommended for future theoretical studies on large chlorinated and brominated polycyclic aromatic hydrocarbons considering both accuracy and computational cost. This work, to the authors' knowledge, is the first to systematically benchmark theoretical methods for the accurate prediction of thermodynamic properties for chlorinated and brominated polycyclic aromatic hydrocarbons.

Hindered rotor benchmarks for the transition states of free radical additions to unsaturated hydrocarbons.

The hindered internal rotors of 32 transition states (TSs) formed through four free radicals, namely methyl, vinyl, ethyl, methoxy (CH3, C2H3, C2H5, CH3) additions to acetylene, ethylene, allene, propyne, and propene (C2H2/C2H4/C3H4-a/C3H4-p/C3H6) are studied. To validate the uncertainties of rate constants that stem from the use of different electronic structure methods to treat hindered rotors, the rotations of the newly formed C-C and/or C-O rotors in the transition states are calculated using commonly used DFT methods (B3LYP, M06-2X, ωB97X-D and B2PLYP-D3 with two Pople basis sets (6-31+G(d,p), 6-311++G(d,p)) and cc-pVTZ). The hindrance potential energies V(χ) calculated using the M06-2X/6-311++G(d,p) method are benchmarked at the CCSD(T), CCSD(T)-F12, DLPNO-CCSD(T) levels of theory with cc-pVTZ-F12 and cc-pVXZ (X = T, Q) basis sets and are extrapolated to the complete basis set (CBS) limit. The DLPNO-CCSD(T)/CBS method is proven to reproduce the CCSD(T)/CBS energies within 0.5 kJ mol-1 and this method is selected as the benchmark for all of the rotors in this study. Rotational constants B(χ) are computed for each method based on the optimized geometries for the hindrance potential via the I(2,3) approximation. Thereafter, the V(χ) and B(χ) values are used to compute hindered internal rotation partition functions, QHR, as a function of temperature. The uncertainties in the V(χ), B(χ) and QHR calculations stem from the use of different DFT methods for the internal rotor treatment are discussed for these newly formed rotors. For rotors formed by + C2 alkenes/alkynes, the V(χ) and QHR values calculated using DFT methods are compared with the DLPNO-CCSD(T)/CBS results and analysed according to reaction types. Based on comparisons of the DFT methods with the benchmarking method, reliable DFT methods are recommended for the treatment of internal rotors for different reaction types considering both accuracy and computational cost. This work, to the authors' knowledge, is the first to systematically benchmark hindrance potentials which can be used to estimate uncertainties in theoretically derived rate constants arising from the choice of different electronic structure methods.

Chemical Kinetics of Hydrogen Atom Abstraction from Propargyl Sites by Hydrogen and Hydroxy Radicals.

Hydrogen atom abstraction from propargyl C-H sites of alkynes plays a critical role in determining the reactivity of alkyne molecules and understanding the formation of soot precursors. This work reports a systematic theoretical study on the reaction mechanisms and rate constants for hydrogen abstraction reactions by hydrogen and hydroxy radicals from a series of alkyne molecules with different structural propargyl C-H atoms. Geometry optimizations and frequency calculations for all species are performed at M06-2X/cc-pVTZ level of theory and the hindered internal rotations are also treated at this level. The high-level W1BD and CCSD(T)/CBS theoretical calculations are used as a benchmark for a series of DFT calculations toward the selection of accurate DFT functionals for large reaction systems in this work. Based on the quantum chemistry calculations, rate constants are computed using the canonical transition state theory with tunneling correction and the treatment of internal rotations. The effects of the structure and reaction site on the energy barriers and rate constants are examined systematically. To the best of our knowledge, this work provides the first systematic study for one of the key initiation abstraction reactions for compounds containing propargyl hydrogen atoms.

Reaction Mechanisms and Kinetics of the Hydrogen Abstraction Reactions of C4⁻C6 Alkenes with Hydroxyl Radical: A Theoretical Exploration.

The reaction of alkenes with hydroxyl (OH) radical is of great importance to atmospheric and combustion chemistry. This work used a combined ab initio/transition state theory (TST) method to study the reaction mechanisms and kinetics for hydrogen abstraction reactions by OH radical on C4⁻C6 alkenes. The elementary abstraction reactions involved were divided into 10 reaction classes depending upon the type of carbon atoms in the reaction center. Geometry optimization was performed by using DFT M06-2X functional with the 6-311+G(d,p) basis set. The energies were computed at the high-level CCSD(T)/CBS level of theory. Linear correlation for the computed reaction barriers and enthalpies between M06-2X/6-311+G(d,p) and CCSD(T)/CBS methods were found. It was shown that the C=C double bond in long alkenes not only affected the related allylic reaction site, but also exhibited a large influence on the reaction sites nearby the allylic site due to steric effects. TST in conjunction with tunneling effects were employed to determine high-pressure limit rate constants of these abstraction reactions and the computed overall rate constants were compared with the available literature data.

The identification of active N species in N-doped carbon carriers that improve the activity of Fe electrocatalysts towards the oxygen evolution reaction.

Nitrogen-doped carbon nanomaterials have become some of the most effective carriers for transition metal-based electrocatalysts towards the oxygen evolution reaction. However, the specific active nitrogen species in nitrogen-doped carriers remains unclear up to now. To identify the active nitrogen species, herein, we prepare nitrogen-doped carbon nanospheres containing different types of nitrogen species and a small amount of Fe atoms. Electrochemical tests demonstrate that the Fe/nitrogen-doped carbon nanospheres with more graphitic nitrogen exhibit much higher activity for the oxygen evolution reaction than those with more pyridinic nitrogens and pyrrolic nitrogens in alkaline media, revealing that the graphitic nitrogen is the active species that greatly improves the activity of Fe catalysts. Density functional theory calculations further reveal that the graphitic nitrogen enhances the activity and stability of Fe-based catalysts mainly through increasing the adsorption energy, charge and spin densities of the Fe atoms loaded around it. These findings provide a brand-new perspective for rationally designing more effective transition metal-based electrocatalysts for the oxygen evolution reaction through controlling the active graphitic nitrogen distribution in carbon carriers.

Reaction Kinetics of Hydrogen Atom Abstraction from C4-C6 Alkenes by the Hydrogen Atom and Methyl Radical.

Alkenes are important ingredients of realistic fuels and are also critical intermediates during the combustion of a series of other fuels including alkanes, cycloalkanes, and biofuels. To provide insights into the combustion behavior of alkenes, detailed quantum chemical studies for crucial reactions are desired. Hydrogen abstractions of alkenes play a very important role in determining the reactivity of fuel molecules. This work is motivated by previous experimental and modeling evidence that current literature rate coefficients for the abstraction reactions of alkenes are still in need of refinement and/or redetermination. In light of this, this work reports a theoretical and kinetic study of hydrogen atom abstraction reactions from C4-C6 alkenes by the hydrogen (H) atom and methyl (CH3) radical. A series of C4-C6 alkene molecules with enough structural diversity are taken into consideration. Geometry and vibrational properties are determined at the B3LYP/6-31G(2df,p) level implemented in the Gaussian-4 (G4) composite method. The G4 level of theory is used to calculate the electronic single point energies for all species to determine the energy barriers. Conventional transition state theory with Eckart tunneling corrections is used to determine the high-pressure-limit rate constants for 47 elementary reaction rate coefficients. To faciliate their applications in kinetic modeling, the obtained rate constants are given in the Arrhenius expression and rate coefficients for typical reaction classes are recommended. The overall rate coefficients for the reaction of H atom and CH3 radical with all the studied alkenes are also compared. Branching ratios of these reaction channels for certain alkenes have also been analyzed.

ReaxFF molecular dynamics simulations of oxidation of toluene at high temperatures.

Aromatic hydrocarbon fuels, such as toluene, are important components in real jet fuels. In this work, reactive molecular dynamics (MD) simulations employing the ReaxFF reactive force field have been performed to study the high-temperature oxidation mechanisms of toluene at different temperatures and densities with equivalence ratios ranging from 0.5 to 2.0. From the ReaxFF MD simulations, we have found that the initiation consumption of toluene is mainly through three ways, (1) the hydrogen abstraction reactions by oxygen molecules or other small radicals to form the benzyl radical, (2) the cleavage of the C-H bond to form benzyl and hydrogen radicals, and (3) the cleavage of the C-C bond to form phenyl and methyl radicals. These basic reaction mechanisms are in good agreement with available chemical kinetic models. The temperatures and densities have composite effects on toluene oxidation; concerning the effect of the equivalence ratio, the oxidation reaction rate is found to decrease with the increasing of equivalence ratio. The analysis of the initiation reaction of toluene shows that the hydrogen abstraction reaction dominates the initial reaction stage at low equivalence ratio (0.5-1.0), while the contribution from the pyrolysis reaction increases significantly as the equivalence ratio increases to 2.0. The apparent activation energies, E(a), for combustion of toluene extracted from ReaxFF MD simulations are consistent with experimental results.

Effects of fuel additives on the thermal cracking of n-decane from reactive molecular dynamics.

Thermal cracking of n-decane and n-decane in the presence of several fuel additives are studied in order to improve the rate of thermal cracking by using reactive molecular dynamics (MD) simulations employing the ReaxFF reactive force field. From MD simulations, we find the initiation mechanisms of pyrolysis of n-decane are mainly through two pathways: (1) the cleavage of a C-C bond to form smaller hydrocarbon radicals, and (2) the dehydrogenation reaction to form an H radical and the corresponding decyl radical. Another pathway is the H-abstraction reactions by small radicals including H, CH(3), and C(2)H(5). The basic reaction mechanisms are in good agreement with existing chemical kinetic models of thermal decomposition of n-decane. Quantum mechanical calculations of reaction enthalpies demonstrate that the H-abstraction channel is easier compared with the direct C-C or C-H bond-breaking in n-decane. The thermal cracking of n-decane with several additives is further investigated. ReaxFF MD simulations lead to reasonable Arrhenius parameters compared with experimental results based on first-order kinetic analysis. The different chemical structures of the fuel additives greatly affect the apparent activation energy and pre-exponential factors. The presence of diethyl ether (DEE), methyl tert-butyl ether (MTBE), 1-nitropropane (NP), 3,6,9-triethyl-3,6,9-trimethyl-1,2,4,5,7,8-hexaoxonane (TEMPO), triethylamine (TEA), and diacetonediperodixe (DADP) exhibit remarkable promoting effect on the thermal cracking rates, compared with that of pure n-decane, in the following order: NP > TEMPO > DADP > DEE (∼MTBE) > TEA, which coincides with experimental results. These results demonstrate that reactive MD simulations can be used to screen for fuel additives and provide useful information for more comprehensive chemical kinetic model studies at the molecular level.

Computational study of the reaction mechanism of the methylperoxy self-reaction.

To provide insight on the reaction mechanism of the methyperoxy (CH(3)O(2)•) self-reaction, stationary points on both the spin-singlet and the spin-triplet potential energy surfaces of 2(CH(3)O(2)•) have been searched at the B3LYP/6-311++G(2df,2p) level. The relative energies, enthalpies, and free energies of these stationary points are calculated using CCSD(T)/cc-pVTZ. Our theoretical results indicate that reactions on a spin-triplet potential energy surface are kinetically unfavorable due to high free energy barriers, while they are more complicated on the spin-singlet surface. CH(3)OOCH(3) + O(2)(1) can be produced directly from 2(CH(3)O(2)•), while in other channels, three spin-singlet chain-structure intermediates are first formed and subsequently dissociated to produce different products. Besides the dominant channels producing 2CH(3)O• + O(2) and CH(3)OH + CH(2)O + O(2) as determined before, the channels leading to CH(3)OOOH + CH(2)O and CH(3)O• + CH(2)O + HO(2)• are also energetically favorable in the self-reaction of CH(3)O(2)• especially at low temperature according to our results.

Nonequilibrium solvation energy by means of constrained equilibrium thermodynamics and its application to self-exchange electron transfer reactions.

This work presents a self-consistent thermodynamic approach to nonequilibrium solvation energy. By imposing an extra electric field onto the nonequilibrium solvation system, a constrained equilibrium state is prepared. New expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. The numerical algorithm combining the new formulation with the dielectric polarizable continuum model has been implemented. As an application, self-exchange electron transfer (ET) reactions between tetramethylhydrazine, tetraethylhydrazine, and tetrapropylhydrazine and their corresponding radical cations have been investigated. The inner and solvent reorganization energies are calculated by the "four-point" method and the new method for nonequilibrium solvation, respectively. Besides, we also calculated the electronic coupling matrix. The rate constants for the three self-exchange ET reactions correlate well with experimental results. We have shown that the inner reorganization energies of these self-exchange ET are not very sensitive to compound size while the compound size has some effect on the solvent reorganization energy in acetonitrile. The new method for nonequilibrium solvation energy based on continuum model provides a reasonable result for the solvent reorganization energy.