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1.
2.
The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems. We show that, when second-order and fourth-order decompositions are employed, they share a remarkable unified analytic form for the partition function of the harmonic oscillator. We are then able to obtain the expression of the thermodynamic property and the leading error terms as well. In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme, we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system. Such a strategy leads to an efficient fourth-order decomposition that produces third-order accurate thermodynamic properties for general systems.  相似文献   

3.
Conformational analysis of three small alcohols--ethanol, propanol, and isopropanol--was carried out by systematically improving the basis set and the level of electron correlation. Correlation energy contributions to conformational energies are strongly basis-set-dependent but accurate energy contributions can be obtained by extrapolation to the basis-set limit. At the basis-set limit, second- and third-order electron correlation effects play a significant role for rotations around the CC-OH, HC-CO, and CC-CO bonds. Specifically, second- and third-order correlation effects strongly stabilize structures in which the hydroxylic hydrogen eclipses with the adjacent carbon; a lesser stabilization is present in structures where the CC-OH moiety is in the gauche form. Fourth-order correlation effects to the CC-OH rotation are small due to a partial cancellation of the singles, doubles, and quadruples contribution by the triples contribution. Electron correlation significantly lowers barriers for methyl-group rotations in ethanol and isopropanol, and in these cases the fourth-order correlation effects are noticeable. The relatively large overall importance of third-order correlation energy contributions raises a concern that the inability to accurately estimate this slowly converging contribution may become a limiting factor when highly accurate conformational energies in larger molecules are sought.  相似文献   

4.
The spectroscopic constants and the potential energy curve of F2 were calculated, using the fourth-order MB-RSPT with a single-determinant RHF starting wave function. With an extended [5s4p2d1f] basis set we obtained the equilibrium bond distance and the harmonic vibrational frequency with a relative error of about 0.5%, these are in very good agreement with experiment. In calculations of the potential energy curve for distances larger than about 1.4 Re the method breaks down. We analysed the effect of the individual fourth-order contributions: single, double, triple and quadruple excitations. The role of the renormalization term was stressed in the discussion of various approximations to the full fourth-order energy and in comparison with other related approaches. The basis set effect has been also examined.  相似文献   

5.
An algebraic approach is proposed to calculate the Franck–Condon factors for the Morse potential of diatomic molecules. The Morse oscillator is approximated by means of a fourth-order anharmonic oscillator. In the second-quantized formalism, this anharmonic Hamiltonian is diagonalized by way of the Bogoliubov–Tyablikov transformation. The Franck–Condon factors are estimated using the harmonic frequency equivalent and the recurrence relations for the Franck–Condon factors of the harmonic oscillator. Overlap integrals are shown for three band systems and compared with values calculated with an RKR potential. Excellent agreement is achieved.  相似文献   

6.
A comparison of different many-body perturbation theory (MBPT ) calculations of the ground state rotational and vibrational constants of SiS is made. The calculations are performed up to the complete fourth-order MBPT level, and in all cases two basis sets are utilized. The results of the third-order and some incomplete fourth-order calculations are in good agreement, but the complete fourth-order is among the worst as compared with the experimental data. Analysis of the different contributions to the calculated correlation eneriges points towards the necessity of including even higher-order terms of the(MBPT ) expansion.  相似文献   

7.
The local environment around the paramagnetic centers formed by the Fe(3+) ions doped into three oxi-spinel crystals (ZnAl(2)O(4), MgAl(2)O(4), and ZnGa(2)O(4)) is investigated utilizing the fourth-order perturbation formula of the axial zero-field splitting parameter D on the basis of the dominant spin-orbit coupling mechanism. In order to fix a plausible cubic space group for B-sites located by Al(3+)/Ga(3+) cations, several modeling approaches are used and the results are discussed in detail.  相似文献   

8.
He-N2O的从头算势能面及振转能级   总被引:1,自引:0,他引:1  
采用超分子MP4方法和较大的基组计算得到了He-N2O体系的分子间势能面,发现该势能面有3个极小值点,分别对应T形构型及两个线性He-ONN和He-NNO构型.同时采用离散变量表象方法预测了体系的振转能级,计算结果表明,MP4势能面支持5个振动束缚态.  相似文献   

9.
Results from full fourth-order perturbation theory [SDTQ MBPT(4)], and the coupled-cluster single- and double-excitation model (CCSD). are compared with recent full CI results for BH, HF, NH3, and H2O. For H2O, studies include large symmetric displacements of the OH bonds, which offer a severe test for any single-reference MBPT/CC method. In every case. CCSD plus fourth-order triple-excitation terms provide agreement with the full CI to < 2 kcal/mole. SDTQ MBPT(4) has an error 10 kcal/mole for displaced H2O.  相似文献   

10.
The densities of binary mixtures of an ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate, [bmim][BF4], with an aromatic compound, aniline, have been determined over the full range of compositions and over the temperature range 298.15 to 313.15 K at atmospheric pressure using a vibrating-tube densimeter (DMA4500). Excess molar volumes ( VmEV_{\mathrm{m}}^{\mathrm{E}} ) have been obtained from these experimental results, and were fitted by the fourth-order Redlich–Kister equation. In addition, partial molar volumes, apparent molar volumes and partial molar volumes at infinite dilution have been calculated for each component. Our results show that values of VmEV_{\mathrm{m}}^{\mathrm{E}} decrease slightly when the temperature increases in this system. The results have been interpreted in terms of ion-dipole interactions and structural factors of the ionic liquid and the organic molecular liquid.  相似文献   

11.
Using the results of a configuration interaction calculation reported by Rosenberg and Shavitt, we derive an approximation to the correlation energy which may be associated with the sum to infinite order of all linked diagrams involving singly- and doubly-excited states. This result is compared with that obtained by calculation of the energy through third-order. The fourth-order linked diagrams involving quadruply-excited states are computed. It is shown that there is a considerable degree of cancellation between the fourth-order linked diagram energy terms involving doubly-excited intermediate states only and those which contain quadruply-excited states.  相似文献   

12.
利用Harris模型, 详细分析了Mazziotti提出的重构方法和Chen提出的一种由低阶约化密度矩阵重构高阶约化密度矩阵的系统方法(Science in China B, 2006, 49: 402)的差异. 如果忽略Mazziotti 方法中的3△M、4△M和Chen方法中的3△、4△, 计算结果显示两种方法的计算误差相近. 更好的近似是只忽略四级项4△M、4△, 而三级项由相应的四级项通过简缩来计算. 采用Mazziotti方法计算出来的有些近似值和精确值连正负号都不同, 而用Chen方法计算出来的近似值和精确值不仅正负符号一致, 而且数值大小也很接近.  相似文献   

13.
A two-dimensional mathematical model was theoretically developed to predict the temperature polarization profile of direct contact membrane distillation (DCMD) processes. A concurrent flat-plate device was designed to verify the theoretical prediction of pure water productivity on saline water desalination. The numerical results from the temperature polarization profile were obtained using the finite difference technique to reduce the two-dimensional partial differential equations into an ordinary differential equations system. The resultant simultaneous linear equations system was solved with the fourth-order Runge-Kutta method. The results show theoretical prediction agreement with the measured values from the experimental runs. A combination of the Knudsen flow and Poiseuille flow models in the present mathematical formulation for membrane coefficient estimation was used to establish theoretical agreement. The influence of the inlet saline water temperature and volumetric flow rate on the pure water productivity as well as the hydraulic dissipated energy are also delineated.  相似文献   

14.
Geometry optimization has been performed on CO3 in the SCF approximation and in the second-, third-, and fourth-order MBPT approximations limited to single and double substitutions using a double-zeta plus polarization basis set. The energetics of the formation and decomposition of CO3 from the reactions CO2 + O(1D) → CO3 and CO3 + CO → 2CO2, respectively, have been calculated in several approximations including full fourth-order MBPT. In addition first-order polarization propagator calculations have been performed to identify the low-lying excited states.  相似文献   

15.
The correlation energies obtained by the fourth-order diagrammatic perturbation theory were analyzed for three diatomic molecules: N2, CO, and F2. The results were compared with correlation energies obtained previously for the ten-electron hydrides HF, H2O, and NH3. The relative importance of contributions which arise from the double excitations, from the quadruple excitations, as well as from the renormalization term was investigated. It is shown that for the diatomic molecules under study these contributions are considerably larger than for the ten-electron hydrides not only in absolute value but also in percentage: they represent about 3, 3, and 5%, respectively, of the valence shell correlation energy obtained by the perturbation theory up to the fourth order. A careful analysis of the fourth-order correlation effects is also presented for the reaction energy of the process ½H2 + ½F2 = HF.  相似文献   

16.
循环流动固定床光催化反应器动力学数学模拟   总被引:7,自引:0,他引:7  
以甲基橙为模型反应物,研究了连续循环固定床光催化反应器的动力学过程.根据光催化氧化过程特点,分析并建立了准一级反应动力学方程,对该反应系统的动力学过程进行动态数学模拟,用四阶Runge-Kutta法进行数值计算,结果表明数学模拟与实验数据相吻合.在该光催化反应体系中,处理量增加时实际反应速率常数k基本不变,而表观反应速率常数kapp变小,二者之间关系与反应器体积对处理量体积比(γ)密切相关;反应速率常数受起始浓度影响很大,在15~150 μmol•L-1浓度范围内,lnk=-0.48ln[c0]+1.42;反应速率常数与光强的关系为k∝I0.5;反应速率常数受溶液pH值的影响也很大.  相似文献   

17.
Ground state properties of condensed helium are calculated using the path integral ground state (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other quantum Monte Carlo (QMC) techniques and different propagators. For this particular application, we find that the fourth-order propagator performs comparably to the pair product approximation, and is far superior to the primitive approximation. Results obtained for the equation of state of condensed helium show that PIGS compares favorably to other QMC methods traditionally utilized for this type of calculation.  相似文献   

18.
The drainage of the intervening continuous phase film between two drops approaching each other at constant velocity under the influence of insoluble surfactant is investigated. The mathematical model to be solved is a coupled pair of fourth-order nonlinear partial differential equations which arise from the relationships governing the evolution of the film thickness and the surfactant interfacial concentration in the lubrication approximation. We adopt a simplified approach which uses lubrication theory to describe the flow within the drop, marking a departure from the conventional framework in which Stokes flow is assumed. When the model is solved numerically together with the relevant initial and boundary conditions, the results obtained are compared with those found in the literature using the "boundary integral" method to solve for the flow in the drop phase. The close agreement between the results inspires confidence in the predictions of the simplified approach adopted. The analysis on the effect of insoluble surfactant indicates that its presence retards the drainage of the film: The fully immobile interface limit is recovered even in the presence of a small amount of surfactant above a critical concentration; film rupture is either prolonged or prevented. The retardation of the film was attributed to gradients of interfacial tension which gave rise to the Marangoni effect. A study of the influence of various system parameters on the drainage dynamics was conducted and three regimes of drainage and possible rupture were identified depending on the relative magnitudes of the drop approach velocity and the van der Waals interaction force: Nose rupture, rim rupture, and film immobilization and flattening. Finally, the possibility of forming secondary droplets by encapsulating the continuous phase film into the coalesced drop at rupture was examined and quantified in light of these regimes.  相似文献   

19.
Ab initio calculations on the formation of carbonic acid from the hydration of carbon dioxide with water dimer are re-examined. Fully optimized geometries of the three stationary points (minima and transition state) with the 3-21G basis set are reported. They possess non-planar structures. The inclusion of polarization (with the 6-31G* basis) and electron correlation (via Møller-Plesset perturbation theory to second through to fourth-order using the 6-31G basis) tends to enlarge the energy barrier (35–40 kcal mol−1) for the double hydrogen transfer. This suggests that the neutral hydrolysis of CO2 could require more water molecules (an oligomer) in an autocatalytic process rather than a dimer.  相似文献   

20.
Many-body perturbation theory (MBPT) and coupled-cluster (CC) calculations are performed on the ethylene molecule employing canonical SCF and simple bond-orbital localized orbitals (LO). Full fourth-order MBPT [i.e. SDTQ MBPT(4)], CC doubles (CCD) and CC singles and doubles (CCSD) energies are compared with the over one-million configuration ‘bench-mark” Cl calculation of Saxe et al. Though the SCF and LO reference determinant energies differ by 0.29706 hartree, the CCSD energy difference is only 1.7 mhartrees (mh). Our most extensive SCF orbital calculation, CCSD plus fourth-order triples, is found to be lower in energy than the CI result by 5.3 mh.  相似文献   

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