Coupled-cluster method tailored by configuration interaction

A method is presented which combines coupled cluster (CC) and configuration interaction (CI) to describe accurately potential-energy surfaces (PESs). We use the cluster amplitudes extracted from the complete active space CI calculation to manipulate nondynamic correlation to tailor a single reference CC theory (TCC). The dynamic correlation is then incorporated through the framework of the CC method. We illustrate the method by describing the PESs for HF, H2O, and N2 molecules which involve single, double, and triple bond-breaking processes. To the dissociation limit, this approach yields far more accurate PESs than those obtained from the conventional CC method and the additional computational cost is negligible compared with the CC calculation steps. We anticipate that TCC offers an effective and generally applicable approach for many problems.     

Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na(3) cluster and present the adiabatic PESs for the electronic states 2(2)E' and 1(2)A(1)', and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 2(2)E' and 1(2)A(1)' demonstrate the numerical validity of so called "Curl Condition," such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the "adiabatic-diabatic transformation (ADT)" equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na(3) cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation.     

First-principle computational study on the full conformational space of L-threonine diamide, the energetic stability of cis and trans isomers

First-principle computations were carried out on the conformational space of trans and cis peptide bond isomers of HCO-Thr-NH2. Using the concept of multidimensional conformational analysis (MDCA), geometry optimizations were performed at the B3LYP/6-31G(d) level of theory, and single-point energies as well as thermodynamic functions were calculated at the G3MP2B3 level of theory for the corresponding optimized structures. Two backbone Ramachandran-type potential energy surfaces (PESs) were computed, one each for the cis and trans isomers, keeping the side chain at the fully extended orientation (chi1=chi2=anti). Similarly, two side chain PESs for the cis and trans isomers were generated for the (phi=psi=anti) orientation corresponding to approximately the betaL backbone conformation. Besides correlating the relative Gibbs free energy of the various stable conformations with the number of stabilizing hydrogen bonds, the process of trans-->cis isomerization is discussed in terms of intrinsic stabilities as measured by the computed thermodynamic functions.     

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

A new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys. 136, 034103 (2012)] that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spin-orbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spin-orbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a well-established test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how one-electron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.     

Numerical Convergence of the Sinc Discrete Variable Representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic Representation

Within the Born-Oppenheimer (BO) approximation, nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface (PES). However, this single PES picture should be reconsidered if a conical intersection (CI) is present, although the energy is well below the CI. The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation, i.e., the diagonal BO correction (DBOC) and the geometric phase (GP), which are divergent at the CI. At the same time, there are cusps in the adiabatic PESs. Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation. A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation (DVR) method. We examine the numerical accuracy of the Sinc DVR method for solving the Schr?dinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation. The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points, without special treatment of the divergence of the DBOC and the GP. The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP, whose accurate form usually is not easy to obtain.     

A theoretical study of the mechanism and kinetics of F+N3 reactions.

Both the singlet(1A') and triplet(3A') potential energy surfaces (PESs) of F+N(3) reactions are investigated using the complete-active-space self-consistent field (CASSCF) and the multireference configuration interaction (MRCI) methods with a proper active space. The minimum energy crossing point (MECP) at the intersection seam between the 1A' and 3A' PESs is located and used to clarify the reaction mechanisms. Two triplet transition states are found, with one in the cis form and the other one in the trans form. Further kinetic calculations are performed with the canonical unified statistical (CUS) theory on the singlet PES and the improved canonical variational transition-state (ICVT) method on the triplet PES. The rate constants are also reported. At 298 K, the calculated rate constant is in reasonably good agreement with experimental values, and spin-orbit coupling effects lower it by 28 %. The spectroscopic constants derived from the fitted potential-energy curves for the singlet and triplet states of NF are in very good agreement with experimental values. Our calculations indicate that the adiabatic reaction on the singlet PES leading to NF(a(1)Delta)+N(2) is the major channel, whereas the nonadiabatic reaction through the MECP, which leads to NF(X(3)Sigma(-))+N(2), is a minor channel.     

化学反应的高精度从头算势能面

势能面是化学反应动力学研究的基础。近年来随着理论方法的发展与计算技术的进步,不但含三、四个原子反应体系的电子基态势能面的构建精度进一步提高,一些反应体系的多电子态耦合势能面的构建和含六个原子以上反应体系的高维从头算势能面的构建也取得了重要进展。本文结合若干典型体系势能面的构建工作,主要介绍了高精度电子基态势能面,包括Renner-Teller、旋轨耦合等非绝热效应的耦合势能面以及高维势能面方面的研究进展。     

Theoretical study of photoinduced ring-opening in furan

The potential energy surfaces (PESs) of the two lowest excited singlet states of furan [correlating with the Rydberg (1)A(2)(3s) and valence (1)B(2)(V) states at the C(2v) ground-state molecular configuration] have been studied in some detail with regard to the photoinduced ring-opening reaction. The surfaces have been characterized in terms of their stationary points and points of minimum energy conical intersections along the ring-opening pathway. The optimization of the geometrical parameters has been performed with the equation of motion coupled cluster singles and doubles method. The ab initio PESs have been modeled by energy grids and Taylor series. The resulting 11-dimensional PESs reproduce the ab initio results to a good accuracy and can be used in dynamical calculations.     

Quasiclassical trajectory study of the postquenching dynamics of OH A 2Σ+ by H2/D2 on a global potential energy surface

We report full-dimensional, electronically adiabatic potential energy surfaces (PESs) for the ground state (1A(')) and excited state (2A(')) of OH(3). The PESs are permutationally invariant fits to roughly 23,000 electronic energies (MRCI + Q/aVTZ). Classical trajectory calculations of the postquenching dynamics of OH A (2)Σ(+) are carried out on the 1A(') PES for H(2) and D(2), at previously identified conical intersections (CoIs) [B. C. Hoffman and D. R. Yarkony, J. Chem. Phys. 113, 10091 (2000)]. The initial momenta are sampled fully and partially microcanonically, corresponding to "adiabatic" and "diabatic" models of the dynamics, respectively. Branching ratios of reactive to nonreactive channels from separate C(2v), C(∞v), and C(s) symmetries of CoIs are calculated, as are final rovibrational state distributions of OH and H(2) products. The rovibrational distributions of the OH and D(2) products, the D/H-atom translational energy distribution are calculated and compared to experimental ones. Agreement for these observable quantities is good. The branching between reactive and nonreactive quenching is sensitive to the momenta sampling; very good agreement with experiment is obtained using the diabatic sampling but not with the adiabatic sampling. The vibrational state distributions of H(2)O and HOD (although not measured by experiment) are also presented.     

New ab initio coupled potential energy surfaces for the Br(2P(3∕2), 2P(1∕2)) + H2 reaction

The three lowest (1A('), 2A('), and 1A(')) adiabatic potential energy surfaces (PESs) for the Br((2)P) + H(2) reactive system have been computed based on the multi-reference configuration interaction (MRCI) method including the Davidson's correction with a large basis set. These three adiabatic PESs have been transformed to a diabatic representation, leading to four coupling potentials. In addition, the spin-orbit matrix elements were also obtained using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Consequently, six coupling potentials were obtained and their characteristics were extensively discussed. Nonadiabatic quantum dynamics calculations for this system have been realized with these realistic diabatic potentials instead of previous semi-empirical diabatic potentials. Based on two-state model nonadiabatic calculations for the Br((2)P(3∕2), (2)P(1∕2)) + H(2) reaction, the Br((2)P(1∕2)) + H(2) reaction was found to show less reactivity than the Br((2)P(3∕2)) + H(2) reaction at collision energies beyond the threshold of the Br((2)P(3∕2)) + H(2) reaction. Our results are consistent with the previous studies on the XH(2) (X = F, Cl) system, which indicate that the adiabatically forbidden channel is dominant at low energies in the open-shell halogen atom plus H(2) reactions.     

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .     

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.     

Flexibility of "polyunsaturated fatty acid chains" and peptide backbones: A comparative ab initio study

The conformational properties of omega-3 type of polyunsaturated fatty acid (PUFA) chains and their fragments were studied using Hartree-Fock (RHF/3-21G) and DFT (B3LYP/6-31G(d)) methods. Comparisons between a unit (U) fragment of the PUFA chain and a mono N-Ac-glycine-NHMe residue show that both structures have the same sequence of sp2-sp3-sp2 atoms. The flexibility of PUFA originates in the internal rotation about the above pairs of sigma bonds. Therefore, potential energy surfaces (PESs) were generated by a scan around the terminal dihedral angles (phi t1 and phi t2) as well as the phi 1 and psi 1 dihedrals of both 1U congeners (Me-CHCH-CH2-CHCHMe and MeCONH-CH2-CONHMe) at the RHF/3-21G level of theory. An interesting similarity was found in the flexibility between the cis allylic structure and the trans peptide models. A flat landscape can be seen in the cis 1U (hepta-2,5-diene) surface, implying that several conformations are expected to be found in this (PES). An exhaustive search carried out on the 1U and 2U models revealed that straight chain structures such as trans and cis beta (phi 1 approximately psi 1 approximately 120 degrees; phi 2 approximately psi 2 approximately -120 degrees) or trans and cis extended (phi 1 approximately psi 1 approximately phi 2 approximately psi 2 approximately 120 degrees) can be formed at the lowest energy of both isomers. However, forming helical structures, such as trans helix (phi 1 approximately -120 degrees, psi 1 approximately 12 degrees; phi 2 approximately -120 degrees, psi 2 approximately 12 degrees) or cis helix (phi 1 approximately -130 degrees, psi 1 approximately 90 degrees; phi 2 approximately -145 degrees, psi 2 approximately 90 degrees) will require more energy. These six conformations, found in 2U, were selected to construct longer chains such as 3U, 4U, 5U, and 6U to obtain the thermochemistry of secondary structures. The variation in the extension or compression of the chain length turned out to be a factor of 2 between the helical and nonhelical structures. The inside diameter of the "tube" of cis helix turned out to be 3.5 A after discounting the internal H atoms. Thermodynamic functions were computed at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d). The cis-trans isomerization energy of 1.7 +/- 0.2 kcal mol(-1) unit(-1) for all structure pairs indicates that the conformer selection was consistent. A folding energy of 0.5 +/- 0.1 kcal mol(-1) unit(-1) has been extracted from the energy comparison of the helices and most extended nonhelical structures. The entropy change associated with the folding (Delta S(folding)) is decreases faster with the degree of polymerization (n) for the cis than for the trans isomer. As a consequence, the linear relationships between (Delta G(folding)) and n for the cis and trans isomer crossed at about n = 3. This suggested that the naturally occurring cis isomer less ready to fold than the trans isomer since a greater degree of organization is exhibited by the cis isomer during the folding process. The result of this work leads to the question within the group additivity rule: could the method applied in our study of the folding of polyallylic hydrocarbons be useful in investigating the thermochemistry of protein folding?     

N(4S)+ NO(X2Π)→N2(X3Σg-)+O(3P) 反应的立体动力学研究

采用准经典轨线方法研究了在不同碰撞能下，碰撞反应N(4S)+NO(X2Π)→ N2(X3Σg- )+O(3P)在两个最低势能面3A 和 3A'上产物与反应物之间的矢量相关. 结果表明，对于不同的碰撞能，在两个势能面上反应产物的转动取向展示了不同的特征和趋势. 随着碰撞能的增加，发生在3A 势能面上的反应主要受外平面机理支配，而发生在 3A' 势能面上的反应倾向于受内平面机理支配. 这些差异来自于两个势能面的不同构型.     

Ab initio quantum dynamical study of photoinduced ring opening in furan

The nonadiabatic photoinduced ring opening occurring in the two lowest excited singlet states of furan is investigated theoretically, using wave-packet propagation techniques. The underlying multidimensional potential energy surfaces (PESs) are obtained from ab initio computations, using the equation-of-motion coupled cluster method restricted to single and double excitations (EOM-CCSD), reported in earlier recent work [E. V. Gromov, A. B. Trofimov, F. Gatti, and H. Ko?ppel, J. Chem. Phys. 133, 164309 (2010)]. Up to five nuclear degrees of freedom are considered in the quantum dynamical treatment. Four of them represent in-plane motion for which the electronic states in question (correlating with the valence (1)B(2)(V) and Rydberg (1)A(2)(3s) states at the C(2v) ground-state molecular configuration) have different symmetries, A(') and A('), respectively. The fifth mode, representing out-of-plane bending of the oxygen atom against the carbon-atom plane, leads to an interaction of these states, as is crucial for the photoreaction. The nonadiabatic coupling and conical intersection cause an electronic population transfer on the order of ～10 fs. Its main features, and that of the wave-packet motion, are interpreted in terms of properties of the PES. The lifetime due to the ring-opening process has been estimated to be around 2 ps. The dependence of this estimate on the nuclear degrees of freedom retained in the computations is discussed.     

New insight into the gas-phase bimolecular self-reaction of the HOO radical

The singlet and triplet potential energy surfaces (PESs) for the gas-phase bimolecular self-reaction of HOO*, a key reaction in atmospheric environments, have been investigated by means of quantum-mechanical electronic structure methods (CASSCF and CASPT2). All the reaction pathways on both PESs consist of a first step involving the barrierless formation of a prereactive doubly hydrogen-bonded complex, which is a diradical species lying about 8 kcal/mol below the energy of the reactants at 0 K. The lowest energy reaction pathway on both PESs is the degenerate double hydrogen exchange between the HOO* moieties of the prereactive complex via a double proton transfer mechanism involving an energy barrier of only 1.1 kcal/mol for the singlet and 3.3 kcal/mol for the triplet at 0 K. The single H-atom transfer between the two HOO* moieties of the prereactive complex (yielding HOOH + O2) through a pathway keeping a planar arrangement of the six atoms involves a conical intersection between either two singlet or two triplet states of A' and A" symmetries. Thus, the lowest energy reaction pathway occurs via a nonplanar cisoid transition structure with an energy barrier of 5.8 kcal/mol for the triplet and 17.5 kcal/mol for the singlet at 0 K. The simple addition between the terminal oxygen atoms of the two HOO* moieties of the prereactive complex, leading to the straight chain H2O4 intermediate on the singlet PES, involves an energy barrier of 7.3 kcal/mol at 0 K. Because the decomposition of such an intermediate into HOOH + O2 entails an energy barrier of 45.2 kcal/mol at 0 K, it is concluded that the single H-atom transfer on the triplet PES is the dominant pathway leading to HOOH + O2. Finally, the strong negative temperature dependence of the rate constant observed for this reaction is attributed to the reversible formation of the prereactive complex in the entrance channel rather than to a short-lived tetraoxide intermediate.     

Insights into the structure and reactivity of acylperoxo complexes in the Kochi-Jacobsen-Katsuki catalytic system. A density functional study

Structural properties of the acylperoxo complexes [(Salen)Mn(III)RCO(3)] (2) and [(Salen)Mn(IV)RCO(3)] (3), the critical intermediates in the Kochi-Jacobsen-Katsuki reaction utilizing organic peracids or O(2)/aldehydes as oxygen source, have been studied with the density functional theory. Four distinct isomers, cis(O,N), cis(N,O), cis(N,N), and trans, of these complexes have been located. The isomer 2-cis(O,N) in its quintet ground state, and nearly degenerate isomers 3-cis(O,N) and 3-cis(N,O) in their quartet ground states are found to be the lowest in energy among the other isomers. The O-O bond cleavage in the cis(O,N), cis(N,O), and trans isomers of 2 and 3 has been elucidated. In complex 3, the O-O bond is inert. On the contrary, in complex 2, the O-O bond cleaves via two distinct pathways. The first pathway occurs exclusively on the quintet potential energy surface (PES) and corresponds to heterolytic O-O bond scission coupled with insertion of an oxygen atom into an Mn-N(Salen) bond to form 2-N-oxo species; this pathway has the lowest barrier of 14.9 kcal/mol and is 15.6 kcal/mol exothermic. The second pathway is tentatively a spin crossover pathway. In particular, for 2-cis(O,N) and 2-cis(N,O) the second pathway proceeds through a crucial minimum on the seam of crossing (MSX) between the quintet and triplet PESs followed by heterolytic O-O cleavage on the triplet PES, and produces unusual triplet 2-cis(O,N)- and 2-cis(N,O)-oxo ([(Salen)Mn(V)(O)RCO(2)]) species; this pathway requires 12.8 kcal/mol and is 1.4 kcal/mol endothermic. In contrast, for the 2-trans isomer, spin crossing is less crucial and the O-O cleavage proceeds homolytically to generate 2-trans-oxo [(Salen)Mn(IV)(O)] species with RCO(2) radical; this pathway, however, cannot compete with that in 2-cis because it needs 21.9 kcal/mol for activation and is 15.3 kcal/mol endothermic. In summary, the O-O cleavage occurs predominantly in the 2-cis complexes, and may proceed either through pure high spin or spin crossover heterolytic pathway to produce 2-cis-oxo and 2-N-oxo species.     

基于CASSCF参考函数的块相关耦合簇方法对烷烃中单键解离势能面研究

用以完全活化空间自洽场(CASSCF)波函数为参考波函数的块相关耦合簇(BCCC)方法(简称CAS-BCCC)研究了烷烃(甲烷和乙烷)中的单键解离过程的势能面(PES). 与其它理论方法比较的结果表明, 该方法可以对所研究的整个解离势能面给出定量准确的描述.