Theoretical study of nonlinear triatomic molecular potential energy surfaces: Lie algebraic method

Triatomic molecular potential energy surfaces (PES) are obtained by using coherent state to take the classical limits of algebraic Hamiltonian. The algebraic Hamiltonian for bent tria-tomic molecules can be obtained using Lie algebraic method (the expansion coefficients are obtained by fitting spectroscopic data). This PES is applied to H2O molecule, and good results are obtained.     

构造SO~2分子势能面的李代数方法

把李代数方法得到的SO~2分子的代数Hamiltonian,利用相干态基经典化并找到一个新的变换,将分子的键角引入,而得到SO~2分子的势能面。由该势能面计算的解离能,所给出的势能面的立体图和相应的等高线以及力常数与其他方法给出的相一致。该方法可以推广到多原子分子及反应体系。     

Potential energy surface for linear triatomic molecules: An algebraic method

Recently, we proposed a new transformation between the angle of canonical coordinates and the bond angle to describe the bending motion in Potential Energy Surfaces (PES) of bent triatomic molecules. In this work we extend the transformation to include linear triatomic molecules. Results for the linear triatomic molecule N₂O are reported.     

A procedure of determining potential energy surfaces of triatomic molecules from inversion of spectroscopic data

In this paper,we have suggested an iterative procedure of optimization of the linearparameters in an analytic potential energy function for a triatomic molecule,by combining both variational and second order perturbation methods.The most important feature of this procedure is that the objective function is an analytical expression which can be optimized easily.The application to the water molecule is presented.     

Theoretical study of highly vibrational states of nonlinear triatomic molecules using Lie algebraic approach

The vibrational excitations of bent triatomic molecules are studied by using Lie algebra. The RMS error of fitting 30 spectroscopic data is 1.66 cm-1 for SO2. The results show that the expansion of a molecular algebraic Hamiltonian can well describe the experimental data. And the total vibrational levels can be calculated using this Hamiltonian. At the same time, the potential energy surface can also be obtained with the algebraic Hamiltonian.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li_2H

A 285-pomt multi-reference configuration-interaction involving single and double excitations ( MRS DCI) potential energy surface for the electronic ground state of L12H is determined by using 6-311G (2df,2pd)basis set.A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a x2 of 4.64×106 The equn librium geometry occurs at Rc=0.172 nm and,LiHL1=94.10°.The dissociation energy for reaction I2H(2A)→L12(1∑g)+H(2S) is 243.910 kJ/mol,and that for reaction L12H(2A')→HL1(1∑) + L1(2S) is 106.445 kl/mol The inversion barrier height is 50.388 kj/mol.The vibrational energy levels are calculated using the discrete variable representation (DVR) method.     

Theoretical investigations on analytical potential energy function and spectroscopic parameters for the state b3Πu of dimer 7Li2

The SAC‐CI (symmetry‐adapted‐cluster configuration‐interaction) method presented in Gaussian 03 program package is applied to investigate the adiabatic potential energy curves (PECs) of ⁷Li₂(b³Π_u). These calculations are performed at numbers of basis sets, such as 6‐311++G(3df,3pd), 6‐311++G(2df,2pd), 6‐311++G(df,pd), D95V++, D95(3df,3pd), D95(d,p), cc‐PVTZ, 6‐311++G and 6‐311++G(d,p). All the ab initio calculated points are fitted to the analytic Murrell‐Sorbie functions and then used to compute the spectroscopic parameters. The analytic potential energy function (APEF) for this b³Π_u state is reported. By comparison, the spectroscopic parameters reproduced by the APEF attained at 6‐311++G(2df,2pd) are found to be very close to the latest experimental findings. With the APEF obtained at the SAC‐CI/6‐311++G(2df,2pd) level of theory, a total of 62 vibrational states is found when J = 0. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants for these vibrational states are also reported. The reasonable dissociation limit for this state is deduced using the calculated results at present. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li2H

A 285-point multi-reference configuration-interaction involving single and double excitations (MRS-DCI) potential energy surface for the electronic ground state of Li₂H is determined by using 6-311G (2df, 2pd) basis set. A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a X² of 4.64 × 10^-6. The equilibrium geometry occurs at R_e =0.172 nm and <LiHLi =94.10. The dissociation energy for reaction Li₂H(²A)⇑ Li₂(¹⌆_g)+H(²S) is 243.910 kJ/mol. and that for reaction Li₂H(²A)⇑HLi(¹be)+Li(²S) is 106.445 kJ/mol. The inversion barrier height is 50.388 kJ/mol. The vibrational energy levels are calculated using the discrete variable representation (DVR) method. Project supported by the National Natural Science Foundation of China (grant No. 29673029) and by the Special Doctoral Research Foundation of the State Education Commission of China.     

An ab initio potential energy surface and vibrational energy levels of ZnH2

A three‐dimensional potential energy surface of the electronic ground state of ZnH₂ (${X}^1\sum _g^ +$ ) molecule is constructed from more than 7500 ab initio points calculated at the internally contracted multireference configuration interaction with the Davidson correction (icMRCI+Q) level employing large basis sets. The calculated relative energies of various dissociation reactions are in good agreement with the previous theoretical/experimental values. Low‐lying vibrational energy levels of ZnH₂, ZnD₂, and HZnD are calculated on the three‐dimensional potential energy surface using the Lanczos algorithm, and found to be in good agreement with the available experimental band origins and the previous theoretical values. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical study of potential energy surface and vibrational spectra of ArF2 system

An ab initio potential energy surface (PES) of ArF2 system has been obtained by using MP4 calculation with a large basis set including bond functions. There are two local minimums on the PES: one is T-shaped and the other is L-shaped. The L-shaped minimum is the global minimum with a well depth of -119.62 cm- 1 at R = 0.3883nm. The T-shaped minimum has a well depth of -85.93cm -1 at R = 0.3486 nm. A saddle point is found at R = 0.3486 and θ = 61° with the well depth of -61.53 cm-1. The vibrational energy levels have been calculated by using VSCF-CI method. The results show that this PES supports 27 vibrational bound states, and the ground states are two degenerate states assigned to the L-type vibration.     

Potential energy surface and highly excited vibrational lines of NO2 via algebraic approach

The algebraic Hamiltonian of NO₂ is optimized using U(4) algebra via fitting to 102 observed vibrational lines. The RMS error of the fitting is 2.39 cm^?1. We calculated highly excited vibrational energy levels using this optimized Hamiltonian, and then obtained the potential energy surface for the electronic ground state by using the classical limit of the U(4) algebraic Hamiltonian. We also calculated the dissociation energies, the force constants etc. Our results are in good agreement with the other theoretical results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

OCS电子基态势能面与振动光谱的理论研究

本文采用键长-键角内标系下的自洽场-组态相互作用方法精确计算了OCS分子的振动高激发态能级,并结合实验观测到的振动能级利用非线性最小二乘法优化电子基态势能函数中的势能参数。由优化所得的势能面计算出的振动激发态能级与50个实验观测到的振动能级比较,标准偏差为0.08cm^-^1。此外,还用该势能面计算了OCS同位素分子的振动能级,计算结果与实验值也十分吻合。     

Sigma,pi, and delta wavefunction forms for the hydrogen molecule

Using variational Monte Carlo methods, we examine simple, explicitly‐correlated trial wavefunction forms for the X¹Σ, B¹Σ, a³Σ, b³Σ, I¹Π_g, C¹Π_u, i³Π_g, c³Π_u, J¹Δ_g, and j³Δ_g states of the hydrogen molecule. The energies produced by our best wavefunctions are slightly above the best values in the literature. When we combine our trial wavefunction forms with the generalized Feynman‐Kac path integral method, our results are in excellent agreement with the best nonrelativistic values for these systems except for the I¹Π_g state. Our best energy for this state, ?0.65951554(6), is lower by several microhartrees than that obtained by Wolniewicz [J Mol Spectrosc 1995, 169, 329]. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ro-vibrating energy states of a diatomic molecule in an empirical potential

An approximate analytical solution of the Schrödinger equation is obtained to represent the rotational–vibrational (ro-vibrating) motion of a diatomic molecule. The ro-vibrating energy states arise from a systematical solution of the Schrödinger equation for an empirical potential (EP) V _±(r) = D _e {1 ? (?/δ)[coth (ηr)]^±1/1 ? (?/δ)}² are determined by means of a mathematical method so-called the Nikiforov–Uvarov (NU). The effect of the potential parameters on the ro-vibrating energy states is discussed in several values of the vibrational and rotational quantum numbers. Moreover, the validity of the method is tested with previous models called the semiclassical (SC) procedure and the quantum mechanical (QM) method. The obtained results are applied to the molecules H₂ and Ar₂.     

Highly excited vibrational levels of triatomic molecule N2O: U(4) algebraic model

In the U(4) algebraic framework, the triatomic molecules are of U₁(4) ? U₂(4) dynamical symmetry. A molecular Hamiltonian is constructed including the third‐order conbination of the invariant operators. Within this framework, the highly vibrational energy levels of the linear triatomic nitrous oxide molecule, including both bending and stretching vibrations, are studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theoretical studies on the potential energy surfaces and vibrational energy levels of HXeF and HXeCl

The potential energy surfaces for the electronic ground state of the HXeCl and HXeF molecules areconstructed by using the internally contracted multi-reference configuration interaction with theDavidson correction(icMRCI Q)method and large basis sets.The stabilities and dissociation barriersare identified from the potential energy surfaces.The three-body dissociation channel is found to bethe dominate dissociation channel for HXeCl,while two dissociation channels are possible and com-petitive for HXeF.Based on the obtained potentials,vibrational energy levels of HXeCl and HXeF arecalculated using the Lanczos algorithm.Our theoretical results are in good agreement with the avail-able observed values.Particularly,the calculated fundamental frequency of the H—Xe stretching vi-bration including the Xe matrix effect of HXeCl is found to be 1666.6 cm-1,which is only 17.6 cm-1higher than the recently observed value of 1649 cm-1.     

An accurate three-dimensional potential energy surface for the He-Na_2 complex

An accurate three-dimensional potential energy surface(PES) for the He-Na2 van der Waals comple was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connecte triple(CCSD(T)) level of theory.A mixed basis set,aug-cc-pVQZ for the He atom and cc-pCVQZ for th sodium atom,and an additional(3s3p2d1f) set of midbond functions were used.The computed inte action energies in 819 configurations were fitted to a 96-parameter analytic potential model by leas squares fitting.The PES has two shallow wells corresponding to the T-shaped structure and the linea configuration,which are located at 12.5a0 and 14 a0 with depths of 1.769 and 1.684 cm-1,respectivel The whole potential energy surface exhibits weak anisotropy.Based on the fitted PES,state-to-stat differential cross sections were calculated.     

O3势能面和振动激发态的理论研究

由于O3在大气化学中的重要作用，近年来针对它的实验和理论研究皆较活跃．尽管对O3的高振动激发态已进行过广泛的研究［“］，得到过多种由实验光谱定出的势能面［‘，’］或由从头算得到的势能函数【‘］，但由于近年来又增加了一些新的高精度的振转光谱实验数据k，’」，而以     

Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009