Intermolecular potentials for ammonia based on the test particle model and the coupled pair functional method

The intermolecular interaction ΔE in (NH₃)₂ is investigated on the SCF level, with inclusion of correlation effects by means of the CPF method and within the simple test particle model. Whereas the linear hydrogen bonded structure is favoured on the SCF level, ΔE = -7·65 kJ mol^-1, the most stable geometry on the highest level of theory is a cyclic structure, ΔE = -12·96 kJ mol^-1. The minimum is very shallow and allows for appreciable angular motions. The test particle model reproduces the general features of ΔE but shows deviations in details. The computed potentials are used in MD simulations to compute static and dynamic properties of liquid NH₃. Good agreement with available experimental results is obtained throughout.     

XeO3和XeOF2与三种不同杂化方式N原子的Xe···N非共价作用的理论研究

本文采用密度泛函理论和二级微扰理论方法研究了XeO₃和XeOF₂与一系列不同杂化含氮给体配合物之间的相互作用. 含氮给体与XeO₃和XeOF₂之间的相互作用能在6.5∽19.9 kcal/mol之间. 相互作用强弱顺序为sp³>sp²>sp,且XeO₃比XeOF₂高. 约化密度梯度图证明,对于sp²和sp³杂化的给体,空间位阻效应在相互作用中起着一定的影响. 能量成分分析发现,Xe···N作用主要的吸引部分是静电相互作用. 在XeO₃配合物中,极化能的占比大于色散,而在XeOF₂配合物中则相反. 除表面静电势(V_s)外,其他5个相互作用参数之间的线性相关系数均较大.     

Accurate ground-state potential energy surfaces of the C2H2–Kr and C2H2–Xe van der Waals complexes

Accurate ab initio intermolecular potential energy surfaces (IPES) have been obtained for the first time for the ground electronic state of the C₂H₂–Kr and C₂H₂–Xe van der Waals complexes. Extensive tests, including complete basis set and all-electron scalar relativistic results, support their calculation at the CCSD(T) level of theory, using small-core relativistic pseudopotentials for the rare-gas atoms and aug-cc-pVQZ basis sets extended with a set of 3s3p2d1f1g mid-bond functions. All results are corrected for the basis set superposition error. The importance of the scalar relativistic and rare-gas outer-core (n–1)d correlation effects is investigated. The calculated IPES, adjusted to analytical functions, are characterized by global minima corresponding to skew T-shaped geometries, in which the Jacobi vector positioning the rare-gas atom with respect to the center of mass of the C₂H₂ moiety corresponds to distances of 4.064 and 4.229?Å, and angles of 65.22° and 68.67° for C₂H₂–Kr and C₂H₂–Xe, respectively. The interaction energy of both complexes is estimated to be ?151.88 (1.817?kJ?mol^?1) and ?182.76?cm^?1 (2.186?kJ?mol^?1), respectively. The evolution of the topology of the IPES as a function of the rare-gas atom, from He to Xe, is also discussed.     

The intermolecular potential and its angular dependence for two H2 molecules

The potential energy surface in the non-reactive region has been determined theoretically for the H₂-H₂ system. The procedure consists of a non-orthogonal configuration interaction calculation using the individual SCF orbitals of the separate molecules. The potential function is expressed as a 5-term sum of Legendre functions, and analytical expressions are given for the R dependence of the terms. The calculated depth of the spherically averaged Van der Waals well is -2·96 meV, which is in essentially complete agreement with the experimental value of -3·00 meV. the position of the minimum is at 3·49 Å both theoretically and experimentally. The value of C ₆ for dispersion forces obtained in this calculation is 12·97 a.u.     

The characterization of the complete set of bound vibronic states of HNO in its excited ÃA″ electronic state

Laser-induced fluorescence excitation spectra of the HNO band system have been recorded with high sensitivity. This has enabled detection of the Franck-Condon unfavored vibronic bands (002)-(000) and (003)-(000), thereby completing the set of fully bound vibronic levels in the à state. Extensions have also been made to other bands. A strong Coriolis resonance between the K_a¹ = 8 levels of the excited (010) vibronic state and the K_a¹ = 9 levels of the (001) state leads to rotational perturbations of up to 9 cm⁻¹. The (100-000) band includes weak axis-tilting branches. It is concluded from the vibrational energy level spacings that vibronic interaction makes an important contribution to the energies of the higher bending levels, consistent with the correlation of the ùA″ state with a component of a ¹Δ state for linear HNO.     

Ab initio intermolecular potential energy surface of Ne···NCCN van der Waals complex: effect of the place of midbond function on the interaction

The intermolecular potential energy surface of Ne···NCCN van der Waals complex was evaluated in the framework of the counterpoise-corrected supermolecular approach using CCSD(T) level and aug-cc-pVDZ basis set extended with a set of midbond (3s3p2d1f1g) functions. The effect of the place of midbond function on the accuracy of the calculated potential energy surface was examined and the optimised position for placing midbond function was determined. The calculated potential energy surface was fitted by an analytical function. The analytical function of intermolecular potential energy surface of Ne···NCCN demonstrated a global minimum energy of ?12.024 meV related to the T-shape geometry at the distance between Ne and the centre of mass of NCCN of 3.28 Å. Finally, the interaction second virial coefficients (B₁₂) of Ne and NCCN were calculated and used to calculate the second virial coefficients for the mixture of neon and cyanogen gases at different mole fractions of Ne gas.     

Quantum states of hydrogen transfer and vibration in malonaldehyde

New ab initio results on the 21D potential energy surface of malonaldehyde and a quantum mechanical treatment of the hydrogen transfer motion and its interaction with all vibrations are presented. An explicit approximate reaction path, close to the minimum energy path but matching the reactive normal mode near equilibrium, allows one to predict the ground state tunnelling frequency even when using small basis sets. With a barrier of 1144 cm^?1 (3.27kcal mol-¹) the tunnelling splitting is predicted to be 22.0cm^?1 for the parent species and 3.8 cm^?1 for the species deuterated in the hydrogen bond, in good agreement with the observed values 21.6 and 2.9 cm^?1, respectively. Predicted energy levels for excited states of the hydrogen transfer motion and for the non-reactive vibrations suggest a re-examination of the vibrational spectra and an extension of the number of vibrational factors in the basis set to improve the results for the vibrationally excited states.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r 12-)MR-CI IV. The helium dimer (He 2)

The helium dimer interaction potential is computed using the recently proposed (explicitly correlated) r ₁₂-MR-ACPF (averaged coupled-pair functional) method and a [11s8p6d5f4g] basis set. With an MR-ACPF ansatz that contains 121 references we obtain interaction energies that are close to full CI. In a smaller reference space containing 9 functions, however, even by successively adding [3h] and [2i] functions to the basis set mentioned above, the basis set limit could not be reached. While convergence to the basis set limit is slow, it nevertheless is monotonic and therefore allows for extrapolation to the limit. We obtain basis set corrections at R = 4 a ₀ and 5.6 a ₀ which we further extend to all distances and which we apply to the potential energy curve mentioned above. From our calculations, we conclude that a very recent potential which has been calculated using the SAPT (symmetry adapted perturbation theory) method, and which previously was assumed to be the most accurate available, is insufficiently repulsive at short distances. We correct our extrapolated potential for retardation and finally calculate the expectation value of the interatomic distance (?R?) and dissociation energy (D ₀) by solving the Schrödinger equation of the vibrating ⁴He₂. Our results (?R? = 41 ± 13 Å and D ₀ = 2.2 ± 1.0 mK) are in acceptable agreement with very recent calculations in the literature, but they disagree with a recent experiment.     

高次激发相关能在构建HCN-He亚光谱精度势能面中的角色:通过实验高分辨率光谱进行严格检测

Interpreting high-resolution rovibrational spectra of weakly bound complexes commonly requires spectroscopic accuracy (<1 cm^-1) potential energy surfaces (PES). Constructing high-accuracy ab initio PES relies on the high-level electronic structure approaches and the accurate physical models to represent the potentials. The coupled cluster approaches including single and double excitations with a perturbational estimate of triple excitations (CCSD(T)) have been termed the "gold standard" of electronic structure theory, and widely used in generating intermolecular interaction energies for most van der Waals complexes. However, for HCN-He complex, the observed millimeter-wave spectroscopy with high-excited resonance states has not been assigned and interpreted even on the ab initio PES computed at CCSD(T) level of theory with the complete basis set (CBS) limit. In this work, an effective three-dimensional ab initio PES for HCN-He, which explicitly incorporates dependence on the Q₁ (C-H) normal-mode coordinate of the HCN monomer has been calculated at the CCSD(T)/CBS level. The post-CCSD(T) interaction energy has been examined and included in our PES. Analytic two-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v₁(C-H)=0, and 1 to the Morse/Long-Range potential function form with root-mean-square deviations (RMSD) smaller than 0.011 cm^-1. The role and significance of the post-CCSD(T) interaction energy contribution are clearly illustrated by comparison with the predicted rovibrational energy levels. With or without post-CCSD(T) corrections, the value of dissociation limit (D₀) is 8.919 or 9.403 cm^-1, respectively. The predicted millimeter-wave transitions and intensities from the PES with post-CCSD(T) excitation corrections are in good agreement with the available experimental data with RMS discrepancy of 0.072 cm^-1. Moreover, the infrared spectrum for HCN-He complex is predicted for the first time. These results will serve as a good starting point and provide reliable guidance for future infrared studies of HCN doped in (He)_n clusters.     

Investigation of negative ion states in HCl and HF by configuration interaction methods

Multi-reference configuration interaction calculations are employed for the study of Born-Oppenheimer potential energy curves in HF/HF^- and HCl/HCl^-. Large gaussian basis sets including negative ion functions as well as diffuse s, p and d AOs are employed thereby. In HCl^- a repulsive 2Σ⁺ state emerges from the calculations approximately 4·2 eV above the HCl X ¹Σ⁺ ground state; no such entity could be observed in HF^- in the energy range treated. All other CI roots which produce potential curves parallel to and above the X ¹Σ⁺ curve are found to possess quite diffuse charge distributions in the basis set variations undertaken and can therefore not be considered resonant states but rather as discrete representations of free-electron species in the HX + e^- continuum. For large internuclear distances the HF^- and HCl^- curves lie below those of the neutral species, whereby the crossing between the X ²Σ⁺ ionic and X ¹Σ⁺ curves are calculated to occur at 3·2 a ₀ in HCl/HCl^- and 2·6 a ₀ in HF/HF^-. Finally it is argued that non-adiabatic effects involving the low energy HX^- continuum states in the Born-Oppenheimer approximation and the bound HX^- species at large internuclear separations (with continuation inside the HX potential well) are ultimately responsible for observed electron scattering resonances, in accordance with recent work of Domcke and Cederbaum and of Nesbet.     

Spin-orbit interactions from self consistent field wavefunctions

Effects of the spin-orbit Hamiltonian H_LS , including both the spin-same orbit and spin-other orbit terms, are studied at the self consistent field (SCF) level of theory. Separate calculations are carried out for each state considered, and biorthogonal orbitals are constructed for the evaluation of matrix elements. Doublet-doublet and singlet-triplet interactions are discussed. The evaluation of the Gaussian basis function integrals is described in a Cartesian component representation, these integrals being directly related to one and two electron second derivative integrals. This new SCF spin-orbit code is used to (i) determine the spatial dependence of the spin-orbit parameters for the Renner-Teller ²B₁, ²A₁ states of H₂O⁺, (ii) determine the spin-orbit splitting of the ²Π states of OH as a function of bond-length and (iii) calculate the radiative lifetime of the a ³Σ⁺ state of NO⁺. In each case these calculations are compared with more sophisticated configuration interaction studies, but it is found that the evaluation of these effects near equilibrium geometries at the SCF level is sufficiently accurate, provided that a large basis set is used.     

Regular approximated scalar relativistic correlated ab initio schemes: applications to rare gas dimers

The ab initio scalar ZORA approach, which was previously tested within the context of numerical and basis set SCF calculations, is generalized to include electron correlation. The technical details of the method are investigated in calculations on the systems Ne₂, Ar₂, Kr₂ and Xe₂. For the weakly bonded rare gas dimers we calculated the bond lengths and well depths using the non-relativistic ZORA and scaled ZORA MP2 method. The relativistic effect on the potential energy minimum, obtained with the most accurate method (scaled ZORA) is shown to be very close to that of the Dirac-Fock MP2 method.     

The distance dependence and spatial distribution of the molecular quadrupole moments of P2, S2 and Cl2

The quadrupole moments (Θ) of the molecules P₂, S₂ and Cl₂ have been computed at the SCF, CASSCF and CASSCF + 1 + 2 levels of theory, using augmented correlation consistent basis sets. The convergence of Θ as a function of basis set and level of theory is discussed. The variation of Θ from the separated atoms to the equilibrium region is reported. Θ is written as the sum of a sigma and pi contribution, and inaccuracies in the SCF values for P₂ and S₂ are due to the poor representation of the pi system in the SCF theory. A reference state dependent quadrupole moment density, - ½(3cos² θ- 1)r ²δη(r; R), is defined whose integral is the mole2 cular quadrupole moment, and the spatial distributions of the density and its relationship to the density difference δη(r; R) are examined.     

Chromium dihydride (CrH2): theoretical evidence for a bent 5B2 ground state

Ab initio molecular electronic structure theory has been used to study two likely candidates for the quintet ground state of CrH₂ at the self-consistent field, the single and double excitation configuration interaction (CISD), the single and double excitation coupled cluster (CCSD), and the single, double, and perturbative triple excitation coupled cluster (CCSD(T)) levels of theory. The largest basis sets utilized for geometry optimizations, designated two-f TZ2P, have a contraction scheme of Cr(14s11p6d2f/10s8p3d2f), H(5s2p/3s2p). At the CCSD(T) level of theory using this two-f TZ2P basis, a bent (C_2v symmetry) ⁵B₂ state is predicted to lie a mere 4·2 kcal mol^-1 (4·5 kcal mol^-1 including zero-point vibrational energy correction) lower in energy than linear (D_∞h symmetry) ⁵Σ_g ⁺ HCrH. Theoretical predictions for the equilibrium geometry, harmonic vibrational frequencies, and isotopic frequency shifts of the ⁵B₂ state compare favourably with the results of recent matrix isolation FT-IR work by Xiao, Hauge, and Margrave. The two-f TZ2P CCSD(T) optimized geometry of ⁵B₂ CrH₂ is r _e = 1·658 Å and ?_e = 114·4° (118° ± 5° is the experimentally estimated bond angle), while the harmonic vibrational frequencies are ω₁(a₁) = 1710, ω₂(a₁) = 582, and ω₃(b₂) = 1683 cm^-1 (experimentally assigned fundamentals in an argon matrix are the symmetric stretch 1651 cm^-1 and asymmetric stretch 1615 cm^-1). Isotopic frequency shifts of CrD₂ relative to CrH₂ are Δω₁(a₁) = -492 and Δω₃(b₂) = -477 cm^-1 (compared with symmetric stretch -462 cm^-1 and asymmetric stretch -448-cm^-1 from experiment).     

Interatomic potentials for the Na+—Rg complexes (Rg = He,Ne and Ar)

Interatomic potential energy curves are presented for the Na⁺—Rg (Rg = He, Ne and Ar) cationic complexes. The curves are calculated at the CCSD(T)/aug-cc-pVQZ level of theory, with correction for basis set superposition error being performed point-by-point. Ninety-six different bond lengths are used in the generation of the curves. From the curves rovibrational energy levels are calculated. These, in turn, are used to calculate the heat of formation of the cationic complexes, both by calculating partition functions under the assumption of a rigid rotor, harmonic oscillator, and also explicitly using the calculated rovibrational energy levels. The long range region of each of the curves is used to derive the D ₄ and D ₆ parameters, the former being used to derive the static polarizability a ₁ of each of the Rg atoms and the latter the first dispersion coefficients, C ₆(Na⁺—Rg).     

用耦合簇方法及相关一致基研究PH$lt;sub$gt;2$lt;/sub$gt;($lt;i$gt;X$lt;/i$gt;$lt;sup$gt;2$lt;/sup$gt;$lt;i$gt;B$lt;/i$gt;$lt;sub$gt;1$lt;/sub$gt;)自由基的解析势能函数

利用耦合簇方法和Dunning等提出的系列相关一致基对PH₂自由基的基态结构进行优化, 并使用优选出的cc-pV5Z基组对其进行频率计算. 结果表明,平衡核间距R_P—H=0.14185 nm, 键角α_HPH=91.8624°, 离解能D_e（HP—H）=3.483 eV, 对称伸缩振动频率ν₁（a₁）=2399.9781 cm^-1, 弯曲振动频率ν₂（a₁）=1128.4213 cm^-1,反对称伸缩振动频率ν₃（b₂）=2407.8374 cm^-1. 在此基础上采用多体项展式理论导出了PH₂自由基的解析势能函数, 其等值势能图准确再现了PH₂自由基分子的平衡结构特征和动力学特征. 关键词： 2自由基')" href="#">PH₂自由基 多体项展式理论 解析势能函数     

A study of basis set imbalance effects on the calculation of intramolecular potentials for van der Waals systems

The effects of using different basis sets have been investigated in the study of the intermolecular potential (IMP) of Ne₂, a prototypical van der Waals system. A balancing effect on the strength of the IMP was observed, whereby basis set inclusion of diffuse atom centred polarization functions (ACPFs) in conjunction with bond functions, at the expense of compact ACPFs, resulted in an overestimated IMP, while the opposite situation resulted in an underestimated IMP. Recent proposals made for monitoring the saturation of the SCF total atomic energy [10] and SCF interaction energy [11] are shown to be insufficient criteria with which to judge whether a basis set predicts an underestimated repulsive contribution to the interaction energy at the MP4(SDTQ) level, and hence whether a basis set predicts an overestimate in the IMP. The observations result in an unresolved ambiguity in choosing an appropriate basis set for larger van der Waals systems, where one is forced to make major concessions in basis set quality and where one does not have the experimental results with which to ‘guide’ the competing balance between the above basis functions.     

Potential of the A 1Σ u + state of He2

The potential of the lowest excited singlet state of He₂ is calculated. The best function includes 209 configurations constructed from 10 σ basis orbitals. Excellent agreement with experimental quantities depending on the shape of the potential near the minimum (equilibrium interatomic separation, vibrational and rotational constants for the lower vibration levels) is obtained. The dissociation energy is 18 600 cm^-1, compared to the experimental 19 910±50 cm^-1. Agreement is not as good for the highest vibrational levels.     

AsH(X3Σ－)及AsH2(X2B1)自由基的分子结构与解析势能函数

运用Gaussian 03程序包中的单双迭代三重激发耦合簇理论和相关一致五重基优化了AsH₂的基态结构,并在优化结构的基础上计算了它的离解能和振动频率. 结果表明：AsH₂基态的平衡构型具有C_2v对称性,键长R_As-H=01508 nm,键角∠HAsH=912231°,离解能D_e(HAs-H)=28795 eV,振动频率ν 关键词： 2')" href="#">AsH₂ Murrell-Sorbie函数 多体项展式理论 解析势能函数     

Theoretical study of ground and excited state potential energy surfaces for the Ca+-H2 complex

The potential energy surfaces of the Ca⁺-H₂ complex are calculated using the internally contracted multireference CI method (ICMR CI) and complete active space SCF (CAS SCF) reference wave functions. The calculations involve both the ground and the excited states correlating to (3d)²D and (4p)²P Ca⁺ terms and are carried out for C_∞v and C_2v configurations. Anisotropy of the potential surfaces has also been analysed by computing the interaction energy for some representative points as a function of the angle between the H₂ molecular axis and the Ca⁺—centre of mass of H₂ bond axis. The calculations have revealed the existence of a conical intersection of the lowest excited (3d)²B₂ potential surface with the ground state one. The obtained global energy minimum of the (3d)²B₂ potential surface lying 0.683 eV below the asymptote indicates a possible stabilization of the Ca⁺-H₂ complex towards formation of an exciplex in the (3d)Ca⁺-H₂(v = 0) collision process. The dependence of the vibrational energy levels of H₂ on the distance from Ca⁺ in the C_2v configuration has also been studied.