Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

The force constants and equilibrium geometry of water were calculated ab initio from Hartree-Fock self-consistent field wavefunctions using the force method, and a 53/31, a 73/3 + 1 and a 95/41 + 2 gaussian lobe basis set. The force method proved to be very economic and numerically accurate.

The calculated values agree well with the experimental ones. Especially good is the agreement for the interaction constant F_rα . Calculated force constants for the 95/41 + 2 basis are: F_r = 9·158 mdyn/å, F_α = 0·8513 mdyn/å, F_rα = +0·3007, F_rr = -0·1724; the experimental values from isotope frequencies are: F_r = 8·456, F_α = 0·762, F_rα = +0·246, F_rr = -0·100 mdyn/å. The agreement in the geometry is also good for the 95/41 + 2 basis r _e = 0·9518 å, α = 107·49°, and the experimental r _e = 0·9572 å, α = 104·52°.

Force constants were found to be quite insensitive to variation in the basis functions, all three sets giving almost the same result. On the other hand, the dipole moment derivative is very sensitive.     

Ab initio calculation of force constants and equilibrium geometries

Force constants of the molecules HF, NH₃, CH₄ and BH₄ ^- have been calculated ab initio by the force method with a 73/3 + 1 gaussian lobe basis set. The results, including a former calculation on H₂O, agree well with experiment: the average relative error is 12 per cent for the diagonal force constants and the average absolute error is 0·06 mdyn/Å for the off-diagonal ones. The trends are also correctly reproduced. It is concluded that ab initio calculations of this accuracy can help to solve a number of spectroscopic problems. Force constants of BH₄ ^- have been determined from a combination of spectroscopic and ab initio information. Geometries have been obtained with little computing work and show good agreement with experiment.     

Ab initio calculation of 14N nuclear quadrupole coupling constants

The use of ab initio Hartree-Fock electric field gradient calculations to predict nitrogen nuclear quadrupole coupling constants is examined using basis sets of split valence to triple zeta plus polarization size. From results on 20 to 35 molecules for each basis, such calculations are shown to be of predictive value if systematic errors are eliminated by using regression-derived scaling factors, and the reliability of each basis is assessed. For field gradient calculations on larger molecules, a significantly better alternative to a minimal basis which adds little extra computational cost, is proposed.     

Ab initio study of the electronic structure of the molecule-based ferromagnet Co[N(CN)2]2

We have investigated the electronic and magnetic properties of the molecule-based magnet Co[N(CN)₂]₂ using the full potential linearized augmented plane wave (FP-LAPW) method. The relative stability of the ground state, density of states and charge distributions were examined. Total energy calculations reveals that the ferromagnetic phase is a stable ground state for Co[N(CN)₂]₂ in agreement with the previous experimental findings. It is noteworthy that we predict the Co[N(CN)₂]₂ is a ferromagnetic semiconductor with a small band gap of 0.027 eV, and the semiconductor property can be connected to the strong crystal field splitting of Co²⁺ 3d states for Co[N(CN)₂]₂. Such a molecule-based ferromagnetic semiconductor would offer a potential for semiconductor applications, therefore, an experimental confirmation of our theoretical predictions is encouraged.     

Ab initio study of the force constants of inorganic molecules ONF and NF3

The force constants of ONF and NF₃ have been determined from Hartree-Fock ab initio wavefunctions by the force method. Three different Gaussian basis sets, ranging from 7s3p augmented with functions on the bonds to 5s2p, were used for ONF. Only the smallest basis was applied to NF₃. The results show remarkable agreement with experiment, especially for the coupling constants. The NF stretching force constant is greatly overestimated in calculations with the 5s2p basis. The calculated force field makes it possible to exclude sets of force constants which are unphysical but compatible with the experimental data. The results show that even calculations with 5s2p basis sets can contribute to the determination of force fields.The experimental value of the $\text{ON}\text{β}$ coupling constant in ONF ranges between 0.27 and 0.54 mdyn; our calculations corroborate the higher value. An estimation of the calculated molecular geometries is given.     

HeNO分子光谱常数和非谐振力场的从头算研究

在本论文中,我们在Gaussian 03软件下,采用密度泛函理论（B3LYP）以及二阶微扰理论（MP2）的方法结合Dunning相关一致基组cc-pVNZ (N=T,D,Q)以及6-311G、6-311G**、6-311G（2df,2pd）、6-311G（3df,3pd）基组优化了HeNO分子的几何结构,然后在此基础上计算了它们的光谱常数和非谐振力场。通过计算得到了分子的平衡几何结构、基频、转动常数、四次和六次离心畸变常数等,并与相关的实验值和理论值进行了比较;预测了部分光谱常数,其中包括谐振频率、非谐性常数、振转相互作用常数、三次力常数、四次力常数和科里奥利耦合常数。结果表明,在MP2方法下计算的结果要优于B3LYP计算的结果;基组6-311G、6-311G**、6-311G（2df,2pd）、6-311G（3df,3pd）下的结果普遍优于cc-PVNZ (N=T,D,Q)得到的结果。结果还表明,MP2理论方法结合基组6-311G、6-311G**、6-311G（2df,2pd）、6-311G（3df,3pd）基组计算的结果非常接近实验值,对实验测量某些光谱数据有较好的预测作用     

Ab initio calculation of spin-orbit coupling constants for gaussian lobe and gaussian-type wave functions

The spin-orbit coupling constants of a series of diatomic compounds containing first row atoms have been calculated using ab initio molecular wave functions with gaussian lobe and gaussian-type basis sets. In most cases, fair agreement with the experimental values has been achieved. It is pointed out that multicentre terms have almost no effect on the spin-orbit coupling constant. Furthermore, suggestions for a one-electron approximation using effective nuclear charges are presented.     

Ab initio anharmonic force field and equilibrium structure of the sulfonium ion

The semi-experimental equilibrium structure of the sulfonium ion, , has been obtained from the experimental ground-state rotational constants available for five isotopologues and the corresponding vibrational corrections computed at the CCSD(T)/cc-pwCVQZ level of theory. This geometry has been found in very good agreement with the pure ab initio equilibrium structure calculated at the CCSD(T) level of theory using a basis set of sextuple-zeta quality and including core correlation corrections. The anharmonic force field has been used for deriving spectroscopic properties: in particular, in addition to the vibrational corrections, the rotational parameters of the SH₂D⁺ isotopic species, not yet experimentally observed, have been predicted to a guessed good accuracy.     

Ab initio study of rovibronic energies of the CH 2 + molecular ion

The potential energy surfaces of the lowest electronic states $ \tilde X The potential energy surfaces of the lowest electronic states ² A ₁ and ² B ₁ of the CH₂⁺ molecular ion are calculated in the second order of the perturbation theory with the reference function obtained by the multiconfiguration self-consistent-field method in the complete-active-space approximation. Based on the ab initio calculated potential energy surfaces, the rovibronic energies of CH₂⁺ are calculated by the variational method using the RENNER Hamiltonian. It is found that the accuracy of the perturbation theory method involving many reference configurations is as good as the accuracy of the best ab initio calculations performed by the configuration interaction method with many reference configurations and by the coupled cluster method with a single reference configuration. Empirical refinement of the two parameters of the potential function leads to good agreement between calculation and experiment, except for the wavenumbers of the (0, 3, 0)¹ ← (0, 0, 0)⁰ transitions. Original Russian Text ? V.G. Solomonik, A. Yu. Yachmenev, 2008, published in Optika i Spektroskopiya, 2008, Vol. 104, No. 6, pp. 904–910.     

Ab initio calculation of the 4He(e, e'd )d reaction

The two-body knock-out reaction ⁴He(e, e'd )d is calculated at various momentum transfers. The full four-nucleon dynamics is taken into account microscopically both in the initial and the final states. As NN interaction the central MT-I/III potential is used. The calculation shows a strong reduction of the coincidence cross-section due to the final-state interaction. Nonetheless, the theoretical results exhibit a considerable overestimation of the experimental cross-section at lower momentum transfer. Comparisons with other, less complete, calculations suggest that consideration of a more realistic ground state might not be sufficient for a good agreement with experiment, rather a more realistic final-state interaction could play an essential role.     

Non-empirical calculation of spin-orbit coupling constants for some linear triatomic molecules

Higher-order sum rules of the form , are derived for the rotatory strengths of randomly oriented and oriented molecules. In randomly oriented molecules R ⁽ⁿ⁾ = 0 for one-electron systems when n<5, whereas R ⁽⁰⁾=R ⁽²⁾=R ⁽⁴⁾=0 for many-electron systems. In oriented molecules R ⁽ⁿ⁾=0 for one-electron systems when n<3, whereas R ⁽⁰⁾=R ⁽²⁾=0 for many-electron systems. The remaining non-vanishing R ⁽ⁿ⁾ can all be evaluated as diagonal matrix elements of the ground-state wave-function. The resulting expressions are applied to the one-electron model of Condon, Altar and Eyring, and to the coupled oscillator model of Born, Oseen and Kuhn. It is found that the rotatory strengths of the latter model do not fulfil some of the general sum rules. The reason for this discrepancy is discussed. Finally the implications of the present results for the controversy of one-electron versus coupled oscillator models are discussed, and it is proposed that the non-vanishing moments be used as ‘chirality indices’ for specific ground-state wave-functions.     

Ab initio calculation of the Gilbert damping parameter via the linear response formalism

A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with coherent potential approximation alloy theory allows it to be applied to a wide range of situations. This is demonstrated with results obtained for the bcc alloy system Fe(1-x)Co(x) as well as for a series of alloys of Permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of α when small amounts of substitutional Cu are introduced.     

自由基-分子反应:F+Propene(CH2CHCH3)的从头算研究

采用从头算CCSD(T)/6-311 G(2d,2p)//B3LYP/6-311G(d,p)方法,研究了自由基-分子反应F CH2CHCH3的各种不同的反应通道．该反应主要是通过复合物形成机制进行,即F分别加到碳碳双键的两端形成自由基复合物1和2．这两种亚稳态自由基会解离成三种产物:H C3H5F、CH3 C2H3F和HF C3H5．理论计算结果表明,生成CH3 C2H3F是反应的主要通道,而生成H C3H5F和HF C3H5对产物也有一定的贡献．这一结果和实验符合得很好．     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.