Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.     

Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order

A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison with spin-free Dirac-Coulomb calculations indicates that the DPT series exhibits a smooth and monotonic convergence. The rate of convergence, however, depends on the charge of the involved nuclei and significantly slows down for heavy-element compounds.     

一系列水合和非水合铀酰卤族(F,Cl,Br)配合物在水溶液中的结构和紫外吸收光谱性质的密度泛函理论研究

本文考虑相对论效应并应用密度泛函理论(DFT)研究水溶液中UO2Xn(H2O)5-n(X=F,Cl,Br;n=1～4)和UO2Xn(X=F,Cl,Br;n=1～6)一系列水合和非水合铀酰化合物的结构和紫外吸收光谱性质。将这一系列物质命名为Xnm(X为F,Cl,和Br;n为卤素配体个数,m为水分子配体的个数)。在水溶液中,溶剂化效应采用类导体屏蔽模型(COSMO)并采用SAS溶剂接触曲面构造空穴模拟水溶剂对配合物的作用。配合物的紫外光谱性质采用考虑旋-轨耦合相对论效应的含时密度泛函(SO-TD-DFT)进行计算。U=O键随着F配体数目的增加而明显伸长,然而随Cl和Br配体数目的增加变化较小。随X配体数目的增加和水分子参与配位,铀与X的结合能逐渐减弱。配合物的紫外光谱计算表明铀酰氟的各种配合物并不出现特征吸收峰,而铀酰氯和铀酰溴的各种配合物均有特征吸收光谱。通过分子轨道分析可以很好解释光谱所体现的特征。     

Local unitary transformation method for large-scale two-component relativistic calculations: case for a one-electron Dirac Hamiltonian

An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X(2) (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)(n) (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor.     

Theoretical study on the low-lying electronic states of NiH and NiAt

The low-lying electronic states of NiH and NiAt are investigated by using multireference second-order perturbation theory with relativistic effects taken into account. The potential energy curves as well as the corresponding spectroscopic constants are reported. The results are grossly in good agreement with the available experimental data and should thus be very useful for guiding future experimental measurements. A cross comparison with other nickel monohalides NiX (X = F, Cl, Br, and I) reveals that the change in the spin-orbit splittings when going from lighter to heavier ligands results more from the state interaction than from the relativistic effects of the ligands.     

Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula

Two expressions for nuclear-magnetic-shielding tensor components based on analytically differentiating the electronic energy of a system are presented. The first is based on a second-order Douglas-Kroll-Hess approach, in which the off-diagonal block terms of the transformed Dirac Hamiltonian are diminished to second order with respect to both the electrostatic nuclear attraction potential V and the magnetic vector potential A. The second expression is based on the method of Barysz-Sadlej-Snijders, in which the off-diagonal block terms in the transformed Dirac Hamiltonian are completely eliminated with respect to purely V terms, while they are diminished to second order with respect to terms including A. The two approaches are applied to the calculation of nuclear magnetic shieldings of HX (X=F, Cl, Br, I), H2X (X=O, S, Se, Te), and noble gas X (X =He,Ne,Ar,Kr,Xe) systems with common gauge origins. The results show that relativistic corrections of higher than second order are negligibly small, except for the paramagnetic parts of I, Te, and Xe shieldings. The present calculations yield very large positive values for the anisotropy of proton shielding, deltasigma(H) = sigmaparallel(H)-sigmaperpendicular(H), of HI compared to previous reports. Unfortunately, no experimental values for the anisotropy of proton shielding in HI are available for verification.     

Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory

In this work, we present relativistic corrections to first-order electrical properties obtained using fourth-order direct perturbation theory (DPT4) at the Hartree-Fock level. The considered properties, i.e., dipole moments and electrical-field gradients, have been calculated using numerical differentiation techniques based on a recently reported DPT4 code for energies [S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011)]. For the hydrogen halides HX, X=F, Cl, Br, I, and At, we study the convergence of the scalar-relativistic contributions by comparing the computed DPT corrections to results from spin-free Dirac-Hartree-Fock calculations. Furthermore, since in the DPT series spin-orbit contributions first appear at fourth order, we investigate their magnitude and judge the performance of the DPT4 treatment by means of Dirac-Hartree-Fock benchmark calculations. Finally, motivated by experimental investigations of the molecules CH(2)FBr, CHF(2)Br, and CH(2)FI, we present theoretical results for their halogen quadrupole-coupling tensors and give recommendations concerning the importance of higher-order scalar-relativistic and spin-orbit corrections.     

Relativistic effects on nuclear magnetic shielding constants in HX and CH3X (X=Br,I) based on the linear response within the elimination of small component approach

Numerical calculations of relativistic effects on nuclear magnetic shielding constants sigma corresponding to all one-body operators obtained within a formalism developed in previous work were carried out. In this formalism, the elimination of small component scheme is applied to evaluate all quantities entering a four-component RSPT(2) expression of magnetic molecular properties. HX and CH3X (X=Br,I) were taken as model compounds. Calculations were carried out at the Hartree-Fock level for first-order quantities, and at the random-phase approximation (RPA) level for second- and third-order ones. It was found that values of sigma(X) are largely affected by several relativistic corrections not previously considered in the bibliography. sigma Values of the H nucleus are in close agreement with four-component RPA ones. Overall relativistic effects on the shift of sigma(X) from HX to CH3X are smaller than the nonrelativistic shifts.     

Relativistic effects on the nuclear magnetic resonance shielding of FX (X = F, Cl, Br, I, and At) molecular systems

We present ab inito full four-component and spin-free calculations of the NMR shielding parameter, σ, in the FX (X = F, Cl, Br, I and At) molecular systems. A different expression that overcomes the traditional non-relativistic (NR) approximation used to calculate the relationship between spin-rotation constants and the paramagnetic terms of σ(p) are given. Large deviations from NR results are obtained for σ(X; X = I and At) and for σ(F; FAt). σ(∥)(p)(I; FI) is zero within the NR approach but -447.4 parts per million from our calculations. The electronic origin of relativistic corrections are analyzed. All passive SO contributions are obtained as a difference between full four-component calculations and spin-free ones. Considering relativistic effects on the anisotropy, we obtain a deviation of 10% for I and 25% for At. σ(∥)(SO)(X) is always negative and σ(∥)(SF)(X) is always positive; the passive SO becomes larger than the SF one for X = Br, I, and At. Both σ(∥)(SO)(X) and σ(⊥)(SO)(X) have a functional dependence such as a Z(X)(b) being the exponent 3.5 and 3.65, respectively. The passive SO contribution to the anisotropy has a similar functional dependence with an exponent of 3.60, meaning that its perpendicular component is larger than its corresponding parallel component.     

Density functional computation of 49Ti NMR chemical shifts

49Ti chemical shifts of TiX4 (X = Cl, Br, F), TiClnMe(4-n) (n = 0-3), Ti(C5H5)2X2 (X = F, Cl, Br) and Ti(CO)6(2-) were computed, using geometries optimized with the gradient-corrected BP86 density functional, at the GIAO (gauge-including atomic orbitals)-Hartree-Fock, BPW91, and B3LYP levels. For this set of compounds, substituent effects on delta(49Ti) are reasonably well described with all methods considered; judged from mean absolute deviations from experiment, B3LYP performs best. Zero-point corrections to the delta(49Ti) values, evaluated from a perturbational approach based on vibrationally averaged effective geometries, turn out to be fairly small. Electric field gradients computed with the B3LYP functional do not correlate with trends in 49Ti NMR linewidths. Attempts are reported to correlate the delta(49Ti) values of Ti[YC(O)CHC(O)Y]2Cl2 (Y = H, Me, CF3, CN, F, Cl and Br) with the rate-limiting propagation barrier for ethylene polymerization using catalysts derived from these precursors.     

Theoretical studies on magnetic circular dichroism by the finite perturbation method with relativistic corrections

A theoretical method for calculating magnetic circular dichroism (MCD) of molecules is presented. We examined the numerical accuracy and the stability of the finite perturbation (FP) method and the sum-over-state (SOS) perturbation method. The relativistic effects are shown to be important for the MCD spectra of molecules containing heavy elements. Calculations using the FP and the SOS methods were carried out for ethylene, para- and ortho-benzoquinone, showing that the FP method is superior to the SOS method, as expected. The relativistic effect was examined using the second-order Douglas-Kroll Hamiltonians for the halogen molecules F2, Cl2, Br2, and I2. The Faraday terms of I2 and Br2 were strongly affected by the relativistic effects, while the effect was negligible for Cl2 and F2.     

Oxidative addition of hydrogen halides and dihalogens to Pd. Trends in reactivity and relativistic effects

We have theoretically studied the oxidative addition of HX and X(2) to palladium for X = F, Cl, Br, I and At, using both nonrelativistic and ZORA-relativistic density functional theory at BLYP/QZ4P. The purpose is 3-fold: (i) to obtain a set of consistent potential energy surfaces (PESs) to infer accurate trends in reactivity for simple, archetypal oxidative addition reactions; (ii) to assess how relativistic effects modify these trends along X = F, Cl, Br, I and At; and (iii) to rationalize the trends in reactivity in terms of the reactants' molecular-orbital (MO) electronic structure and the H-X and X-X bond strengths. For the latter, we provide full Dirac-Coulomb CCSD(T) benchmarks. All oxidative additions to Pd are exothermic and have a negative overall barrier, except that of HF which is approximately thermoneutral and has a positive overall barrier. The activation barriers of the HX oxidative additions decrease systematically as X descends in group 17 of the periodic table; those of X(2) first increase, from F to Cl, but then also decrease further down group 17. On the other hand, HX and X(2) show clearly opposite trends regarding the heat of reaction: that of HX becomes more exothermic and that of X(2) less exothermic as X descends in group 17. Relativistic effects can be as large as 15-20 kcal/mol but they do not change the qualitative trends. Interestingly, the influence of relativistic effects on activation barriers and heats of reaction decreases for the heavier halogens due to counteracting relativistic effects in palladium and the halogens.     

Influence of ligand polarizability on the reversible binding of O2 by trans-[Rh(X)(XNC)(PPh3)2] (X = Cl, Br, SC6F5, C2Ph; XNC = xylyl isocyanide). Structures and a kinetic study

The complexes trans-[Rh(X)(XNC)(PPh 3) 2] (X = Cl, 1; Br, 2; SC 6F 5, 3; C 2Ph, 4; XNC = xylyl isocyanide) combine reversibly with molecular oxygen to give [Rh(X)(O 2)(XNC)(PPh 3) 2] of which [Rh(SC 6F 5)(O 2)(XNC)(PPh 3) 2] ( 7) and [Rh(C 2Ph)(O 2)(XNC)(PPh 3) 2] ( 8) are sufficiently stable to be isolated in crystalline form. Complexes 2, 3, 4, and 7 have been structurally characterized. Kinetic data for the dissociation of O 2 from the dioxygen adducts of 1- 4 were obtained using (31)P NMR to monitor changes in the concentration of [Rh(X)(O 2)(XNC)(PPh 3) 2] (X = Cl, Br, SC 6F 5, C 2Ph) resulting from the bubbling of argon through the respective warmed solutions (solvent chlorobenzene). From data recorded at temperatures in the range 30-70 degrees C, activation parameters were obtained as follows: Delta H (++) (kJ mol (-1)): 31.7 +/- 1.6 (X = Cl), 52.1 +/- 4.3 (X = Br), 66.0 +/- 5.8 (X = SC 6F 5), 101.3 +/- 1.8 (X = C 2Ph); Delta S (++) (J K (-1) mol (-1)): -170.3 +/- 5.0 (X = Cl), -120 +/- 13.6 (X = Br), -89 +/- 18.2 (X = SC 6F 5), -6.4 +/- 5.4 (X = C 2Ph). The values of Delta H (++) and Delta S (++) are closely correlated (R (2) = 0.9997), consistent with a common dissociation pathway along which the rate-determining step occurs at a different position for each X. Relative magnitudes of Delta H (++) are interpreted in terms of differing polarizabilities of ligands X.     

Theoretical study of XPO (X=H,F,Cl,Br) molecules: Structural and molecular properties

A theoretical study has been performed on the ground state of XPO systems, where X=H, F, Cl, and Br. Structural and molecular properties have been calculated at high level of theory: the CCSD(T) method in conjunction with a hierarchical series of correlation consistent basis sets has been employed. Extrapolation to complete basis set as well as core-valence and scalar relativistic effects have been considered.     

Atomic Contributions from Spin‐Orbit Coupling to 29Si NMR Chemical Shifts in Metallasilatrane Complexes

New members of a novel class of metallasilatrane complexes [X‐Si‐(μ‐mt)₄‐M‐Y], with M=Ni, Pd, Pt, X=F, Cl, Y=Cl, Br, I, and mt=2‐mercapto‐1‐methylimidazolide, have been synthesized and characterized structurally by X‐ray diffraction and by ²⁹Si solid‐state NMR. Spin‐orbit (SO) effects on the ²⁹Si chemical shifts induced by the metal, by the sulfur atoms in the ligand, and by heavy halide ligands Y=Cl, Br, I were investigated with the help of relativistic density functional calculations. Operators used in the calculations were constructed such that SO coupling can selectively be switched off for certain atoms. The unexpectedly large SO effects on the ²⁹Si shielding in the Ni complex with X=Y=Cl reported recently originate directly from the Ni atom, not from other moderately heavy atoms in the complex. With respect to Pd, SO effects are amplified for Ni owing to its smaller ligand‐field splitting, despite the smaller nuclear charge. In the X=Cl, Y=Cl, Br, I series of complexes the Y ligand strongly modulates the ²⁹Si shift by amplifying or suppressing the metal SO effects. The pronounced delocalization of the partially covalent M←Y bond plays an important role in modulating the ²⁹Si shielding. We also demonstrate an influence from the X ligand on the ²⁹Si SO shielding contributions originating at Y. The NMR spectra for [X‐Si‐(μ‐mt)₄‐M‐Y] must be interpreted mainly based on electronic and relativistic effects, rather than structural differences between the complexes. The results highlight the sometimes unintuitive role of SO coupling in NMR spectra of complexes containing heavy atoms.     

Microhydration of X2 gas (X = Cl, Br, and I): a theoretical study on X2.nH2O clusters (n = 1-8)

Structure and properties of hydrated clusters of halogen gas, X2.nH2O (X = Cl, Br, and I; n = 1-8) are presented following first principle based electronic structure theory, namely, BHHLYP density functional and second-order Moller-Plesset perturbation (MP2) methods. Several geometrical arrangements are considered as initial guess structures to look for the minimum energy equilibrium structures by applying the 6-311++G(d,p) set of the basis function. Results on X2-water clusters (X = Br and I) suggest that X2 exists as a charge separated ion pair, X+delta-X-delta in the hydrated clusters, X2.nH2O (n > or = 2). Though the optimized structures of Cl2.nH2O clusters look like X2.nH2O (X = Br and I) clusters, Cl2 does not exist as a charge separated ion pair in the presence of solvent water molecules. The calculated interaction energy between X2 and solvent water cluster increases from Cl2.nH2O to I2.nH2O clusters, suggesting solubility of gas-phase I2 in water to be a maximum among these three systems. Static and dynamic polarizabilities of hydrated X2 clusters, X2.nH2O, are calculated and observed to vary linearly with the size (n) of these water clusters with correlation coefficient >0.999. This suggests that the polarizability of the larger size hydrated clusters can be reliably predicted. Static and dynamic polarizabilities of these hydrated clusters grow exponentially with the frequency of an external applied field for a particular size (n) of hydrated cluster.     

Investigations of hydrogen-bonded systems: Local density approximation and gradient corrections

The applicability of the local density approximation (LDA ) and of corresponding gradient corrections (for the exchange and correlation energy) for the treatment of the hydrogen bond is investigated. As test systems, we consider the water dimer and the H₂O…?HX complexes (X = F, Cl, Br): Using an LCAO scheme, their equilibrium geometries and interaction energies are ?alculated and compared with experimental data and with other calculations. We obtain that the LDA gives the geometries in qualitative agreement with other data, whereas the energies are overestimated. The use of the gradient corrections (GC ) according to Becke and Perdew leads to a significant improvement of the geometry, and especially of the interaction energies. The calculations indicate further that LDA + GC should also be able to describe weaker intermolecular interactions than the usual hydrogen bond. Finally, a short discussion of the charge distribution and the dipole moments of the H₂O…?HX complexes is performed. © 1994 John Wiley & Sons, Inc.     

苯-卤素(X2, X=F, Cl, Br, I)相互作用本质的对称性匹配微扰理论研究

在MP2水平下对被定义为"电荷转移复合物(CTC)"的苯(C6H6)-卤素分子X2(X＝F, Cl, Br, I)相互作用体系进行了量子化学研究. 在优化所得C6H6-X2(X＝F, Cl, Br, I)复合物的平衡几何结构中, 卤素分子X2接近垂直指向苯环上碳-碳双键的中心. 自然键轨道(NBO)分析结果表明, 苯-卤素体系中电荷转移的数量很少. 对称性匹配微扰理论(Symmetry-adapted perturbation theory, SAPT) 能量分解结果显示, 在4个复合物体系中, 静电作用的贡献相对较小(只占总吸引作用的20%左右), 对于C6H6-F2体系, 色散作用是其主要吸引作用, 对于C6H6-Cl2, C6H6-Br2和C6H6-I2 体系, 诱导作用则是其主要的吸引作用, 从F到I, 色散作用逐渐减弱, 诱导作用逐渐增强, 表明在电子相关水平上将苯-卤素体系称为"电荷转移复合物"的说法并不确切.     

卤代甲烷的赝势从头算研究I. CH~3X(X=F,Cl, Br,I)的化学键 和电离势

我们使用相对论赝势从头计算方法系统地研究了CH~3X(X=F,Cl,Br,I)系列分子的电子结构及其变化规律,并根据Koopmans定理指定了光电子能谱。