Ab initio calculation of maximum bond order hybrid orbitals

Summary The maximum bond order hybrid orbital (MBOHO) procedure is tested onab initio level by use of the density matrix in Löwdin orthogonalized atomic orbital basis. The direct MBOHO calculation based on the whole density matrix includes also the hybridization of the inner atomic orbitals, and the MBOHO calculation based on the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The concrete MBOHO calculations based on theab initio calculation with STO-3G basis show that the components of the s atomic orbitals in MBOHOs and the maximum bond orders obtained from the two kinds of MBOHO calculations are very close to each other, and that the two kinds of MBOHOs all have the excellent correlativity with the nuclear spin-spin coupling constants.The project supported by National Natural Science Foundation of China and the Excellent Young University Teacher's Foundation of State Education Commission of China.     

NMR偶合常数的从头算级别自然杂化轨道研究

为了研究自然杂化轨道计算结果与核自旋偶合常数的相关性,本文进行了从头算级别的自然杂化轨道计算。采用STO－3G基组,利用Lowdin正交化原子轨道基组下的密度矩阵,得到了分子中各原子的杂化轨道、净电荷与^13C-H、^13C-^13C键自旋偶合常数^1Jcn和^1Jcc之间关系式。利用这些式子计算得到的结果与实验数据非常一致。     

A theoretical study on the hyperfine coupling constant of the radical cations of aliphatic ethers

Summary The hyperfine coupling constants of the radical cations of dimethylether, oxetane (oxacyclobutane), and tetrahydrofuran (oxacyclopentane) are studied byab-initio molecular orbital theories. The extraordinarily large hyperfine coupling constants of the protons of the ethers that have been found experimentally are analyzed to conclude that an important mechanism of the hole delocalization is the spin polarization in the H-C-O-C-H bond. It is also found that for the ethereal systems conventional molecular orbital calculations give glaringly small spin densities but the SAC-CI calculation gives remarkably improved values.     

Spin-Phonon Coupling and Slow-Magnetic Relaxation in Pristine Ferrocenium

We report the spin dynamic properties of non-substituted ferrocenium complexes. Ferrocenium shows a field-induced single-molecule magnet behaviour in DMF solution while cobaltocene lacks slow spin relaxation neither in powder nor in solution. Multireference quantum mechanical calculations give a non-Aufbau orbital occupation for ferrocenium with small first excitation energy that agrees with the relatively large measured magnetic anisotropy for a transition metal S=1/2 system. The analysis of the spin relaxation shows an important participation of quantum tunnelling, Raman, direct and local-mode mechanisms which depend on temperature and the external field conditions. The calculation of spin-phonon coupling constants for the vibrational modes shows that the first vibrational mode, despite having a low spin-phonon constant, is the most efficient process for the spin relaxation at low temperatures. In such conditions, vibrational modes with higher spin-phonon coupling constants are not populated. Additionally, the vibrational energy of this first mode is in excellent agreement with the experimental fitted value obtained from the local-mode mechanism.     

Evaluation of a new procedure for quantum-chemical estimates of constants of isotropic hyperfine coupling with protons in free radicals

A new procedure for quantum-chemical estimates of the constants of isotropic hyperfine coupling (IHFC) with protons using the orbital spin populations calculated in the basis set of symmetrically orthogonalized (according to Löwdin) atomic orbitals is tested taking 16 well-studied simplest π-electron and σ-electron radicals as examples. The most probable reasons for and possible ways of correcting large deviations of calculated IHFC constants from experimental values are considered. The efficiency of the semiempirical MNDORU scheme, which makes it possible to consistently estimate the delocalization and spin-polarization contributions to the constants of IHFC with protons in free radicals, is demonstrated.     

An AB initio molecular orbital study of the PF2 radical

Gaussian orbital calculation of the ESR coupling constants in the PF₂ radical are presented, in excellent agreement with experiment.     

Calculations of the indirect nuclear spin–spin coupling constants of PbH4

We report ab initio calculations of the indirect nuclear spin–spin coupling constants of PbH₄ using a basis set which was specially optimized for correlated calculations of spin–spin coupling constants. All nonrelativistic contributions and the most important part of the spin–orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multiconfigurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The effects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We find that the Fermi contact term dominates the Pb‐H coupling, whereas for the H‐H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation affects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the different correlated methods give ambiguous results for the Fermi contact contribution to the H‐H couplings. The dependence of both coupling constants on the Pb‐H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation. Received: 16 November 1998 / Accepted: 30 March 1999 / Published online: 14 July 1999     

Maximum bond order hybrid orbitals

Summary Based on the simplified calculation scheme of the maximum bond order principle and the basic idea of the maximum overlap symmetry orbital method, a simple procedure is suggested for constructing systematically the bonding hybrid orbitals, called maximum bond order hybrid orbitals, for a given molecule from the first-order density matrix obtained from a molecular orbital calculation. As an example, the proposed procedure is performed for some typical small molecules by use of the density matrix obtained from CNDO/2 calculation. It is shown that the bonding hybrid orbitals constructed by using the procedure are extremely close to those by using the natural hybrid orbital procedure and in good agreement with chemical intuition, and that the proposed procedure can be performed more easily than the natural hybrid orbital procedure and can given simultaneously the values of the maximum bond order for all bonds in molecules.The project was supported by National Natural Science Foundation of China and also supported partly by Foundation of Hubei Education Commission     

HFI and DFT study of the bonding in complexes of halogen and interhalogen diatomics with Lewis base

We have analyzed by means of DFT calculations with use of the pseudo-potential the nuclear quadrupole coupling constants of a range of XYB complexes (n aσ type in Mulliken notation) formed between diatomic interhalogen molecules XY and Lewis bases B. The geometrical parameters, rotational and halogen nuclear quadrupole coupling constants obtained by these calculations substantially corresponded to the data of microwave spectroscopy in the gas phase. An analysis of the quality of the calculations that employ the pseudo-potential and the expanded basis set for the halogen compounds was carried out. The ZORA model is shown to be a viable alternative to the computationally demanding BH and HLYP model for the calculation of halogen and nitrogen coupling constants in molecules. In addition, the ZORA model, in contrast to the pseudo-potential model, leads to realistic values of iodine nuclear quadrupole coupling constants. From electron partitioning analyses and Klopman's approach it follows that for the IClB complexes the electrostatic bonding is predominant relative to covalent bonding.     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

Core model calculation of the electric field gradient: Projection operator formalism with application to NH3

A core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH₃ as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N—D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single-center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.     

Bond orbital analysis of the deuteron quadrupole coupling constants in MD4 molecules

The deuteron quadrupole coupling constants were used as constraints on the bond orbital functions of a series of MD₄ molecules (M=B, C, N, Al, Si, P). It was demonstrated that a minimal basis set may be sufficient to describe first row deuterates, but not for second row deuterates, where double zeta orbitals are needed.This work was started when the author was a post doctoral fellow at Battelle Memorial Institute, Columbus, Ohio.     

The absolute sign of J coupling constants determined using the order matrix calculation

A novel methodology using the order matrix calculation to determine the absolute sign of spin-spin couplings based on the structure of organic compounds is presented. The sign of the residual dipolar coupling (RDC) depends on the sign of corresponding scalar spin-spin coupling constant and the sign of the RDC has a dramatic influence on the order matrix calculation. Therefore, the sign of the spin-spin coupling constant can be obtained by an order matrix calculation through the corresponding RDC. Six types of spin-spin coupling constants, including 2J(H,H), 1J(C,F), 2J(C,F), 3J(C,F), 2J(F,H) and 3J(F,H), were obtained simultaneously. Except for 3J(C,F) where the measured RDCs have very small magnitudes, the signs were determined unambiguously.     

系列化合物C-H伸缩频率的自然杂化轨道研究

在计算C-H核自旋-自旋偶合常数的新公式及其与C-H伸缩频率之间的关系的基础上, 得出了计算C-H伸缩频率的新的一般关系式。并利用CNDO/2分子轨道和自然杂化轨道方法, 具体计算了三种不同系列化合物的原子净电荷和自然杂化轨道。给出了计算不同系列化合物C-H伸缩频率的良好线性关系式。结果表明, 碳氢化合物中的C-H伸缩频率主要由原子的轨道杂化作用所决定, 而对于含杂原子的取代碳氢化合物, C-H键的极性成为影响伸缩频率的重要因素。     

Fluorine nuclear spin coupling constants in fluoro-substituted furans

In order to assist experimental assignments in olefinic and aromatic fluorine compounds, fluorine nuclear coupling constants have been obtained from the first-order self-consistent perturbation theory equation with the INDO molecular orbital approximation in a series of fluoro-substituted furans. There is a clear distinction between the magnitudes and signs for the four fluorine coupling positions; the importance of the orbital and spin-dipolar contributions is very clear. Tentative signs are suggested for all the coupling constants.     

Ab initio molecular orbital calculations of nuclear spin-spin coupling constants in PH2, PH3, PH4 and P2H4

Ab initio molecular orbital calculations of nuclear spin-spin coupling constants in PH⁻₂, PH₃, PH⁺₄ and P₂H₄ have been carried out employing SCF perturbation theory. Basis set dependence of all the four contributing terms has been studied in order to find the criterion for the selection of basis sets to be employed for computing this property. The dependence of the coupling constants of PH⁻₂ on its geometry has also been found. This study also discusses the requirement for satisfactory computation of couplings in cases where none of the coupling nuclei is a proton. It is found that bond-centred functions along with at least double zeta basis sets reproduce coupling constants quite satisfactorily. In all the cases studied, uncontracted core basis functions yield couplings which are in better agreement with experimental couplings than those obtained with contracted core functions.     

Theoretical prediction and assignment of vicinal 1H-1H coupling constants of diastereomeric 3-alkoxy-6,7-epoxy-2-oxabicyclo[3.3.0]octanes

Spin-spin coupling constants between nuclei in NMR spectroscopy reflect their spatial arrangement. A number of calculation methods, applying different levels of theory, have been developed to support the stereochemical assignment of novel compounds. Nevertheless, revisions of the assignment of structures in the literature are not rare. In the present work, the reliability of the calculation methods amenable for a theoretical prediction of spin-spin coupling constants of vicinal protons to support correct stereochemical assignment of substitution at five-membered rings of 3-alkoxy-6,7-epoxy-2-oxabicyclo[3.3.0]octanes was studied. Experimental (3)J(H,H) coupling constants were compared with the coupling constants calculated for all possible diastereomers. The fully quantum chemical approach provided theoretical (3)J(H,H) coupling constants with an absolute deviation of no more than 1.1 Hz for 91% of the experimentally studied coupled spins, whereas the methods without quantum chemical geometry optimization resulted in completely unreliable predictions. Consequently, for a reliable stereochemical assignment of small and medium size molecules, the protocol for calculating the coupling constants based on the results of the quantum chemical geometry optimization is recommended.     

A systematic preparation of new contracted Gaussian-type orbital sets. VIII. MINI-1 and MIDI-1 sets for Ga through Cd

Minimal contracted Gaussian basis sets are presented for Ga through Cd. Characteristically these Gaussian-based minimal sets give far better d orbital energies than those by minimal STO basis sets. These new basis sets were tested on Br₂ for which a new benchmark calculation was also performed. The test result is satisfactory in that these basis sets produce good general agreement with the near Hartree–Fock calculation with respect to the molecular spectroscopic constants.     

Calculation of exchange coupling constants in solid state transition metal compounds using localized atomic orbital basis sets

The application of theoretical methods based on density functional theory using hybrid functionals and localized, atomic orbital type basis sets is shown to provide good estimates for exchange coupling constants in non-metallic, solid state transition metal compounds with relatively complex crystal structures. The accuracy of the calculated exchange coupling constants is similar to that previously obtained for dinuclear and polynuclear molecular compounds. As an application of this procedure, the magnetic properties of the high-temperature phase of CuGeO₃, the recently synthesized silver copper oxide Ag₂Cu₂O₃, and the family of M[N(CN)₂]₂ (M=Cr(II), Mn(II), Fe(II), Co(II), Ni(II) and Cu(II)) compounds are analyzed via the computation of their most relevant exchange coupling constants.