Relativistic Zeroth-order Regular Approximation Research Articles

Electron-nucleus cusp correction scheme for the relativistic zeroth-order regular approximation quantum Monte Carlo method

A cusp correction scheme for the relativistic zeroth-order regular approximation (ZORA) quantum Monte Carlo method is proposed by extending the nonrelativistic cusp correction scheme of Ma et al. [J. Chem. Phys. 122, 224322 (2005)]. In this scheme, molecular orbitals that appear in Slater-Jastrow type wave functions are replaced with the exponential-type correction functions within a correction radius. Analysis of the behavior of the ZORA local energy in electron-nucleus collisions reveals that the Kato's cusp condition is not applicable to the ZORA QMC method. The divergence of the electron-nucleus Coulomb potential term in the ZORA local energy is remedied by adding a new logarithmic correction term. This method is shown to be useful for improving the numerical stability of the ZORA-QMC calculations using both Gaussian and Slater basis functions.

Probing the Solvent Shell with 195Pt Chemical Shifts: Density Functional Theory Molecular Dynamics Study of PtII and PtIV Anionic Complexes in Aqueous Solution

Ab initio molecular dynamics (aiMD) simulations based on density functional theory (DFT) were performed on a set of five anionic platinum complexes in aqueous solution. (195)Pt nuclear magnetic shielding constants were computed with DFT as averages over the aiMD trajectories, using the two-component relativistic zeroth-order regular approximation (ZORA) in order to treat relativistic effects on the Pt shielding tensors. The chemical shifts obtained from the aiMD averages are in good agreement with experimental data. For Pt(II) and Pt(IV) halide complexes we found an intermediate solvent shell interacting with the complexes that causes pronounced solvent effects on the Pt chemical shifts. For these complexes, the magnitude of solvent effects on the Pt shielding constant can be correlated with the surface charge density. For square-planar Pt complexes the aiMD simulations also clearly demonstrate the influence of closely coordinated non-equatorial water molecules on the Pt chemical shift, relating the structure of the solution around the complex to the solvent effects on the metal NMR chemical shift. For the complex [Pt(CN)(4)](2-), the solvent effects on the Pt shielding constant are surprisingly small.

A relativistic DFT study of the electron affinity of the biscyclopentadienyl uranium complexes Cp∗ 2UX 2

Electron affinities (EA) of a series of biscyclopentadienyl uranium complexes Cp∗ 2UX 2 (X 2 = (BH 4) 2, Me 2, (NEt 2)Cl and (OEt) 2) related to the U(III)/U(IV) redox system were calculated using Density Functional Theory (DFT) in the framework of the relativistic Zero Order Regular Approximation (ZORA) coupled with the Conductor-like Screening Model (COSMO) for a realistic solvation approach, implemented in the ADF (Amsterdam Density Functional) package. A good correlation ( r 2 = 0.992–0.996) is obtained between the calculated EA values at the ZORA/BP86/TZP and ZORA/BP86/TZ2P levels and the measured half-wave potentials in THF for the series of complexes under consideration. The importance of spin–orbit coupling and solvent effect which must be taken into account in order to achieve the good agreement between theory and experiment, as well as the basis set extension, are brought to light. The influence of the non aromatic ligands X 2 on electron affinities was studied. The role of involved orbitals (singled occupied molecular orbital –SOMO– of anionic species or lowest unoccupied molecular orbital –LUMO– of neutral species) in the redox process is discussed.

Relativistic Zeroth-Order Regular Approximation Combined with Nonhybrid and Hybrid Density Functional Theory: Performance for NMR Indirect Nuclear Spin-Spin Coupling in Heavy Metal Compounds.

A benchmark study for relativistic density functional calculations of NMR spin-spin coupling constants has been performed. The test set contained 47 complexes with heavy metal atoms (W, Pt, Hg, Tl, Pb) with a total of 88 coupling constants involving one or two heavy metal atoms. One-, two-, three-, and four-bond spin-spin couplings have been computed at different levels of theory (nonhybrid vs hybrid DFT, scalar vs two-component relativistic). The computational model was based on geometries fully optimized at the BP/TZP scalar relativistic zeroth-order regular approximation (ZORA) and the conductor-like screening model (COSMO) to include solvent effects. The NMR computations also employed the continuum solvent model. Computations in the gas phase were performed in order to assess the importance of the solvation model. The relative median deviations between various computational models and experiment were found to range between 13% and 21%, with the highest-level computational model (hybrid density functional computations including scalar plus spin-orbit relativistic effects, the COSMO solvent model, and a Gaussian finite-nucleus model) performing best.

Measurement of Δ 1J( 199Hg, 31P) in [HgPCy 3(OAc) 2] 2 and relativistic ZORA DFT investigations of mercury–phosphorus coupling tensors

Using 31P solid-state NMR spectroscopy, anisotropy in the indirect 199Hg- 31P spin–spin coupling tensor (Δ J) for powdered [HgPCy 3(OAc) 2] 2 ( 1) has been measured as 4700±300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that Δ J( 199Hg, 31P) arises entirely from the ZORA Fermi-contact–spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of Δ J in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor ( D). Agreement between experiment and theory for various 199Hg, 31P spin–spin coupling anisotropies is reasonable; however, experimental values of 1 J( 199Hg, 31P) iso are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for 1 J( 199Hg, 31P) iso in [HgPPh 3(NO 3) 2] 2 depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the 31P NMR spectrum of 199Hg– 31P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.

Relativistic hybrid density functional calculations of indirect nuclear spin–spin coupling tensors — Comparison with experiment for diatomic alkali metal halides,

The accurate calculation of the isotropic (Jiso) and anisotropic (ΔJ) parts of indirect nuclear spin–spin coupling tensors is a stringent test for quantum chemistry, particularly for couplings involving heavy isotopes where relativistic effects and relativity – electron correlation cross terms are expected to play an important role. Experimental measurements on diatomic molecules in the gas phase offer ideal data for testing the success of computational approaches, since the data are essentially free from intermolecular effects, and precise coupling anisotropies may be reliably extracted in favourable cases. On the basis of available experimental molecular-beam coupling-tensor parameters for diatomic alkali metal halides, we tabulate known values of Jiso and, taking rotational–vibrational corrections to the direct dipolar coupling constant into account, precise values of ΔJ are determined for the ground rovibrational state. First-principles calculations of the coupling tensors were performed using a recently developed program based on hybrid density functional theory using the two-component relativistic zeroth-order regular approximation (ZORA). Experimental trends in Jiso and ΔJ are reproduced with correlation coefficients of 0.993 and 0.977, respectively. Periodic trends in the coupling constants and their dependence on the product of the atomic numbers of the coupled nuclei are discussed. Finally, the hybrid functional method is also successfully tested against experimental data for a series of polyatomic xenon fluorides and group-17 fluorides.

77Se NMR Spectroscopic, DFT MO, and VBT Investigations of the Reversible Dissociation of Solid (Se6I2)[AsF6]2·2SO2in Liquid SO2to Solutions Containing 1,4-Se6I22+in Equilibrium with Sen2+(n= 4, 8, 10) and Seven Binary Selenium Iodine Cations: Preliminary Evidence for 1,1,4,4-Se4Br42+andcyclo-Se7Br+

The composition of a complex equilibrium mixture formed upon dissolution of (Se(6)I(2))[AsF(6)](2).2SO(2) in SO(2)(l) was studied by (77)Se NMR spectroscopy at -70 degrees C with both natural-abundance and enriched (77)Se-isotope samples (enrichment 92%). Both the natural-abundance and enriched NMR spectra showed the presence of previously known cations 1,4-Se(6)I(2)(2+), SeI(3)(+), 1,1,4,4-Se(4)I(4)(2+), Se(10)(2+), Se(8)(2+), and Se(4)(2+). The structure and bonding in 1,4-Se(6)I(2)(2+) and 1,1,4,4-Se(4)I(4)(2+) were explored using DFT calculations. It was shown that the observed Se-Se bond alternation and presence of thermodynamically stable 4ppi-4ppi Se-Se and 4ppi-5ppi Se-I bonds arise from positive charge delocalization from the formally positively charged tricoordinate Se(+). The (77)Se chemical shifts for cations were calculated using the relativistic zeroth-order regular approximation (ZORA). In addition, calculations adding a small number of explicit solvent molecules and an implicit conductor-like screening model were conducted to include the effect that solvent has on the chemical shifts. The calculations yielded reasonable agreement with experimental chemical shifts, and inclusion of solvent effects was shown to improve the agreement over vacuum values. The (77)Se NMR spectrum of the equilibrium solution showed 22 additional resonances. These were assigned on the basis of (77)Se-(77)Se correlation spectroscopy, selective irradiation experiments, and spectral simulation. By combining this information with the trends in the chemical shifts, with iodine, selenium, and charge balances, as well as with ZORA chemical shift predictions, these resonances were assigned to acyclic 1,1,2-Se(2)I(3)(+), 1,1,6,6-Se(6)I(4)(2+), and 1,1,6-Se(6)I(3)(+), as well as to cyclic Se(7)I(+) and (4-Se(7)I)(2)I(3+). A preliminary natural-abundance (77)Se NMR study of the soluble products of the reaction of (Se(4))[AsF(6)](2) and bromine in liquid SO(2) included resonances attributable to 1,1,4,4-Se(4)Br(4)(2+)(.) These assignments are supported by the agreement of the observed and calculated (77)Se chemical shifts. Resonances attributable to cyclic Se(7)Br(+) were also observed. The thermal stability of (Se(6)I(2))[AsF(6)](2).2SO(2)(s) was consistent with estimates of thermodynamic values obtained using volume-based thermodynamics (VBT) and the first application of the thermodynamic solvate difference rule for nonaqueous solvates. (Se(6)I(2))[AsF(6)](2).2SO(2)(s) is the first example of a SO(2) solvate for which the nonsolvated parent salt, (Se(6)I(2))[AsF(6)](2)(s), is not thermodynamically stable, disproportionating to Se(4)I(4)(AsF(6))(2)(s) and Se(8)(AsF(6))(2)(s) (DeltaG degrees for the disproportion reaction is estimated to be -17 +/- 15 kJ mol(-1) at 298 K from VBT theory).

Spin−Orbit Relativistic Time-Dependent Density Functional Calculations of the Metal and Ligand Pre-Edge XAS Intensities of Organotitanium Complexes: TiCl4, Ti(η5-C5H5)Cl3, and Ti(η5-C5H5)2Cl2

Time-dependent density functional theory (TDDFT) coupled to the relativistic two-component zeroth-order regular approximation, both available in the last version of the ADF package, have been successfully used to simulate X-ray absorption spectra of TiCl4, Ti(eta5-C5H5)Cl3, and Ti(eta5-C5H5)2Cl2 in terms of their oscillator strength distributions. Besides allowing a first principle assignment of Ti 1s, Cl 1s, and Ti 2p (L2,3 edges) core excitation spectra, theoretical outcomes provide a rationale for deviations from the expected L3/L2 branching ratio.

A Density Functional Study of the Electronic Structure and Spin Hamiltonian Parameters of Mononuclear Thiomolybdenyl Complexes

The electron paramagnetic resonance spin Hamiltonian parameters of mononuclear thiomolybdenyl complexes based upon the tris(pyrazolyl)borate ligand, together with their molybdenyl analogues, are calculated using density functional theory. The electronic g matrix and 95Mo hyperfine matrix are calculated as second-order response properties from the coupled-perturbed Kohn-Sham equations. The scalar relativistic zero-order regular approximation (ZORA) is used with an all-electron basis and an accurate mean-field spin-orbit operator which includes all one- and two-electron terms. The principal values and relative orientations of the g and A interaction matrices obtained from the experimental spectra in a previous EPR study are compared with those obtained from unrestricted Kohn-Sham calculations at the BP86 and B3LYP level, and the latter are found to be in good quantitative agreement. A quasi-restricted approach is used to analyze the influence of the various molecular orbitals on g and A. In all complexes the ground state magnetic orbital is dX2-Y2-based and the orientation of the A matrix is directly related to the orientation of this orbital. The largest single contribution to the orientation of the g matrix arises from the spin-orbit coupling of the dYZ-based lowest-unoccupied molecular orbital into the ground state. A number of smaller, cumulative charge-transfer contributions augment the d-d contributions. A comparison of the theoretical EPR parameters obtained using both crystallographic and gas-phase geometry-optimized structures of Tp*MoO(bdt) (Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate, bdt = 1,2-benzenedithiolate) suggests a correspondence between the metal-dithiolate fold angle and the angle of noncoincidence between g and A.

A relativistic DFT study of cyclopentadienyl actinide complexes with no transition-metal analogues

The geometry and electronic structure of several tris and tetrakis-cyclopentadienyl thorium and uranium complexes have been investigated using Density Functional theory (DFT) calculations in the framework of the relativistic zeroth-order regular approximation (ZORA) implemented in the ADF (Amsterdam density functional) program. In all cases, the important interaction between the metal 5f orbitals and the Cp 3 moiety is brought to light. However, coordination with a fourth ligand like H − or Cl − leading to Cp 3AnL species involves mainly the metal 6d orbitals, whereas in the case of L = Cp −, the 5f uranium orbitals act also efficiently. The actinide 5f orbitals are more efficient in uranium than in thorium for metal to ligand bonding. Cyclopentadienyl to uranium donation is enhanced when the metal ion charge increases. Finally, our calculations indicate that the Cp 3UH structure could be thermodynamically stable, although it has not yet been synthesized.

An Investigation of Lanthanum Coordination Compounds by Using Solid‐State 139La NMR Spectroscopy and Relativistic Density Functional Theory

Lanthanum-139 NMR spectra of stationary samples of several solid La(III) coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the 139La NMR spectra of the central transition are dominated by the interaction between the 139La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical-shift anisotropy on the NMR spectra is non-negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the 139La quadrupolar coupling constants (C(Q)) range from 10.0 to 35.6 MHz, the spans of the chemical-shift tensor (Omega) range from 50 to 260 ppm, and the isotropic chemical shifts (delta(iso)) range from -80 to 178 ppm. In general, there is a correlation between the magnitudes of C(Q) and Omega, and delta(iso) is shown to depend on the La coordination number. Magnetic-shielding tensors, calculated by using relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) and incorporating scalar only or scalar plus spin-orbit relativistic effects, qualitatively reproduce the experimental chemical-shift tensors. In general, the inclusion of spin-orbit coupling yields results that are in better agreement with those from the experiment. The magnetic-shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical-shift and EFG tensors in the molecular frame. This study demonstrates that solid-state 139La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.

The actinide–imide bonding revisited: A relativistic DFT study

The electronic structure of mono and bis(imide) cyclopentadienyl thorium and uranium complexes have been investigated using density functional theory (DFT) calculations in the framework of the relativistic zero order regular approximation (ZORA) implemented in the ADF (Amsterdam density functional) program. In the case of N-phenyl imido ligands, these complexes exhibit both σ and π interaction between the central metal atom and the three electron pairs borne by the nitrogen atom. These electron pairs interact strongly with the uranium orbitals, especially the 5f ones, insuring a great stability to these species. A triple bond is thus expected for the uranium–nitrogen interaction in these complexes. The geometry of the bis(imide) species is very peculiar. It is characterized by coplanar Nph phenylimide groups, very short U–N bond lengths and a linear U–N–C ph coordination angle. These features could not be observed for a transition metal complex, as this has been demonstrated on the example of molybdenum Mo(VI) species which exhibit a bent Mo–N–C ph coordination angle. We show that the 5f uranium orbitals are mainly responsible for this peculiar geometry.

The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry

In the present work, we propose a relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. This two-component TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closed-shell systems with full use of double-group symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closed-shell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.

A relativistic DFT study of one-bond fluorine-X indirect spin-spin coupling tensors.

The relativistic zeroth-order regular approximation (ZORA) DFT method was employed to investigate indirect spin-spin coupling tensors involving fluorine, (1)J(X, F). The relative contributions of the mechanisms contributing to (1)J(X, F) are discussed, with special attention paid to the magnitude and origin of the anisotropy in this tensor, DeltaJ. This quantum chemical study demonstrates that, for the systems investigated, the ZORA-DFT method reproduces the magnitude of (1)J(X, F)(iso) and indicates that DeltaJ(X, F) is of the same order of magnitude as (1)J(X, F)(iso). Several examples are provided that demonstrate the importance of considering contributions of DeltaJ to the experimental measurement of effective dipolar coupling constants, R(eff). Given the difficulties with determining DeltaJ experimentally and the promising computational results, we suggest that the quantum chemical calculation of (1)J(X, F) be used as a complementary tool to aid in the analysis of data from NMR experiments designed to measure dipolar coupling constants.

A Theoretical Investigation of One-Bond Phosphorus−Phosphorus Indirect Nuclear Spin−Spin Coupling Tensors, 1J(31P,31P), Using Density Functional Theory

In the present study, one-bond 3 1 P, 3 1 P indirect nuclear spin-spin coupling tensors, 1 J( 3 1 P, 3 1 P), are calculated using nonrelativistic and relativistic zeroth-order regular approximation (ZORA) density functional theory (DFT) methods for the following model molecules and ions: P 2 , cis-MeP=PMe, trans-RP=PR (R = H, Me, Ph), (cis-η 1 -PhP=PPh)Cr(CO) 5 , (cis- and trans-η 1 -MeP=PMe)Cr(CO) 5 , H 2 P-PH 2 , H 2 P-PF 2 , cis- and trans-diphosphetes, a phosphole tetramer, [O 3 P-PO 3 ] 4 - , [HO 3 P-PO 3 H] 2 - , [FO 2 P-PO 2 F] 2 - , Me 2 (S)P-P(S)Me 2 , [MeN≡P-PMe 3 ] + , and Me 3 P-PF 5 . These compounds have been chosen because the values of 1 J( 3 1 P, 3 1 P) i s o in these systems vary from approximately -480 to +770 Hz, thereby spanning the known range of experimentally measured one-bond 3 1 P, 3 1 P indirect nuclear spin-spin coupling constants. However, in many cases, the sign of 1 J( 3 1 P, 3 1 P) i s o has not been determined by experiment. Our DFT results for 1 J( 3 1 P, 3 1 P) i s o and the anisotropy of J are in qualitative agreement with experimental values; furthermore, our calculations provide the absolute sign of 1 J( 3 1 P, 3 1 P) i s o in cases where it is unknown experimentally. A number of empirical trends between 1 J( 3 1 P, 3 1 P) i s o and various structural parameters have been reproduced by our calculations. Inspection of the mechanisms which contribute to 1 J( 3 1 P, 3 1 P) i s o indicates that the Fermi contact (FC) mechanism dominates in all cases where formal single P,P bonds exist and that the paramagnetic spin-orbit mechanism is of equal or greater importance in comparison with the FC mechanism in cases where formal multiple P,P bonds exist. Results from relativistic ZORA DFT calculations differ from the nonrelativistic calculations by less than 10%, indicating that inclusion of relativistic effects is not crucial, as anticipated, given that the systems investigated herein contain relatively light atoms (Z ≤ 24).

Investigation of Magnetic Shielding in Xenon Difluoride Using Solid-State NMR Spectroscopy and Relativistic Density Functional Theory

The xenon and fluorine magnetic shielding tensors, σ, of XeF2 are characterized using solid-state 129Xe and 19F NMR spectroscopy and nonrelativistic and spin−orbit relativistic zeroth-order regular approximation density functional theory (ZORA DFT). Analysis of 129Xe and 19F NMR spectra acquired with magic-angle spinning at several spinning rates indicates that the Xe and F magnetic shielding tensors are axially symmetric, as dictated by the crystal symmetry. The isotropic 129Xe chemical shift is −1603 ± 5 ppm with respect to OXeF4 (neat liquid, 24 °C) and the Xe magnetic shielding anisotropy, Ω, is 4245 ± 20 ppm, the first anisotropy measured directly for a xenon compound. The parallel component of the experimentally determined xenon chemical shift tensor, δ∥ = −4433 ppm differs from δ(Xe(free atom)) by ∼1000 ppm, providing the first experimental demonstration that relativistic effects play an important role in the nuclear magnetic shielding for xenon. Both the sign and magnitude of the isotropic indirect 129Xe,19F nuclear spin−spin coupling constant are determined, −5560 ± 50 Hz. Analysis of the 19F NMR spectra yield Ω(F) = 150 ± 20 ppm. The ZORA DFT method has been employed to calculate σ(Xe) and σ(F) for isolated XeF2 and XeF4 molecules, as well as σ(Kr) and σ(F) for an isolated KrF2 molecule, at the relativistic and nonrelativistic levels of theory. Spin−orbit relativistic DFT results for Ω(Xe) are in very good agreement with those determined experimentally and highlight the importance of relativistic effects.

Phosphorus magnetic shielding tensors for transition-metal compounds containing phosphine, phosphido, and phosphinidene ligands: Insights from computational chemistry

The present study examines the quality of the restricted Hartree–Fock (RHF) ab initio, B3LYP hybrid density functional theory (DFT), and relativistic zeroth-order regular approximation (ZORA) DFT methods for the calculation of phosphorus chemical shift (CS) tensors in phosphine, phosphido, and phosphinidene transition-metal complexes. A detailed comparison of calculated and experimental 31P CS tensors allows us to identify the characteristic advantages of each computational method. The results from B3LYP and ZORA-DFT calculations indicate that a double-ζ quality basis set reproduces experimental values of the principal components of the 31P CS tensor in many of the phosphorus-containing transition-metal complexes investigated, whereas the RHF method requires a triple-ζ doubly polarized basis set, yet fails in the case of the terminal phosphido group. Inclusion of the spin-orbit relativistic correction with the ZORA-DFT formalism requires a triple-ζ quality basis set to reproduce the experimental data. We demonstrate the merit of modern computational methods for investigating theoretically the effect of geometric variations upon the phosphorus CS tensor by systematically altering the W—P bond length and the W-P-CMe bond angle in W(CO)5(PMe3). Additionally, a previously reported correlation, determined experimentally, relating the 31P CS tensor to the Fe-P-Fe bond angle in a series of iron phosphido-bridging compounds, has been reproduced with calculations using the model compound Fe2(CO)6(µ2-PPh2)(µ2-Cl). The results presented demonstrate the value of modern computational techniques for obtaining a greater understanding of the relationship between phosphorus chemical shifts and molecular structure.Key words: 31P chemical shift, phosphine, phosphido, phosphinidene, RHF, B3LYP, relativistic, ZORA-DFT.

Halogen Bond in (CH3)nX (X = N, P, n = 3; X = S, n = 2) and (CH3)nXO (X = N, P, n = 3; X = S, n = 2) Adducts with CF3I. Structural and Energy Analysis Including Relativistic Zero-Order Regular Approximation Approach in a Density Functional Theory Framework

Density functional theory (DFT) calculations on the geometry and bonding energy of the X- - -I intermolecular interaction of CF3I and (CH3)nX (X = N, P, n = 3; X = S, n = 2) and (CH3)nXO (X = N, P, n = 3; X = S, n = 2) are reported. The effect of the basis set, Effective Core Potential (ECP), and relativistic corrections have been investigated to gain insight into the origin and nature of this interaction. Energy decomposition in terms of different contributions allows us to understand the different donor behavior of second and third row atoms toward perfluorinated iodo hydrocarbon compounds, suggesting that bond energies are mainly due to orbital contribution. TD-DFT calculations of the van der Waals coefficient C6 for CF3I- - -N(CH3)3 and CF3I- - -P(CH3)3 adducts estimate values of −2.02 and −1.30 kcal/mol, respectively, for their dispersion energy, thus representing only a small contribution to the total bonding energy (−5.64 and −5.76 kcal/mol, respectively). The role of competition between intra- and...

Insight into the structure of silver cyanide from (13)C and (15)N solid-state NMR spectroscopy.

The structure of silver cyanide has been investigated by solid-state multinuclear magnetic resonance spectroscopy. Carbon-13 and nitrogen-15 NMR spectra of magic-angle-spinning (MAS) and stationary powder samples of isotopically enriched Ag(13)CN, Ag(13)C(15)N, and AgC(15)N have been acquired at the external applied magnetic field strengths 4.7, 7.05, and 9.4 T. Axially symmetric carbon and nitrogen chemical shift (CS) tensors provide evidence for linearity of the polymeric (-Ag-CN-)(n)() chains. A two-site model is required to successfully simulate the (13)C MAS NMR line shape, which is dominated by indirect nuclear spin-spin coupling between (109/107)Ag and (13)C nuclei. In combination with relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) calculations on model AgCN fragments, the (13)C MAS NMR results show that 30 +/- 10% of the silver sites are disordered, that is, either -NC-Ag-CN- or -CN-Ag-NC-, and 70 +/- 10% of the silver sites are ordered, that is, -NC-Ag-NC-. Effective dipolar coupling data extracted from (13)C NMR spectra of stationary samples allow an upper limit of 1.194 A to be placed on the carbon-nitrogen internuclear distance. After incorporation of the effects of anisotropic indirect nuclear spin-spin coupling and motional averaging on the NMR-derived distance, a corrected value of r(CN) = 1.16 +/- 0.03 A is obtained. This work provides an example of the type of information which may be obtained from solid-state NMR studies of disordered materials and how such information may complement that available from diffraction studies.

A 95Mo and 13C solid-state NMR and relativistic DFT investigation of mesitylenetricarbonylmolybdenum(0) – a typical transition metal piano-stool complex

The chemical shift (CS) and electric field gradient (EFG) tensors in the piano-stool compound mesitylenetricarbonylmolybdenum(0), 1, have been investigated via95Mo and 13C solid-state magic-angle spinning (MAS) NMR as well as relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) calculations. Molybdenum-95 (I = 5/2) MAS NMR spectra acquired at 18.8 T are dominated by the anisotropic chemical shift interaction (Ω = 775 ± 30 ppm) rather than the 2nd-order quadrupolar interaction (CQ = −0.96 ± 0.15 MHz), an unusual situation for a quadrupolar nucleus. ZORA-DFT calculations of the 95Mo EFG and CS tensors are in agreement with the experimental data. Mixing of appropriate occupied and virtual d-orbital dominated MOs in the region of the HOMO-LUMO gap are shown to be responsible for the large chemical shift anisotropy. The small, but non-negligible, 95Mo quadrupolar interaction is discussed in terms of the geometry about Mo. Carbon-13 CPMAS spectra acquired at 4.7 T demonstrate the crystallographic and magnetic nonequivalence of the twelve 13C nuclei in 1, despite the chemical equivalence of some of these nuclei in isotropic solutions. The principal components of the carbon CS tensors are determined via a Herzfeld–Berger analysis, and indicate that motion of the mesitylene ring is slow compared to a rate which would influence the carbon CS tensors (i.e. tens of μs). ZORA-DFT calculations reproduce the experimental carbon CS tensors accurately. Oxygen-17 EFG and CS tensors for 1 are also calculated and discussed in terms of existing experimental data for related molybdenum carbonyl compounds. This work provides an example of the information available from combined multi-field solid-state multinuclear magnetic resonance and computational investigations of transition metal compounds, in particular the direct study of quadrupolar transition metal nuclei with relatively small magnetic moments.