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

Exploring Spin-Orbit Effects in a [Cu6Tl]+ Nanocluster Featuring an Uncommon Tl-H Interaction

Reaction of [CuH(PPh3)]6 with 1 equiv. of Tl(OTf) results in formation of [Cu6TlH6(PPh3)6][OTf] ([1]OTf]), which can be isolated in good yields. Variable-temperature 1H NMR spectroscopy, in combination with density functional theory (DFT) calculations, confirms the presence of a rare Tl-H orbital interaction. According to DFT, the 1H chemical shift of the Tl-adjacent hydride ligands of [1]+ includes 7.7 ppm of deshielding due to spin-orbit effects from the heavy Tl atom. This study provides valuable new insights into a rare class of metal hydrides, given that [1][OTf] is only the third isolable species reported to contain a Tl-H interaction.

Dynamic and relativistic effects on Pt-Pt indirect spin-spin coupling in aqueous solution studied by ab initio molecular dynamics and two- vs four-component density functional NMR calculations

Treating 195Pt nuclear magnetic resonance parameters in solution remains a considerable challenge from a quantum chemistry point of view, requiring a high level of theory that simultaneously takes into account the relativistic effects, the dynamic treatment of the solvent-solute system, and the dynamic electron correlation. A combination of Car-Parrinello molecular dynamics (CPMD) and relativistic calculations based on two-component zeroth order regular approximation spin-orbit Kohn-Sham (2c-ZKS) and four-component Dirac-Kohn-Sham (4c-DKS) Hamiltonians is performed to address the solvent effect (water) on the conformational changes and JPtPt1 coupling. A series of bridged PtIII dinuclear complexes [L1-Pt2(NH3)4(Am)2-L2]n+ (Am = α-pyrrolidonate and pivalamidate; L = H2O, Cl-, and Br-) are studied. The computed Pt-Pt coupling is strongly dependent on the conformational dynamics of the complexes, which, in turn, is correlated with the trans influence among axial ligands and with the angle N-C-O from the bridging ligands. The J-coupling is decomposed in terms of dynamic contributions. The decomposition reveals that the vibrational and explicit solvation contributions reduce JPtPt1 of diaquo complexes (L1 = L2 = H2O) in comparison to the static gas-phase magnitude, whereas the implicit solvation and bulk contributions correspond to an increase in JPtPt1 in dihalo (L1 = L2 = X-) and aquahalo (L1 = H2O; L2 = X-) complexes. Relativistic treatment combined with CPMD shows that the 2c-ZKS Hamiltonian performs as well as 4c-DKS for the JPtPt1 coupling.

Machine learning-based correction for spin-orbit coupling effects in NMR chemical shift calculations

As one of the most powerful analytical methods for molecular and solid-state structure elucidation, NMR spectroscopy is an integral part of chemical laboratories associated with a great research interest in its computational simulation. Particularly when heavy atoms are present, a relativistic treatment is essential in the calculations as these influence also the nearby light atoms. In this work, we present a Δ-machine learning method that approximates the contribution to 13C and 1H NMR chemical shifts that stems from spin-orbit (SO) coupling effects. It is built on computed reference data at the spin-orbit zeroth-order regular approximation (ZORA) DFT level for a set of 6388 structures with 38 740 13C and 64 436 1H NMR chemical shifts. The scope of the methods covers the 17 most important heavy p-block elements that exhibit heavy atom on the light atom (HALA) effects to covalently bound carbon or hydrogen atoms. Evaluated on the test data set, the approach is able to recover roughly 85% of the SO contribution for 13C and 70% for 1H from a scalar-relativistic PBE0/ZORA-def2-TZVP calculation at virtually no extra computational costs. Moreover, the method is transferable to other baseline DFT methods even without retraining the model and performs well for realistic organotin and -lead compounds. Finally, we show that using a combination of the new approach with our previous Δ-ML method for correlation contributions to NMR chemical shifts, the mean absolute NMR shift deviations from non-relativistic DFT calculations to experimental values can be halved.

Inquiring 199Hg NMR Parameters by Combining Ab Initio Molecular Dynamics and Relativistic NMR Calculations

Ab initio molecular dynamics (AIMD) sampling followed by relativistic density functional theory (DFT) 199Hg NMR calculations were performed for Hg organometallic complexes in water, dimethyl sulfoxide, and chloroform. The spin-orbit coupling, a relativistic effect, is a key factor for predicting δ(Hg) and 1J(Hg-C) accurately, in conjunction with a dynamic treatment of the systems. Good agreement between the theoretical and experimental results is reached by adopting implicit (based on a continuum model) and explicit (solvent molecules treated quantum mechanically) solvation models. Broader trends appearing in the experimental data available in the literature are reproduced by the calculations, and therefore, quantum chemistry is able to assist in the assignment and interpretation of 199Hg NMR data. Less pronounced trends, such as changes in the 199Hg chemical shift in different systems with the same atom types bound to Hg, are too weak to be predicted reliably by the current state-of-the-art theoretical methods based on AIMD sampling and relativistic DFT with hybrid functionals for NMR calculations.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Solvent effect on the 195Pt NMR properties in pyridonate-bridged PtIII dinuclear complex derivatives investigated by ab initio molecular dynamics and localized orbital analysis

An ab initio molecular dynamics investigation of the solvent effect (water) on the structural parameters, ¹⁹⁵Pt NMR spin-spin coupling constants (SSCCs) and chemical shifts of a series of pyridonate-bridged Pt^III dinuclear complexes is performed using Kohn-Sham (KS) Car-Parrinello molecular dynamics (CPMD) and relativistic hybrid KS NMR calculations. The indirect solvent effect (via structural changes) has a dramatic effect on the ¹J_PtPt SSCCs. The complexes exhibit a strong trans influence in solution, where the Pt-Pt bond lengthens with increasing axial ligand σ-donor strength. In the diaqua complex, where the solvent effect is more pronounced, the SSCCs averaged for CPMD configurations with explicit plus implicit solvation agree much better with the experimental data, while the calculations for static geometry and CPMD unsolvated configurations show large deviations with respect to experiment. The combination of CPMD with hybrid KS NMR calculations provides a much more realistic computational model that reproduces the large magnitudes of ¹J_PtPt and ¹⁹⁵Pt chemical shifts. An analysis of ¹J_PtPt in terms of localized and canonical orbitals shows that the SSCCs are driven by changes in the s-character of the natural atomic orbitals of Pt atoms, which affect the 'Fermi contact' mechanism.

Temperature Dependence of 1 H Paramagnetic Chemical Shifts in Actinide Complexes, Beyond Bleaney's Theory: The AnVI O2 2+ -Dipicolinic Acid Complexes (An=Np, Pu) as an Example

Actinide +VI complexes ( A n V I = U V I , N p V I and P u V I ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, N p V I and P u V I complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹ H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans' method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the N p V I complex. The temperature dependence of the pNMR chemical shifts has a strong 1 / T contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the N p V I complex and a non-Kramers-doublet model for the P u V I complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.

Relativistic DFT Calculations of 1JWH and 1JWC Provide Detailed Structural Insight of Cyclopentadienyl Binding in Cp2WH2

Experimental measurements of the one-bond scalar coupling of Cp₂WH₂ in tetrahydrofuran (¹J_WH = 73.4 Hz and ¹J_WC = 4.8 Hz) are compared to density functional theory calculations of the same based upon geometries minimized utilizing a variety of approximate functionals typically utilized to calculate organometallic geometries. One difference between the various functionals is the Cp-W distance, and d_CpW is linearly correlated to the calculated values for both ¹J_WH and ¹J_WC. Differences in the structures of the Cp₂WH₂ reported in the literature are compared to the calculated geometries, utilizing calculated values of ¹J_WH to provide insight into the differences. The distance between the tungsten and attached hydride as well as the angle of the cyclopentadienyl plane with respect to the tungsten cyclopentadienyl centroid vector also have a strong effect on ¹J_WH. A natural bond orbital (NBO) analysis of the orbital origins of ¹J_WH indicates that the W-H σ-bonding orbital is the primary contributor to the coupling constant.

"Through-Space" Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹ H, ¹³ C, and ¹⁵ N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃ ] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I^- and I₃ ^- . A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.

Similar ligand-metal bonding for transition metals and actinides? 5f1 U(C7H7)2-versus 3d n metallocenes

U(C7H7)2- is a fascinating 5f1 complex whose metal-ligand bonding was assigned in the literature as being very similar to 3d7 cobaltocene, based on a crystal-field theoretical interpretation of the experimental magnetic resonance data. The present work provides an in-depth theoretical study of the electronic structure, bonding, and magnetic properties of the 5f1 U(C7H7)2-vs. 3d metallocenes with V, Co, and Ni, performed with relativistic wavefunction and density functional methods. The ligand to metal donation bonding in U(C7H7)2- is strong and in fact similar to that in vanadocene, in the sense that the highest occupied arene orbitals donate electron density into empty metal orbitals of the same symmetry with respect to the rotational axis (3dπ for V, 5fδ for U), but selectively with α spin (↑). For Co and Ni, the dative bonding from the ligands is β spin (↓) selective into partially filled 3dπ orbitals. In all systems, this spin delocalization triggers spin polarization in the arene σ bonding framework, causing proton spin densities opposite to those of the carbons. As a consequence, the proton spin densities and hyperfine coupling constants are negative for the Co and Ni complex, but positive for vanadocene. The of U(C7H7)2- is negative and similar to that of cobaltocene, but only because of the strong spin-orbit coupling in the actinocene, which causes to be opposite to the sign of the proton spin density. The study contributes to a better understanding of actinide 5f vs. transition metal 3d covalency, and highlights potential pitfalls when interpreting experimental magnetic resonance data in terms of covalent bonding for actinide complexes.

Influence of the nuclear charge distribution and electron correlation effects on magnetic shieldings and spin-rotation tensors of linear molecules

The nuclear charge distribution effects (NChDE) on two response properties, the NMR magnetic shielding ( σ ) and the nuclear spin-rotation (SR) constants ( M ), are analyzed. We do it employing point-like and Gaussian-like models for describing the nuclear charge density of three linear molecules: HBr, HI and HAt. According to our results, both properties are sensitive to the NChDE. We show that the NChDE are almost completely relativistic, i.e., they nearly vanish in the non-relativistic limit of both properties. We calculated the NChDE on σ and M , and analyzed the differences between them in terms of a relativistic relation between these two properties. Using that relation we found that the electronic core mechanisms are the main ones for the NChDE on the shielding of nuclei of both, molecules and free atoms. The NChDE are smaller on SR constants than on shieldings. Nevertheless, within the relativistic polarization propagator formalism at the RPA level of approach they are very important for SR constants of nuclei in heavy-atom-containing compounds. Astatine in HAt has the largest influence: M At = -9.95 kHz for a point-like model and -50.10 kHz for a Gaussian-like model. Correlation effects must be included and we do it using different DFT schemes. The PBE0 functional gives results that are closest to experiments for Br and I, though the LDA gives the closest for hydrogen. The value of the SR constant of At is reduced among 350 kHz and 500 kHz from its RPA value, when different and usual functionals are applied. Given that the NChDE on M and σ are mostly relativistic in their origin, these effects are also dependent on electron correlation. They have also a nonvanishing dependence with the Gaunt electron-electron interactions.

31P and 195Pt solid-state NMR and DFT studies on platinum(i) and platinum(ii) complexes

³¹P and ¹⁹⁵Pt solid state NMR spectra on anti-[(PHCy)ClPt(μ-PCy₂)₂Pt(PHCy)Cl] (3) and [(PHCy₂)Pt(μ-PCy₂)(κ²P,O-μ-POCy₂)Pt(PHCy₂)] (Pt–Pt) (4) were recorded under CP/MAS conditions (³¹P) or with the CP/CPMG pulse sequence (¹⁹⁵Pt) and compared to data obtained by relativistic DFT calculations of ³¹P and ¹⁹⁵Pt CS tensors and isotropic shielding at the ZORA Spin Orbit level.

Relativistic Effect on 1 J(M,C) in Me4 M, Me3 M- , Ph4 M, and Ph3 M- (M=Pb, Sn, Ge, Si, and/or C): Role of s-Type Lone Pair Orbitals in the Distinct Effect for the Anionic Species

Indirect one-bond nuclear spin-spin couplings between M and C [¹ J(M,C)] in Me₄ M, Me₃ M^- , Ph₄ M, and Ph₃ M^- (M=Pb, Sn, Ge, Si, C) are analyzed with consideration of the relativistic effect and by employing Slater-type basis sets. The evaluated total values ¹ J_TL (M,C) reproduced the observed values with some systematic calculation errors. Fermi contact terms ¹ J_FC (M,C) contribute predominantly to ¹ J_TL (M,C) (≈99 %). A distinct relativistic effect on ¹ J(Pb,C) is predicted for Me₃ Pb^- and Ph₃ Pb^- . The mechanisms for the distinct effect are elucidated by using the comparison between Me₃ Pb^- and Me₄ Pb as an example. The contributions to ¹ J_FC (M,C) [or ¹ J_SD+FC (M,C), where SD denotes the spin-dipolar term] are decomposed into those of occupied orbitals and occupied-to-unoccupied transitions. The s-type lone-pair orbitals are demonstrated to contribute to the distinct relativistic effect on ¹ J(Pb,C) of Me₃ Pb^- (and Ph₃ Pb^- ). The results are in sharp contrast to the cases of ¹ J(M,C) for M atoms lighter than Pb, such as Si, and are explained by the s character of the M-C bonds. This treatment enables visualization and clear recognition the origin of the nuclear couplings for the species exhibiting a relativistic effect.

Value of NMR Parameters and DFT Calculations for Quantum Information Processing Utilizing Phosphorus Heterocycles

Quantum computing is the field of science that uses quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. The fundamental information unit used in quantum computing is the quantum bit or qubit. It is well-known that quantum computers could theoretically be able to solve problems much more quickly than any classical computers. Currently, the first and still the most successful implementations of quantum information processing (QIP) have been based on nuclear spins in liquids. However, molecules that enable many qubits NMR QIP implementations should meet some conditions: have large chemical shifts and be appropriately dispersed for qubit addressability, appreciable spin-spin coupling between any pair of spins, and a long relaxation time. In this line, benzyldene-2,3-dihydro-1H-[1,3]diphosphole (BDF) derivatives have been theoretically tested for maximizing large chemical shifts, spin-spin coupling, and minimizing the hyperfine coupling constant. Thus, the structures were optimized at the B3LYP/6-311G(d,p) level and showed a significant similarity with the experimental geometrical parameters. The NMR spectroscopic parameters (δ and J) were calculated with six different DFT functionals. The τ-HCTH/6-31G(2d) level is in better agreement with the experimental data of ³¹P and ¹³C chemical shifts, while PCM-B3LYP/cc-pVDZ level shows a decrease on deviation between calculated and experimental values for P-P and P-C SSCC. The surface response technique was employed to rationalize how the hyperfine constant varies with the chemical shifts and coupling constants values. From our findings, BDF-NO₂ was the best candidate for NMR quantum computations (NMR-QC) among the studied series.

Synthesis of a labile sulfur-centred ligand, [S(H)C(PPh2S)2](-): structural diversity in lithium(i), zinc(ii) and nickel(ii) complexes

A high-yield synthesis of [Li{S(H)C(PPh2S)2}]2 [Li2·(3)2] was developed and this reagent was used in metathesis with ZnCl2 and NiCl2 to produce homoleptic complexes 4 and 5b in 85 and 93% yields, respectively. The solid-state structure of the octahedral complex [Zn{S(H)C(PPh2S)2}2] (4) reveals notable inequivalence between the Zn-S(C) and Zn-S(P) contacts (2.274(1) Å vs. 2.842(1) and 2.884(1) Å, respectively). Two structural isomers of the homoleptic complex [Ni{S(H)C(PPh2S)2}2] were isolated after prolonged crystallization processes. The octahedral green Ni(ii) isomer 5a exhibits the two monoprotonated ligands bonded in a tridentate (S,S',S'') mode to the Ni(ii) centre with three distinctly different Ni-S bond lengths (2.3487(8), 2.4500(9) and 2.5953(10) Å). By contrast, in the red-brown square-planar complex 5b the two ligands are S,S'-chelated to Ni(ii) (d(Ni-S) = 2.165(2) and 2.195(2) Å) with one pendant PPh2S group. DFT calculations revealed that the energetic difference between singlet and triplet state octahedral and square-planar isomers of the Ni(ii) complex is essentially indistinguishable. Consistently, VT and (31)P CP/MAS NMR spectroscopic investigations indicated that a mixture of isomers exists in solution at room temperature, while the singlet state square-planar isomer 5b becomes favoured at -40 °C.

The Relativistic Effects on the Carbon-Carbon Coupling Constants Mediated by a Heavy Atom

The (2)JCC, (3)JCC, and (4)JCC spin-spin coupling constants in the systems with a heavy atom (Cd, In, Sn, Sb, Te, Hg, Tl, Pb, Bi, and Po) in the coupling path have been calculated by means of density functional theory. The main goal was to estimate the relativistic effects on spin-spin coupling constants and to explore the factors which may influence them, including the nature of the heavy atom and carbon hybridization. The methods applied range, in order of reduced complexity, from the Dirac-Kohn-Sham (DKS) method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component zeroth-order regular approximation (ZORA) Hamiltonians, to scalar effective core potentials (ECPs) with the nonrelativistic Hamiltonian. The use of DKS and ZORA methods leads to very similar results, and small-core ECPs of the MDF and MWB variety reproduce correctly the scalar relativistic effects. Scalar relativistic effects usually are larger than the spin-orbit coupling effects. The latter tend to influence the most the coupling constants of the sp(3)-hybridized carbon atoms and in compounds of the p-block heavy atoms. Large spin-orbit coupling contributions for the Po compounds are probably connected with the inverse of the lowest triplet excitation energy.

Uncovering Intramolecular π-Type Hydrogen Bonds in Solution by NMR Spectroscopy and DFT Calculations

Reaction between the phosphinito bridged diplatinum species [(PHCy2 )Pt(μ-PCy2 ){κ(2) P,O-μ-P(O)Cy2 }Pt(PHCy2 )](Pt-Pt) (1), and (trimethylsilyl)acetylene at 273 K affords the σ-acetylide complex [(PHCy2 )(η(1) -Me3 SiC≡C)Pt(μ-PCy2 )Pt(PHCy2 ){κP-P(OH)Cy2 }](Pt-Pt) (2) featuring an intramolecular π-type hydrogen bond. Scalar and dipolar couplings involving the POH proton were detected by 2D NMR experiments. Relativistic DFT calculations of the geometry, relative energy, and NMR properties of model systems of 2 confirmed the structural assignment and allowed the energy of the π-type hydrogen bond to be estimated (ca. 22 kJ mol(-1) ).

Relativistic Calculations of Nuclear Magnetic Resonance Parameters

Relativistic effects are important for the accurate evaluation of the observables of nuclear magnetic resonance (NMR) spectroscopy, the nuclear magnetic shielding and the indirect spin–spin coupling tensors. Some of the most notable relativistic effects, in particular for light elements in the vicinity of heavy nuclei, are due to spin–orbit effects, an effect difficult to evaluate when starting from a non-relativistic wavefunction. Two- and four-component relativistic methods include spin–orbit effects variationally, and the recent improvements in the computational efficiency of these methods open new opportunities for accurate calculations of NMR parameters also for molecules with heavy elements. We here present an overview of the different approximations that have been introduced for calculating relativistic effects with two- and four-component methods and how these methods can be used to calculate the NMR parameters. We will also give some examples of systems that have been studied computationally with two- and four-component relativistic methods and discuss the importance of relativistic effects on the shielding and indirect spin–spin coupling constants.

Kohn–Sham calculations of NMR shifts for paramagnetic 3d metal complexes: protocols, delocalization error, and the curious amide proton shifts of a high-spin iron(ii) macrocycle complex

Ligand chemical shifts (pNMR shifts) are analyzed using DFT. A large difference in the amide proton shifts of a high-spin Fe(ii) complex arises from O → Fe dative bonding which only transfers β spin density to the metal.

Microsolvation of methylmercury: structures, energies, bonding and NMR constants (199Hg,13C and17O)

Hartree–Fock (HF) and second order perturbation theory (MP2) calculations within the scalar and full relativistic frames were carried out in order to determine the equilibrium geometries and interaction energies between cationic methylmercury (CH₃Hg⁺) and up to three water molecules.

Relativistic Effects on Metal-Metal Bonding: Comparison of the Performance of ECP and Scalar DKH Description on the Picture of Metal-Metal Bonding in Re2Cl8(2.)

This paper reports a systematic comparison of the performance of alternative methods of including relativistic effects on the nature of metal-metal bonding in the Re2Cl8(2-) anion. The comparison involved the description using a scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian with all-electron basis sets and the relativistic effective core potential (ECP) basis sets. The impact of the above methods on the picture of the bonding was analyzed using the so-called domain averaged Fermi holes (DAFH). Besides comparing the impact on the picture of the bonding of the two above methods, the focus was also put on the systematic comparison of the "exact" AIM generalized form of DAFH analysis with the approximate Mulliken-like approach used in an earlier DAFH study of ReRe bonding. It has been shown that in contrast to descriptions using ECP basis sets where the differences in the picture of the bonding emerging from the approximate and "exact" DAFH analysis are only marginal, the approximate DAFH approach has been found to dramatically fail in the case of all-electron basis sets required for the description in terms of the Douglas-Kroll-Hess (DKH2) Hamiltonian.

Interpretation of the longitudinal (13)C nuclear spin relaxation and chemical shift data for five bromoazaheterocycles supported by nonrelativistic and relativistic DFT calculations

The longitudinal relaxation times of (13)C nuclei and NOE enhancement factors for 2-bromopyridine (1), 6-bromo-9-methylpurine (2), 3,5-dibromopyridine (3), 2,4-dibromopyrimidine (4), and 2,4,6-tribromopyrimidine (5) have been measured at 25 °C and B0 = 11.7 T. The most important contributions to the overall relaxation rates of nonbrominated carbons, i.e., the relaxation rates due to the (13)C-(1)H dipolar interactions and the shielding anisotropy mechanism, have been separated out. For 3 and 5, additionally, the T2,Q((14)N) values have been established from (14)N NMR line widths. All of these data have been used to determine rotational diffusion tensors for the investigated molecules. The measured saturation recovery curves of brominated carbons have been decomposed into two components to yield relaxation times, which after proper corrections provided parameters characterizing the scalar relaxation of the second kind for (13)C nuclei of (79)Br- and (81)Br-bonded carbons. These parameters and theoretically calculated quadrupole coupling constants for bromine nuclei have allowed the values of one-bond (13)C-(79)Br spin-spin coupling constants to be calculated. Independently, the coupling constants and magnetic shielding constants of the carbon nuclei have been calculated theoretically using the nonrelativistic and relativistic DFT methods F/6-311++G(2d,p)/PCM and so-ZORA/F/TZ2P/COSMO (F = BHandH or B3LYP), respectively. The agreement between the experimental and theoretical values of these parameters is remarkably dependent on the theoretical method used.

Reactivity of low-oxidation state tin compounds: an overview of the benefits of combining DFT Theory and experimental NMR spectroscopy

The reactivity and complexation properties of dicoordinated Sn(II) and Sn(0) compounds are reviewed. The (dominant) electrophilicity of the stannylenes was confirmed and quantified through density functional theory (DFT) based reactivity indices. For these compounds, combining theoretical DFT calculations and experimental nuclear magnetic resonance (NMR) spectroscopic results has evidenced their potential to undergo π-complexation from aromatic π clouds in addition to significantly stronger σ-complexation. Moreover, their potential as Lewis bases was scrutinized in their interactions and reactions with iron and tungsten carbonyl Lewis acids. Finally, a prospective comparison of the reactivity of divalent stannylenes and stannylones, with a 0 oxidation state at the Sn atom, is presented.

Relativistic calculations of magnetic resonance parameters: background and some recent developments

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

Evaluation of Approximate Exchange-Correlation Functionals in Predicting One-Bond (31)P-(1)H NMR Indirect Spin-Spin Coupling Constants

This work benchmarks density functional theory, with several different exchange-correlation functionals, for prediction of isotropic one-bond phosphorus-hydrogen NMR spin-spin coupling constants (SSCCs). Our test set consists of experimental SSCCs from 30 diverse molecules representing multiple phosphorus bonding environments. The results suggest the importance of a balance between the choice of correlation functional and the admixture of nonlocal exchange. Overall, standard DFT methods appear to suffice for usefully accurate predictions of (31)P-(1)H SSCCs.

Perspective: relativistic effects

This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts.

Computational study and molecular orbital analysis of NMR shielding, spin-spin coupling, and electric field gradients of azido platinum complexes

(195)Pt, (14)N, and (15)N NMR data for five azido (N(3)(-)) complexes are studied using relativistic density functional theory (DFT). Good agreement with experiment is obtained for Pt and N chemical shifts as well as Pt-N J-coupling constants. Calculated (14)N electric field gradients (EFGs) reflect experimentally observed trends for the line broadening of azido (14)N NMR signals. A localized molecular orbital analysis of the nitrogen EFGs and chemical shifts is performed to explain some interesting trends seen experimentally and in the first-principles calculations: (i) (14)N NMR signals for the Pt-coordinating (N(α)) nuclei in the azido ligands are much broader than for the central (N(β)) or terminal (N(γ)) atoms. The N(β) signals are particularly narrow; (ii) compared to N(γ), the N(α) nuclei are particularly strongly shielded; (iii) N(β) nuclei have much larger chemical shifts than N(α) and N(γ) ; and (iv) The Pt-N(α) J-coupling constants are small in magnitude when considering the formal sp hybridization of N(α). It is found that for N(α) a significant shielding reduction due to formation of the dative N(α)-Pt bond is counterbalanced by an increased shielding from spin-orbit (SO) coupling originating at Pt. Upon coordination, the strongly delocalized π system of free azide localizes somewhat on N(β) and N(γ). This effect, along with rehybridization at N(α) upon bond formation with Pt, is shown to cause a deshielding of N(γ) relative to N(α) and a strong increase of the EFG at N(α). The large 2p character of the azide σ bonds is responsible for the particularly high N(β) chemical shifts. The nitrogen s-character of the Pt-N(α) bond is low, which is the reason for the small J-coupling. Similar bonding situations are likely to be found in azide complexes with other transition metals.

[Pt@Pb12]2– — A challenging system for relativistic density functional theory calculations of 195Pt and 207Pb NMR parameters

We report computations of NMR chemical shifts and indirect spin-spin coupling constants (J couplings) for the [Pt@Pb12]2– “superatom”. The system is strongly influenced by relativistic effects. The Pt–Pb coupling constant is predicted to be negative, with its magnitude being in reasonable agreement with experiment. Pt and Pb chemical shifts also agree reasonably well with experiment. The Pb shielding tensor is strongly anisotropic, with a large deshielding principal component dominated by magnetic coupling between frontier orbitals of the cluster that resemble atomic g orbitals. The NMR parameters are sensitive to approximations made in the computations and require the inclusion of spin-orbit coupling in the theoretical model to achieve reliable results. Computing the NMR parameters of the compact [Pt@Pb12]2– system with its many electrons proves to be a challenging test case for relativistic density functional methods.