Decomposition of nuclear magnetic resonance spin–spin coupling constants into active and passive orbital contributions

On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants

It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

Opsin Effect on the Electronic Structure of the Retinylidene Chromophore in Rhodopsin

Direct examination of experimental NMR parameters combined with electronic structure analysis was used to provide a first-principle interpretation of NMR experiments and give a precise evaluation of how the electronic perturbation of the protein environment affects the electronic properties of the retinylidene chromophere in rhodopsin. To this end, we pursued a theoretical analysis using a combination of tools including quantum mechanics/molecular mechanics (QM/MM) at the Density Functional Theory (DFT) level, in conjunction with gauge independent atomic orbital (GIAO) calculations of (13)C NMR chemical shieldings and (1)J(CC) spin-spin coupling constants obtained with the Coupled Perturbed DFT (CPDFT) method. The opsin effect on the retinylidene chromophere is interpreted as an inductive effect of Glu-113 which readjusts the weighting factors of resonance substructures of the conjugated chain of the chromophere. These changes give a rationalization to the alternating effect of the (13)C chemical shifts magnitudes when comparing the retinylidene chromophere in the presence and absence of the protein environment. Conversely, perturbation of π orbitals has little to no effect over (1)J (13)C-(13)C spin-spin coupling constants, as they are mainly dominated by the Fermi contact term, and hence the counteraion effect is restricted to the vicinity of the perturbation. Thus, the apparent contradiction between experimental findings based on chemical shifts (deep penetration) and one-bond J-couplings (localized effects of the protonated Schiff base at the chain terminus) is in fact a consequence of different properties responding differently to the same external perturbation.

Unusual long-range spin-spin coupling in fluorinated polyenes: a mechanistic analysis

Nuclear magnetic resonance (NMR) is a prospective means to realize quantum computers. The performance of a NMR quantum computer depends sensitively on the properties of the NMR-active molecule used, where one requirement is a large indirect spin-spin coupling over large distances. F-F spin-spin coupling constants (SSCCs) for fluorinated polyenes F-(CH==CH)n-F (n=1cdots, three dots, centered5) are >9 Hz across distances of more than 10 A. Analysis of the F,F spin-spin coupling mechanism with our recently developed decomposition of J into Orbital Contributions with the help of Orbital Currents and Partial Spin Polarization (J-OCOC-PSP=J-OC-PSP) method reveals that coupling is dominated by the spin-dipole (SD) term due to an interplay between the pi lone-pair orbitals at the F atoms and the pi(C2n) electron system. From our investigations we conclude that SD-dominated SSCCs should occur commonly in molecules with a contiguous pi-electron system between the two coupling nuclei and that a large SD coupling generally is the most prospective way to provide large long-range spin-spin coupling. Our results give guidelines for the design of suitable active molecules for NMR quantum computers.

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.

Calculation and analysis of NMR spin-spin coupling constants

The analysis of NMR spin-spin coupling leads to a unique insight into the electronic structure of closed-shell molecules, provided one is able to decode the different features of the spin-spin coupling mechanism. For this purpose, the physics of spin-spin coupling is described and the way how spin-spin coupling constants (SSCCs) can be quantum mechanically determined. Based on this insight, a set of requirements is derived that guide the development of a quantum mechanical analysis of spin-spin coupling. It is demonstrated that the J-OC-PSP (=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization) analysis method fulfills all requirements. J-OC-PSP makes it possible to partition the isotropic indirect SSCC J or its reduced analogue K as well as the four Ramsey terms (Fermi contact (FC), spin dipole (SD), diamagnetic spin orbit (DSO), paramagnetic spin orbit (PSO)) leading to J (or K) into Cartesian components (for the anisotropic Ramsey terms SD, DSO, PSO), orbital contributions or electron interaction terms. For the purpose of decoding the spin-spin coupling mechanism, FC, SD, DSO, and PSO coupling is discussed in detail and related to electronic and bonding features of the molecules in question. The myth of empirical and semiempirical relationships between SSCCs and bonding features is unveiled. It is found that most relationships are only of limited, partly dubious value, often arising from a fortuitous cancellation of terms that cannot be expected in general. These relationships are replaced by quantum chemical relations and descriptions that directly reflect the complex electronic processes leading to spin-spin coupling.

One-electron versus electron–electron interaction contributions to the spin–spin coupling mechanism in nuclear magnetic resonance spectroscopy: Analysis of basic electronic effects

For the first time, the nuclear magnetic resonance (NMR) spin-spin coupling mechanism is decomposed into one-electron and electron-electron interaction contributions to demonstrate that spin-information transport between different orbitals is not exclusively an electron-exchange phenomenon. This is done using coupled perturbed density-functional theory in conjunction with the recently developed J-OC-PSP [=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization)] method. One-orbital contributions comprise Ramsey response and self-exchange effects and the two-orbital contributions describe first-order delocalization and steric exchange. The two-orbital effects can be characterized as external orbital, echo, and spin transport contributions. A relationship of these electronic effects to zeroth-order orbital theory is demonstrated and their sign and magnitude predicted using simple models and graphical representations of first order orbitals. In the case of methane the two NMR spin-spin coupling constants result from totally different Fermi contact coupling mechanisms. (1)J(C,H) is the result of the Ramsey response and the self-exchange of the bond orbital diminished by external first-order delocalization external one-orbital effects whereas (2)J(H,H) spin-spin coupling is almost exclusively mitigated by a two-orbital steric exchange effect. From this analysis, a series of prediction can be made how geometrical deformations, electron lone pairs, and substituent effects lead to a change in the values of (1)J(C,H) and (2)J(H,H), respectively, for hydrocarbons.