Analysis of the paramagnetic spin–orbit transmission mechanism for NMR spin–spin coupling constants using the paramagnetic spin–orbit density distribution

Covalence and π-electron delocalization influence on hydrogen bonds in proton transfer process of o-hydroxy aryl Schiff bases: A combined NMR and QTAIM analysis

Within the framework of the density functional theory approach, we studied the relationship between the chemical nature of intramolecular hydrogen bonds (HBs) and nuclear magnetic resonance (NMR) parameters, J-couplings and ¹H-chemical shifts [δ(¹H)], of the atoms involved in such bonds in o-hydroxyaryl Schiff bases during the proton transfer process. For the first time, the shape of the dependence of the degree of covalence in HBs on ¹J(N-H), ¹J(O-H), ^2hJ(O-N), and δ(¹H) during the proton transfer process in o-hydroxyaryl Schiff bases was analyzed. Parameters obtained from Bader's theory of atoms in molecules were used to assess the dependence of covalent character in HBs with both the NMR properties. The influence of π-electronic delocalization on ^2hJ(N-O) under the proton transfer process was investigated. ^2hJ(O-N) in a Mannich base was also studied in order to compare the results with an unsaturated system. In addition, substituent effects on the phenolic ring were investigated. Our results indicate that the covalent character of HBs on both sides of the transition state undergoes a smooth exponential increase as the δ(¹H) moves downfield. The degree of covalence of the N⋯H (O⋯H) bond increases linearly as ¹J(N-H) (¹J(O-H)) becomes more negative, even after reaching the transition state. Non-vanishing values of spin dipolar (SD) and paramagnetic spin orbital terms of ^2hJ(O-N) show that π-electronic delocalization has a non-negligible effect on tautomeric equilibrium and gives evidence of the presence of the resonance assisted HB.Variation of the SD term of ^2hJ(O-N) follows a similar pattern as the change in the para-delocalization aromaticity index of the chelate ring.

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.

Investigation of the resonance-assisted hydrogen bond in model β-diketones through localized molecular orbital analysis of the spin-spin coupling constants related to the O-H···O hydrogen bond

The resonance-assisted hydrogen bond (HB) phenomenon has been studied theoretically by a localized molecular orbital (LMO) decomposition of the spin-spin coupling constants between atoms either involved or close to the O-H···O system of some β-diketones and their saturated counterparts. The analysis, carried out at the level of the second-order polarization propagator approximation, shows that the contributions in terms of LMO to the paramagnetic spin orbital and the spin dipolar Ramsey terms proof the importance of the delocalized π-electron structure supporting the idea of the existence of the resonance-assisted HB phenomenon phenomenon. The LMO contributions to the Fermi contact term indicate mainly the presence of the HB that may or not be linked to the π-electrons.

(19)F-(19)F and (19)F-(1)H spin-spin coupling constants in cyclic FH polymers (FH)(n), n=2-6

Spin-spin coupling constants (2h)J(F-F), (1)J(F-H), and (1h)J(H-F) have been obtained for cyclic complexes (FH)(n), with n=2-6, from ab initio equation-of-motion coupled cluster singles and doubles (EOM-CCSD) calculations. Although both the Fermi-contact (FC) term and (2h)J(F-F) increase and become positive as the cluster size increases, the FC term is not a good quantitative approximation to (2h)J(F-F). The paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms which contribute to (2h)J(F-F) appear to be sensitive to the orientation of the hydrogen-bonded pair. However, the large increase in the FC term and (2h)J(F-F) as the size of the cluster increases is due primarily to the reorganization of sigma electron densities in both ground and excited states, and is another manifestation of cooperativity effects in hydrogen-bonded cyclic polymers. The FC term and (1)J(F-H) always increase upon complex formation, but (1)J(F-H) increases only slightly as the size of the cluster increases due to a concurrent decrease in the PSO term. The changes in (1)J(F-H) as a function of polymer size reflect the polarization of electron density away from H and toward F in the ground state, and the electron reorganization which occurs in the excited states which couple to the ground states through the FC and PSO operators. The FC term is a good approximation to (1h)J(H-F), and is always negative, indicating that the hydrogen bonds in the FH clusters are traditional hydrogen bonds.

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.

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.

Variation of One-bond X−Y Coupling Constants 1J(X−Y) and the Components of 1J(X−Y) with Rotation about the X−Y Bond for Molecules HmX−YHn, with X, Y = 15N, 17O, 31P, 33S: The Importance of Nonbonding Pairs of Electrons

Ab initio EOM-CCSD calculations have been performed on molecules HmX-YHn, for X, Y = 15N, 17O, 31P, and 33S, to investigate the variation of one-bond X-Y spin-spin coupling constants 1J(X-Y) and the components of J with rotation about the X-Y single bond. The reduced Fermi-contact (FC) terms for all 10 molecules are negative and decrease in absolute value as the rotational angle theta changes from 0 degrees, at which point the lone pairs of electrons are on the same side of the X-Y bond, to 180 degrees where they are trans with respect to the X-Y bond. The signs of reduced paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms are opposite that of the FC term and exhibit extremum values as theta approaches 90 degrees, the gauche conformation. While the FC term tends to dominate for molecules H2X-YH2 and H2X-YH, such is not the case for HX-YH, where the PSO and SD terms assume increased importance. Curves for 1K(X-Y) as a function of rotational angle are readily grouped according to formula H2X-YH2, H2X-YH, and HX-YH, which suggests that it is the lone pairs of electrons on X and Y which are primarily responsible for the trends observed.

Elucidation of the Electronic Structure of Molecules with the Help of NMR Spin−Spin Coupling Constants: The FH Molecule

It is demonstrated how the one-bond NMR spin-spin coupling constant (SSCC) (1)J(FH) can be used as a source of information on the electronic structure of the FH molecule. For this purpose, the best possible agreement between measured and calculated SSCC is achieved by large basis set coupled perturbed density functional theory calculations. Then, the calculated value is dissected into its four Ramsey terms: Fermi contact, the paramagnetic spin-orbit term, the diamagnetic spin-orbit term, and the spin dipole term, which in turn are decomposed into orbital contributions and then described by their spin densities and orbital current densities. In this way, the SSCC gives detailed information about the electronegativity of F, the bond polarity, the bond polarizability, the volume and the polarizability of sigma and pi lone pair orbitals, the s- or p-character of the bond orbital, the nature of the LUMO, and the density distribution around F.

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

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.

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.