Understanding the kinetics of spin-forbidden chemical reactions

Many chemical reactions involve a change in spin-state and are formally forbidden. This article summarises a number of previously published applications showing that a form of Transition State Theory (TST) can account for the kinetics of these reactions. New calculations for the emblematic spin-forbidden reaction HC + N(2) are also reported. The observed reactivity is determined by two factors. The first is the critical energy required for reaction to occur, which in spin-forbidden reactions is often defined by the relative energy of the Minimum Energy Crossing Point (MECP) between potential energy surfaces corresponding to the different spin states. The second factor is the probability of hopping from one surface to the other in the vicinity of the crossing region, which is largely defined by the spin-orbit coupling matrix element between the two electronic wavefunctions. The spin-forbidden transition state theory takes both factors into account and gives good results. The shortcomings of the theory, which are largely analogous to those of standard TST, are discussed. Finally, it is shown that in cases where the surface-hopping probability is low, the kinetics of spin-forbidden reactions will be characterised by unusually unfavourable entropies of activation. As a consequence, reactions involving a spin-state change can be expected to compete poorly with spin-allowed reactions at high temperatures (or energies).     

Analysis of wave functions for open-shell molecules

During the past decade we have looked at several ways to track the distribution of unpaired electrons during chemical reactions and in different spin states. These methods were inspired by our previous work on singlet di-radicals where the spin density is zero yet there are clearly singly occupied orbitals. More recently we have been concerned with analysis of wave functions for single molecule magnets. This review discusses the mathematical framework by which open-shell systems can be described, in addition to methods that extract the effectively unpaired electron density, the spin state of atoms in a molecule, and other useful properties from a molecular wave function. Some of the difficulties associated with using broken spin Slater determinants to evaluate the exchange coupling parameters in the Heisenberg Hamiltonian are also mentioned.     

Conformational Spin Switching and Spin‐Selective Hydrogenation of a Magnetically Bistable Carbene

The control of the spin states of molecules opens the path to tuning selectivity in chemical reactions and to developing novel magnetically switchable materials. 3‐Methoxy‐9‐fluorenylidene is a carbene that is generated in cryogenic matrices both in its lowest energy singlet and triplet states, and the ratio of these states can be shifted by selective irradiation. The interconversion of the nearly degenerate spin states is induced by a conformational change of the methoxy group: switching the methoxy group into the “up” position results in the singlet state and switching into the “down” position in the triplet state. The spin control via a remote functional group makes this carbene unique for the study of spin‐specific reactions, which is demonstrated for the hydrogenation reaction. Spin switching by switching the conformation of a remote functional group is a novel phenomenon with potential applications in the design of functional materials.     

A general approach for prediction of motional EPR spectra from Molecular Dynamics (MD) simulations: application to spin labelled protein

A general approach for the prediction of EPR spectra directly and completely from single dynamical trajectories generated from Molecular Dynamics (MD) simulations is described. The approach is applicable to an arbitrary system of electron and nuclear spins described by a general form of the spin-Hamiltonian for the entire motional range. It is shown that for a reliable simulation of motional EPR spectra only a single truncated dynamical trajectory generated until the point when correlation functions of rotational dynamics are completely relaxed is required. The simulation algorithm is based on a combination of the propagation of the spin density matrix in the Liouville space for this initial time interval and the use of well defined parameters calculated entirely from the dynamical trajectory for prediction of the evolution of the spin density matrix at longer times. A new approach is illustrated with the application to a nitroxide spin label MTSL attached to the protein sperm whale myoglobin. It is shown that simulation of the EPR spectrum, which is in excellent agreement with experiment, can be achieved from a single MD trajectory. Calculations reveal the complex nature of the dynamics of a spin label which is a superposition of the fast librational motions within dihedral states, of slow rotameric dynamics among different conformational states of the nitroxide tether and of the slow rotational diffusion of the protein itself. The significance of the slow rotameric dynamics of the nitroxide tether on the overall shape of the EPR spectrum is analysed and discussed.     

Hydrogen Bonding Switches the Spin State of Diphenylcarbene from Triplet to Singlet

Spin specificity is one of the most important properties of carbenes in their reactions. Alcohols are typically used to probe the reactive spin states of carbenes: O? H insertions are assumed to be characteristic of singlet states, whereas C? H insertions are typical for the triplets. Surprisingly, the experiments presented here suggest that the spin ground state of diphenylcarbene 1 switches from triplet to singlet if the carbene is allowed to interact with methanol. Carbene 1 and methanol form a strongly hydrogen‐bonded singlet ground state complex that was synthesized in low‐temperature matrices and characterized by IR spectroscopy. This methanol complex is only metastable, and even at 3 K slowly rearranges to form the product of O? H insertion through quantum chemical tunneling. Thus, the ground state triplet (in the gas phase) carbene 1 forms exclusively the products expected from a singlet carbene. Whereas the assumption of spin specific reactions of carbenes is correct, the spin state itself can be changed by solvent interactions, and therefore widely accepted conclusions drawn from earlier experiments have to be revisited.     

A diabatic representation including both valence nonadiabatic interactions and spin-orbit effects for reaction dynamics

A diabatic representation is convenient in the study of electronically nonadiabatic chemical reactions because the diabatic energies and couplings are smooth functions of the nuclear coordinates and the couplings are scalar quantities. A method called the fourfold way was devised in our group to generate diabatic representations for spin-free electronic states. One drawback of diabatic states computed from the spin-free Hamiltonian, called a valence diabatic representation, for systems in which spin-orbit coupling cannot be ignored is that the couplings between the states are not zero in asymptotic regions, leading to difficulties in the calculation of reaction probabilities and other properties by semiclassical dynamics methods. Here we report an extension of the fourfold way to construct diabatic representations suitable for spin-coupled systems. In this article we formulate the method for the case of even-electron systems that yield pairs of fragments with doublet spin multiplicity. For this type of system, we introduce the further simplification of calculating the triplet diabatic energies in terms of the singlet diabatic energies via Slater's rules and assuming constant ratios of Coulomb to exchange integrals. Furthermore, the valence diabatic couplings in the triplet manifold are taken equal to the singlet ones. An important feature of the method is the introduction of scaling functions, as they allow one to deal with multibond reactions without having to include high-energy diabatic states. The global transformation matrix to the new diabatic representation, called the spin-valence diabatic representation, is constructed as the product of channel-specific transformation matrices, each one taken as the product of an asymptotic transformation matrix and a scaling function that depends on ratios of the spin-orbit splitting and the valence splittings. Thus the underlying basis functions are recoupled into suitable diabatic basis functions in a manner that provides a multibond generalization of the switch between Hund's cases in diatomic spectroscopy. The spin-orbit matrix elements in this representation are taken equal to their atomic values times a scaling function that depends on the internuclear distances. The spin-valence diabatic potential energy matrix is suitable for semiclassical dynamics simulations. Diagonalization of this matrix produces the spin-coupled adiabatic energies. For the sake of illustration, diabatic potential energy matrices are constructed along bond-fission coordinates for the HBr and the BrCH(2)Cl molecules. Comparison of the spin-coupled adiabatic energies obtained from the spin-valence diabatics with those obtained by ab initio calculations with geometry-dependent spin-orbit matrix elements shows that the new method is sufficiently accurate for practical purposes. The method formulated here should be most useful for systems with a large number of atoms, especially heavy atoms, and/or a large number of spin-coupled electronic states.     

The creation of off-diagonal elements in chemically induced dynamic nuclear polarization experiments

The nuclear density matrix created in pulsed CIDNP experiments contains off-diagonal elements whenever the resulting nuclear spin system is strongly coupled. These off-diagonal elements, which connect spin states with the same magnetic quantum number, are due to the mixing of nuclear state functions during the process of product formation. The observation of these elements by means of a two-pulse experiment is described.     

Two states and two more in the mechanisms of hydroxylation and epoxidation by cytochrome P450

Past studies have shown that oxidation reactions by P450 Compound I (Cpd I) can be described by two competing quartet and doublet spin states, which possess three unpaired electrons, hence tri-radicals. One electron excitation from the delta orbital to sigma* xy generates two states that possess five unpaired electrons, so-called penta-radicals, in sextet and quartet situations, and which were shown by theory to lie only approximately 12-14 kcal/mol higher in energy than the tri-radical ground states (ref 7). The present study focuses on the C-H hydroxylation and C=C epoxidation of propene by these penta-radical states. It is shown that the initial energy differences, between the penta-radical and tri-radical states, diminish along the reaction pathway, due to the favorable and cumulative exchange stabilization of the more open-shell species. Furthermore, theory suggests that hydrogen bonding to the thiolate ligand, and general polarity of the environment, reduce these gaps further, thereby making the penta-radical states accessible to ground-state reactivity. The interconversion between the tri-radical and penta-radical states along the reaction coordinate will depend on the dynamics of spin-flips and energy barriers between the states. Especially interesting should be the region of the reaction intermediates; for both epoxidation and hydroxylation, this region is typified by a dense manifold of spin states and electromeric states (that differ by the oxidation state of iron), such that the total reactivity would be expected to reflect the interplay of these states, giving rise to multistate reactivity.     

Open-shell reduced density matrix functional theory

Open-shell reduced density matrix functional theory is established by investigating the domain of the exact functional. For spin states that are the ground state, a particularly simple set is found to be the domain. It cannot be generalized to other spin states. A number of conditions satisfied by the exact density matrix functional is formulated and tested for approximate functionals. The exact functional does not suffer from fractional spin error, which is the source of the static correlation error in dissociated molecules. We prove that a simple approximation (called the Buijse-Baerends functional, Mu?ller or square root functional) has a non-positive fractional spin error. In the case of the H atom the error is zero. Numerical results for a few atoms are given for approximate density and density matrix functionals as well as a recently developed range-separated combination of both.     

Effective interactions and block diagonalization in quantum-mechanical problems

Many models of condensed-matter systems have interactions with unexpected features: for example, exclusively distant-neighbor spin–orbit interactions. On first inspection these interactions seem physically questionable in view of the basis states used. However, such interactions can be physically reasonable if the model is an effective one, in which the basis states are not exactly as described, but instead include components of states removed from the problem. Mathematically, an effective model results from partitioning the Hamiltonian matrix, which can be accomplished by energy-dependent or energy-independent methods. We examine effective models of both types, with a special emphasis on energy-independent approaches. We show that an appropriate choice of basis makes the partitioning simpler and more accurate. We illustrate the method by calculating the spin–orbit splitting in graphene.     

Inelastic collisions of cold polar molecules in nonparallel electric and magnetic fields

The authors present a detailed study of low-temperature collisions between CaD molecules and He atoms in superimposed electric and magnetic fields with arbitrary orientations. Electric fields do not interact with the electron spin of the molecules directly but modify their rotational structure and, consequently, the spin-rotation interactions. The authors examine molecular Stark and Zeeman energy levels as functions of the angle between the fields and show that rotating fields may induce and shift avoided crossings between the Zeeman levels of the rotationally ground and rotationally excited states of the molecule. The dynamics of molecular collisions are extremely sensitive to external fields near these avoided crossings and it is shown that molecular collisions may be controlled by varying both the strength and the relative orientation of the fields. The effects observed in this study are due to interactions of the isolated molecules with external fields so the conclusions should be relevant for collisions of molecules with other atoms or collisions of molecules with each other. This study demonstrates that electric fields may be used to enhance or suppress spin-rotation interactions in molecules. The spin-rotation interactions induce nonadiabatic couplings between states of different total spins in systems of two open-shell species and it is suggested that electric fields might be used for controlling nonadiabatic spin transitions and spin-forbidden chemical reactions of cold molecules in a magnetic trap.     

New Applications of Computers in Chemistry

The mathematical model of constitutional chemistry described here is based on a concept of isomerism which has been extended from molecules to ensembles of molecules. A chemical reaction is the conversion of an ensemble of molecules into an isomeric ensemble. An ensemble of molecules is representable by an atomic vector and an associated bond and electron (BE)- matrix, and a reaction by a reaction (R)-matrix. These BE-and R-matrices serve as a basis for computer programs for the deductive solution of chemical problems. We present here algorithms and computer programs based on the theory of BE- and R-matrices. They enable the classification and documentation of structrues, substructures and reactions, the prognosis of reaction products,the design of syntheses, the construction of networks of mechanistic and synthetic pathways and the prediction of chemical reactions.     

Automated reaction path searches for spin‐forbidden reactions

Many catalytic and biomolecular reactions containing transition metals involve changes in the electronic spin state. These processes are referred to as “spin‐forbidden” reactions within nonrelativistic quantum mechanics framework. To understand detailed reaction mechanisms of spin‐forbidden reactions, one must characterize reaction pathways on potential energy surfaces with different spin states and then identify crossing points. Here we propose a practical computational scheme, where only the lowest mixed‐spin eigenstate obtained from the diagonalization of the spin‐coupled Hamiltonian matrix is used in reaction path search calculations. We applied this method to the ^6,4FeO⁺ + H₂ → ^6,4Fe⁺ + H₂O, ^6,4FeO⁺ + CH₄ → ^6,4Fe⁺ + CH₃OH, and ⁷Mn⁺ + OCS → ⁵MnS⁺ + CO reactions, for which crossings between the different spin states are known to play essential roles in the overall reaction kinetics. © 2018 Wiley Periodicals, Inc.     

Carbenes and Nitrenes: Recent Developments in Fundamental Chemistry

Carbenes and nitrenes can exist in both singlet and triplet states, sometimes equally stable and interconverting either thermally or photochemically. Many carbene and nitrene reactions proceed via tunneling at low temperatures. Numerous singlet and triplet states have been characterized spectroscopically, and a detailed understanding of the chemical and physical properties of carbenes and nitrenes is emerging. There has been significant progress in the direct observation of carbenes, nitrenes, and many other reactive intermediates in recent years through the application of matrix photolysis and flash vacuum pyrolysis linked with matrix isolation at cryogenic temperatures. Our understanding of singlet and triplet states has improved through the interplay of spectroscopy and computations. Bistable carbenes and nitrenes as well as many examples of tunneling have been discovered and numerous rearrangements and fragmentations have been documented. The correlation of the zero‐field splitting parameter D with calculated spin densities on nitrenes and carbenes is discussed. This Minireview gives an overview of some of these developments.     

A theoretical and optical spectroscopic study of the mechanism of a tautomeric transformation in the 7-azaindole dimer and the 7-azaindole complex with a water molecule

Electronic, vibrational, and electronic vibrational spectra of the 7-azaindole dimer, the 7-azaindole complex with a water molecule, and their tautomers are calculated. Transition states are considered based on the analysis of frequencies and shapes of low-frequency vibrations and the Mulliken charge redistribution. The performed quantum chemical calculation of chemical reactions enabled the determination of the structure of transition states and proton transfer conditions. It is shown that in the 7-AzI dimer the proton transfer has a character consistent with the formation of a zwitterionic form. The structure of excited states is calculated and the fluorescence spectra of the first electronic transitions that can be used as a criterion of the formation of 7-AzI tautomers as a result of chemical reactions proceeding through a proton transfer in the 7-azaindole dimer and the 7-azaindole complex with a water molecule, are interpreted.     

Spectroscopic Characterization and Reactivity of Triplet and Quintet Iron(IV) Oxo Complexes in the Gas Phase

Closely structurally related triplet and quintet iron(IV) oxo complexes with a tetradentate aminopyridine ligand were generated in the gas phase, spectroscopically characterized, and their reactivities in hydrogen‐transfer and oxygen‐transfer reactions were compared. The spin states were unambiguously assigned based on helium tagging infrared photodissociation (IRPD) spectra of the mass‐selected iron complexes. It is shown that the stretching vibrations of the nitrate counterion can be used as a spectral marker of the central iron spin state.     

The symmetrized basis function method for SU(2) and its application to the total spin states of many-electron systems

In this paper, the symmetrized basis function method is extended and used for the classification of the total spin states of many-electron systems. The reduction matrix, which is expressed as a series of products and direct products of matrices is derived. It is very advantageous that the method can be completed by computer. As an example, the reduction matrix for a 5-electron system calculated by IBM PC computer and the classification of the total spin states is presented.     

Laser-muon spin spectroscopy in liquids - a technique to study the excited state chemistry of transients

This study introduces laser-muon spin spectroscopy in the liquid phase, which extends muonium chemistry in liquids to the realm of excited states and enables the detection of muoniated molecules by their spin evolution after laser excitation. This leads to new opportunities to study the Kinetic Isotope Effects (KIEs) of muonium/atomic hydrogen reactions and to probe transient chemistry in radiolysis processes involved in muonium formation, as well as muoniated intermediates in excited states.