Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: The importance of level crossings

We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T(1e) is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.     

Spin resolved electron number distribution functions: how spins couple in real space

The probabilities of finding arbitrary partitions of the N(alpha)m(s)=12 and N(beta)m(s)=-12 electrons of a molecule into m arbitrary regions that exhaust the physical space are developed and computed, both for atomic and electron localization function basins, in a number of test systems. These spin resolved electron number distribution functions provide access to the coarse-grained distribution of spins in space even for singlet states, a nontrivial result. It is found that atoms within molecules partially retain their in vacuo preferences for certain spin configurations. This may lead to long range spin coupling among basins. An aufbaulike rule favoring spin coupling, particularly for Hartree-Fock wave functions, has also been found.     

A new mechanism for electron spin echo envelope modulation

Electron spin echo envelope modulation (ESEEM) has been observed for the first time from a coupled heterospin pair of electron and nucleus in liquid solution. Previously, modulation effects in spin-echo experiments have only been described in liquid solutions for a coupled pair of homonuclear spins in nuclear magnetic resonance or a pair of resonant electron spins in electron paramagnetic resonance. We observe low-frequency ESEEM (26 and 52 kHz) due to a new mechanism present for any electron spin with S > 12 that is hyperfine coupled to a nuclear spin. In our case these are electron spin (S = 32) and nuclear spin (I = 1) in the endohedral fullerene N@C(60). The modulation is shown to arise from second-order effects in the isotropic hyperfine coupling of an electron and (14)N nucleus.     

A study of interaction in the lowest singlet and triplet states of H2

The potential energy curves of the ground state and the first excited state of H₂ are examined in terms of the electronic force acting on each nucleus. The results reveal the detailed course of events that occur when two hydrogen atoms with parallel and antiparallel electron spins approach one another from a large internuclear separation.     

Projected electron density method of π-eletron systems II. Excited states

A perturbation theory based on the time-dependent Schrödinger equation is presented; Coulombic interactions are taken into account and spin properties are neglected. Using wave functions given by the projected electron density method described in Part I as a basis set the energies of excited π-electron states are calculated. For a series of porphyrin compounds the electronic spectra are calculated and are found to be in good agreement with experiment.     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Application of the electron localization function to radical systems

An application of the topological electron localization function (ELF) analysis to free radical systems is presented. A separation of the ELF function into its α‐spin and β‐spin contributions has been performed. Methyl and phenyl radicals, ortho‐, meta‐, and para‐benzyne biradicals, and their corresponding radical anions have been chosen with the aim to validate the new ELF_α and ELF_β proposed functions. The results show that the ELF separation yields complementary information about the localization of the unpaired electron. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

A partially projected wave function for radicals

A partially projected wave function for odd electron systems with quantum number M=1/2, containing μu spin functions α and μ spin functions α, with fractional spin component αS_z=1/2 and 3/2 are derived from the totally projected wave function. To obtain these wave functions new symmetry relations between Sanibel coefficients for the odd electron case have been found, as well as the relations between primitive spin functions and their spin permutations. The wave function for the doublet state is shown not to contain contamination of the quadruplet state, and the wave function for the quadruplet does not have contamination of the duplet. Both wave functions exhibit equal forms except in the signs of their summation terms. The number of primitive spin functions depends on the number of electrons (n_s), it grows linearly as n_s=(N+3)/2. It can be considered as a generalization of the half projected Hartree–Fock wave function to the odd electron case. The HPHF wave function is defined for even electron systems and consists of only two Slater determinants, it has been shown to introduce some correlation effects and it has been successfully applied to calculate the low-lying excited states of molecules. Therefore, this investigation is the first step to propose a method to calculate the excited states of radicals when other methods are impracticable. This revised version was published online in July 2006 with corrections to the Cover Date.     

Angular aspects of exchange correlation and the fermi hole

The complete (nonreduced) αα probability density functions evaluated from the Hartree–Fock and simple Hartree product wavefunctions have been used to elucidate the angular features of spin correlation and the Fermi hole in the 2³S state of helium and the ground state of beryllium. This approach shows that the local Fermi holes in these two cases are very similar and that the Fermi hole is essentially spherically symmetric when the reference electron is close to the nucleus. As the reference electron is removed to larger radial distances, appreciable polarization of the Fermi hole is observed. The polarization is greater in the direction of the nucleus than away from the nucleus, contrary to the situation in the Coulomb hole of the helium ground state where the polarization is greater away from the nucleus than toward the nucleus. Several other differences between the He 2³S Fermi hole and the He 1¹S Coulomb hole are noted.     

Charge and spin correlation structures of conjugated π systems: Analysis of full CI wave functions of the PPP hamiltonian

An analysis of the electronic correlation structures by means of the charge and spin correlation functions is carried out for full CI wave functions of four, five, and six membered conjugated π systems described by the Pariser–Parr–Pople Hamiltonian. The low-lying states of these systems are classified as covalent (CV ) and ionic (IN ) states depending on whether the probability of finding two electrons simultaneously at the same position is small or large. It is found that many of excited CV states, the typical ones of which are the 2¹A_g state of linear π systems, have stronger CV character than the ground CV state, and their spin coupling structures are different from each other as well as from that of the ground CV state. The spin coupling structure in the ground CV state has an “antiferromagnetic” spin arrangement in favor of antiparallel coupling between nearest neighbor spins while in excited CV states the extent of the antiparallel spin coupling between nearest neighbor sites is decreased. IN states, which are less common for low-lying states than CV ones, are also found to have characteristic modulations in the charge correlation. In particular, the charge correlations in the lowest singlet IN states, 1¹B_u of linear π systems, 1¹B_2g of cyclobutadiene and 1¹B_1U of benzene, are alternating.     

Coherent spin control of matrix isolated molecules by IR+UV laser pulses: quantum simulations for ClF in Ar

Two coherent sequential IR+UV laser pulses may be used to generate two time-dependent nuclear wave functions in electronic excited triplet and singlet states via single (UV) and two photon (IR+UV) excitation pathways, exploiting spin-orbit coupling and vibrational pre-excitation, respectively. These wave functions evolve from different Franck-Condon domains until they overlap in a domain of bond stretching with efficient intersystem crossing. Here, the coherence of the laser pulses is turned into optimal interferences of the wave packets, yielding the total wave packet at the target place, time, and with dominant target spin. The time resolution of spin control is few femtoseconds. The mechanism is demonstrated by means of quantum model simulations for ClF in an Ar matrix.     

A Nitroxide‐Tagged Platinum(II) Complex Enables the Identification of a DNA G‐Quadruplex Binding Mode

We reported a novel strategy for investigating small molecule binding to G‐quadruplexes (GQs). A newly synthesized dinuclear platinum(II) complex (Pt₂L) containing a nitroxide radical was shown to selectively bind a GQ‐forming sequence derived from human telomere (hTel). Using the nitroxide moiety as a spin label, electron paramagnetic resonance (EPR) spectroscopy was carried out to investigate binding between Pt₂L and hTel GQ. Measurements indicated that two molecules of Pt₂L bind with one molecule of hTel GQ. The inter‐spin distance measured between the two bound Pt₂L, together with molecular docking analyses, revealed that Pt₂L predominately binds to the neighboring narrow and wide grooves of the G‐tetrads as hTel adopts the antiparallel conformation. The design and synthesis of nitroxide tagged GQ binders, and the use of spin‐labeling/EPR to investigate their interactions with GQs, will aid the development of small molecules for manipulating GQs involved in crucial biological processes.     

A measure of electron localizability

A functional of the same‐spin electron pair density is proposed as a measure of electron localizability. This functional yields the average number of same‐spin electron pairs in a region Ω enclosing a fixed charge. The functional equals zero if the fixed charge in Ω originates from one electron only, with all other same‐spin electrons outside the region Ω. Then, the correlation of the electronic motion in Ω and thus the localizability of an electron is high. If the motion of the same‐spin electrons becomes less correlated, more electrons participate in the fixed charge contained in Ω, the average number of same‐spin electron pairs (the functional) increases. In the Hartree–Fock approximation the Taylor expansion of the proposed localizability functional can be related to the electron localization function of Becke and Edgecombe without using an arbitrary reference to the uniform electron gas. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Role of electron correlation in hyperfine interaction

The spin density near the nucleus of a magnetic atom is examined in the first order with respect to the nondiagonal matrix element for the electron interaction with the corresponding excitation level. A system containing one electron outside the closed shells is discussed.     

Quantum chemical modeling of electrochromism of tungsten oxide films

A cluster model is proposed to describe the excitations in solid tungsten oxide. The density-functional theory approach is used to calculate the ground-state electronic structure of the model cluster and its optimum geometry; subsequently, time-dependent density-functional theory calculations are performed to obtain the oscillator strengths and energies of the excited states. The results are reported both for the electrically neutral cluster and for the cluster with an extra electron (mimicking the effect of electron injection from the cathode). They correctly locate the electrochemically active transition. The corresponding wave functions are delocalized, suggesting that electron localization at one tungsten center is rather unlikely, thereby shedding doubt as to the validity of the polaron model. Local lattice distortions presumably created at the stage of sample preparation are found to affect the excitation energies to a considerable extent, which explains the experimentally observable large width of optical absorption responsible for electrochromism.     

Time-dependent multiconfiguration theory for electronic dynamics of molecules in intense laser fields: a description in terms of numerical orbital functions

The equations of motion (EOMs) for spin orbitals in the coordinate representation are derived within the framework of the time-dependent multiconfiguration theory developed for electronic dynamics of molecules in intense laser fields. We then tailor the EOMs for diatomic (or linear) molecules to apply the theory to the electronic dynamics of a hydrogen molecule in an intense, near-infrared laser field. Numerical results are presented to demonstrate that the time-dependent numerical multiconfiguration wave function is able to describe the correlated electron motions as well as the ionization processes of a molecule in intense laser fields.     

Two-site-hopping time correlation functions. Application to radical pair recombination

The two-site-hopping problem is studied in the time domain. The relaxation can be described as a product of two time correlation functions. One describes the time evolution for the average over the two sites, while the other accounts for the difference of the two sites. The latter exhibits an anomalous slow decay at long times and does not decay for fast hopping rates. The first does not depend on the hopping rate at all. The results are applied to the spin dynamics of novel pairwise-connected molecules carrying an unpaired electron spin.     

Observation of magnetic multilayers by electron holography.

Magnetic structures of Co/Cu multilayers in cross section are observed by two kinds of electron holography: a Fourier method and a phase-shifting method, which is introduced briefly. The Fourier method can easily reconstruct wave functions and is applied to many specimens, whereas the phase-shifting method requires longer time for processing, but has a higher spatial resolution that permits us to discuss fine structures. Magnetization vectors in Co layers aligning parallel and separating into two blocks with antiparallel alignment are observed. Magnetic blurring on the boundary between Co and Cu in the reconstructed phase images is larger than the estimated atomic roughness.     

Curvilinear and surficial electron holes in atoms and molecules

The antisymmetric property of many-electron wave functions results in the well-known Fermi hole, which implies that any two electrons with the same spin cannot be at the same point in space. We here point out that for certain types of antisymmetric wave functions, there exist curvilinear and surficial electron holes which imply that two electrons cannot be on particular curves and surfaces in space.