Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. I. Singlet states in low magnetic field

We have recently demonstrated the existence of exceptionally long-lived nuclear spin states in solution-state nuclear magnetic resonance. The lifetime of nuclear spin singlet states in systems containing coupled pairs of spins-12 may exceed the conventional relaxation time constant T1 by more than an order of magnitude. These long lifetimes may be observed if the long-lived singlet states are prevented from mixing with rapidly relaxing triplet states. In this paper we provide the detailed theory of an experiment which uses magnetic field cycling to observe slow singlet relaxation. An approximate expression is given for the magnetic field dependence of the singlet relaxation rate constant, using a model of intramolecular dipole-dipole couplings and fluctuating external random fields.     

Singlet state relaxation via scalar coupling of the second kind

The contribution of scalar coupling relaxation of the second kind on the relaxation behaviour of nuclear spin singlet states has been derived. The analytical equation found for the relaxation rate constant of singlet state has been compared to the equation for the relaxation of longitudinal magnetization in order to find the conditions for which the singlet state remains long-lived even in the presence of this scalar relaxation mechanism. These results are relevant when the singlet state is formed in molecules with more than two interacting spins.     

About long-lived nuclear spin states involved in para-hydrogenated molecules

This study deals with a spin system constituted of three nonequivalent protons, two of them originating from para-hydrogen (p-H(2)) after a hydrogenation reaction carried out in the earth magnetic field. It is shown that three singlet states are created provided indirect (J) couplings exist between the three spins, implying hyperpolarization transfer toward the third spin. Upon insertion of the sample in the NMR (Nuclear Magnetic Resonance) high field magnet, the following events occur: (i) the longitudinal two-spin orders which are parts of the singlet states survive; (ii) the other two terms (of these singlet states) tend to be destroyed by magnetic field gradients but at the same time are partly converted into differences of longitudinal polarizations. Nuclear spin relaxation is studied by appropriate NMR measurements when evolution takes place in the high field magnet or in the earth field. In the former case, relaxation is classical although complicated by numerous relaxation rates associated with both longitudinal two-spin orders and longitudinal polarizations. In the latter case, an equilibration between the singlet states first occur, their disappearance being thereafter driven by relaxation rates which remain very small because of the absence of any dipolar contribution. Thus, even in the case of a three-spin system, long-lived states exist; this unexpected property could be very useful for many applications.     

Extending the Scope of Singlet‐State Spectroscopy

Different decoupling sequences are tested—using various shaped radio‐frequency (RF) pulses—to achieve the longest possible lifetimes of singlet‐state populations over the widest possible bandwidths, that is, ranges of offsets and relative chemical shifts of the nuclei involved in the singlet states. The use of sinc or refocusing broadband universal rotation pulses (RE‐BURP) for decoupling during the intervals where singlet‐state populations are preserved allows one to extend the useful bandwidth with respect to prior state‐of‐the‐art methods based on composite‐pulse WALTZ decoupling. The improved sinc decoupling sequences afford a more reliable and sensitive measure of the lifetimes of singlet states in pairs of spins that have widely different chemical shifts, such as the two aromatic protons H⁵ and H⁶ in uracil. Similar advantages are expected for nucleotides in RNA and DNA. Alternative approaches, in particular frequency‐modulated decoupling sequences, also appear to be effective in preserving singlet‐state populations, even though the profiles of the apparent relaxation rate constants as a function of the offset are somewhat perturbed. The best decoupling sequences prove their utility in sustaining longer lifetimes of singlet states than previously achieved for the side‐chain tyrosine protons in bovine pancreatic trypsin inhibitor (BPTI) at 600 MHz (14.1 T), where the differences of chemical shifts between coupled protons are a challenge.     

Singlet-state exchange NMR spectroscopy for the study of very slow dynamic processes

Singlet states with lifetimes that are longer than spin-lattice relaxation times TS > T1 offer unique opportunities for studying very slow dynamic processes in solution-state NMR. A set of novel experiments can achieve broadband excitation of singlet states in pairs of coupled spins. The most elaborate of these experiments, two-dimensional singlet-state exchange spectroscopy (SS-EXSY), is independent of the offsets of the two spins, their relative chemical shifts, and their scalar couplings. The new methods open the way to study very slow chemical exchange or translational diffusion using mixing times taum = Ts > T1. The lifetimes TS of singlet states of pairs of protons in a partially deuterated saccharide are shown to be longer than the longitudinal proton relaxation times T1 in the same compound by a factor of ca. 37.     

Long-lived states to monitor protein unfolding by proton NMR

The relaxation of long-lived states (LLS) corresponds to the slow return to statistical thermal equilibrium between symmetric and antisymmetric proton spin states. This process is remarkably sensitive to the presence of external spins and can be used to obtain information about partial unfolding of proteins. We detected the appearance of a destabilized conformer of ubiquitin when urea is added to the protein in its native state. This conformer shows increased mobility in the C-terminus, which significantly extends the lifetimes of proton LLS magnetisation in Ser-65. These changes could not be detected by conventional measurements of T(1) and T(2) relaxation times of protons, and would hardly be sensed by carbon-13 or nitrogen-15 relaxation measurements. Conformers with similar dynamic and structural features, as revealed by LLS relaxation times, could be observed, in the absence of urea, in two ubiquitin mutants, L67S and L69S.     

Singlet nuclear magnetic resonance of nearly-equivalent spins

Nuclear singlet states may display lifetimes that are an order of magnitude greater than conventional relaxation times. Existing methods for accessing these long-lived states require a resolved chemical shift difference between the nuclei involved. Here, we demonstrate a new method for accessing singlet states that works even when the nuclei are almost magnetically equivalent, such that the chemical shift difference is unresolved. The method involves trains of 180° pulses that are synchronized with the spin-spin coupling between the nuclei. We demonstrate experiments on the terminal glycine resonances of the tripeptide alanylglycylglycine (AGG) in aqueous solution, showing that the nuclear singlet order of this system is long-lived even when no resonant locking field is applied. Variation of the pulse sequence parameters allows the estimation of small chemical shift differences that are normally obscured by larger J-couplings.     

Determination of conformational preferences of dipeptides using vibrational spectroscopy

The NMR coupling constants ((3)J(H(N), H(alpha))) of dipeptides indicate that the backbone conformational preferences vary strikingly among dipeptides. These preferences are similar to those of residues in small peptides, denatured proteins, and the coil regions of native proteins. Detailed characterization of the conformational preferences of dipeptides is therefore of fundamental importance for understanding protein structure and folding. Here, we studied the conformational preferences of 13 dipeptides using infrared and Raman spectroscopy. The main advantage of vibrational spectroscopy over NMR spectroscopy is in its much shorter time scale, which enables the determination of the conformational preferences of short-lived states. Accuracy of structure determination using vibrational spectroscopy depends critically on identification of the vibrational parameters that are sensitive to changes in conformation. We show that the frequencies of the amide I band and the A12 ratio of the amide I components of dipeptides correlate with the (3)J(H(N), H(alpha)). These two infrared vibrational parameters are thus analogous to (3)J(H(N), H(alpha)), indicators for the preference for the dihedral angle phi. We also show that the intensities of the components of the amide III bands in infrared spectra and the intensities of the skeletal vibrations in Raman spectra are indicators of populations of the P(II), beta, and alpha(R) conformations. The results show that alanine dipeptide adopts predominantly a PII conformation. The population of the beta conformation increases in valine dipeptides. The populations of the alpha(R) conformation are generally small. These data are in accord with the electrostatic screening model of conformational preferences.     

Time-Resolved Studies of the Excited-State Dynamics of meso-Tetra(hydroxylphenyl)chlorin in Solution

Meso-tetra(hydroxyphenyl)chlorin (m-THPC) is a new photosensitizer developed for potential use in photodynamic therapy (PDT) for cancer treatment. In PDT, the accepted mechanism of tumor destruction involves the formation of excited singlet oxygen via intermolecular energy transfer from the excited triplet-state dye to the ground triplet-state oxygen. Femtosecond transient absorption measurements are reported here for the excited singlet state dynamics of m-THPC in solution. The observed early time kinetics were best fit using a triple exponential function with time constants of 350 fs, 80 ps and > or = 3.3 ns. The fastest decay (350 fs) was attributed to either internal conversion from S2 to S1 or vibrational relaxation in S2. Multichannel time-resolved absorption and emission spectroscopies were also used to characterize the excited singlet and triplet states of the dye on nanosecond to microsecond time scales at varying concentrations of oxygen. The nanosecond time-resolved absorption data were fit with a double exponential with time constants of 14 ns and 250 ns in ambient air, corresponding to lifetimes of the S1 and T1 states, respectively. The decay of the T1 state varied linearly with oxygen concentration, from which the intrinsic decay rate constant, ki, of 1.5 x 10(6) s-1 and the biomolecular collisional quenching constant, kc, of 1.7 x 10(9) M-1 s-1 were determined. The lifetime of the S1 state of 10 ns was confirmed by fluorescence measurements. It was found to be independent of oxygen concentration and longer than lifetimes of other photosensitizers.     

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.     

Ultrafast intersystem crossing in 9,10-anthraquinones and intramolecular charge separation in an anthraquinone-based dyad

Femtosecond transient absorption spectroscopy was employed to determine quantitatively the ultrafast S1-T1 intersystem crossing in a 2-substituted 9,10-anthraquinone derivative (3), kisc = 2.5 x 10(12) s-1. Notwithstanding this rapid process, photoexcitation of dyad 1 is followed by competition between intersystem crossing and intramolecular charge separation, the latter leading to a short-lived (2 ps) singlet charge-transfer (CT) state. The local triplet state itself undergoes slower charge separation to populate a relatively long-lived (130 ns) triplet CT state. An earlier report about the formation of an extremely long-lived CT state (> 900 micros) in 1 was found to be erroneous and was related to the sacrificial photo-oxidation of the dimethylsulfoxide solvent used in that study. Finally, some important criteria have been formulated for future experimental validation of "unusually long-lived" CT states.     

Negatively charged pi-(C60-)2 dimer with biradical state at room temperature

A negatively charged pi-(C60-)2 dimer bonded by two single bonds was found in the ionic multicomponent complex {(MDABCO+).CoIITMPP}2.(C60-)2.(C6H4Cl2)2.5.(C6H5CN)1.5 (1). In contrast to the previously described diamagnetic sigma-(C60-)2 dimer, the negatively charged pi-dimer has a biradical state at room temperature: (C60*-)2 (S = 1). The behavior of spins in this dimer can be described by a model with a singlet ground state (S = 0) and a close lying excited triplet (S = 1) state with the energy gap of 2|JAF| = 70 +/- 2 cm-1. On the whole, complex 1 shows a strong antiferromagnetic interaction of spins with a Weiss constant of -34 K.     

Volume-based thermodynamics: estimations for 2:2 salts

The lattice energy of an ionic crystal, U(POT), can be expressed as a linear function of the inverse cube root of its formula unit volume (i.e., Vm(-1/3)); thus, U(POT) approximately 2I(alpha/Vm(1/3) + beta), where alpha and beta are fitted constants and I is the readily calculated ionic strength factor of the lattice. The standard entropy, S, is a linear function of Vm itself: S approximately kVm + c, with fitted constants k and c. The constants alpha and beta have previously been evaluated for salts with charge ratios of 1:1, 1:2, and 2:1 and for the general case q:p, while values of k and c applicable to ionic solids generally have earlier been reported. In this paper, we obtain alpha and beta, k and c, specifically for 2:2 salts (by studying the ionic oxides, sulfates, and carbonates), finding that U(POT)[MX 2:2]/(kJ mol(-1)) approximately 8(119/Vm(1/3) + 60) and S degree [MX 2:2]/(J K(-1) mol(-1)) approximately 1382V(m) + 16.     

Quantum chemistry studies of electronically excited nitrobenzene, TNA, and TNT

The electronic excitation energies and excited-state potential energy surfaces of nitrobenzene, 2,4,6-trinitroaniline (TNA), and 2,4,6-trinitrotoluene (TNT) are calculated using time-dependent density functional theory and multiconfigurational ab initio methods. We describe the geometrical and energetic character of excited-state minima, reaction coordinates, and nonadiabatic regions in these systems. In addition, the potential energy surfaces for the lowest two singlet (S(0) and S(1)) and lowest two triplet (T(1) and T(2)) electronic states are investigated, with particular emphasis on the S(1) relaxation pathway and the nonadiabatic region leading to radiationless decay of S(1) population. In nitrobenzene, relaxation on S(1) occurs by out-of-plane rotation and pyramidalization of the nitro group. Radiationless decay can take place through a nonadiabatic region, which, at the TD-DFT level, is characterized by near-degeneracy of three electronic states, namely, S(1), S(0), and T(2). Moreover, spin-orbit coupling constants for the S(0)/T(2) and S(1)/T(2) electronic state pairs were calculated to be as high as 60 cm(-1) in this region. Our results suggest that the S(1) population should quench primarily to the T(2) state. This finding is in support of recent experimental results and sheds light on the photochemistry of heavier nitroarenes. In TNT and TNA, the dominant pathway for relaxation on S(1) is through geometric distortions, similar to that found for nitrobenzene, of a single ortho-substituted NO(2). The two singlet and lowest two triplet electronic states are qualitatively similar to those of nitrobenzene along a minimal S(1) energy pathway.     

Measurement of NMR cross-polarization (CP) rate constants in the slow CP regime: relevance to structure determinations of zeolite-sorbate and other complexes by cp magic-angle spinning NMR

When analyzing I --> S variable contact time cross-polarization (CP) curves, the spin dynamics are usually assumed to be describable in the "fast CP regime" in which the growth of the S spin magnetization is governed by the rate of cross polarization while its decay is governed by the rate of I spin T1rho relaxation. However, in the investigation of the structures of zeolite-sorbate and other complexes by polarization transfer this will not necessarily be the case. We discuss the measurement of I --> S CP rate constants under the "slow CP regime" in which the rate of T1rho relaxation is fast compared to the rate of cross polarization, leading to a reversal of the usual assumptions such that the rate or growth is governed by the rate of I spin T1rho relaxation while the decay is governed by the rate of cross polarization (and the S spin T1rho relaxation). It is very important to recognize when a system is in the slow CP regime, as an analysis assuming the normal fast CP will lead to erroneous data. However, even when the slow CP regime is recognized, it is difficult to obtain absolute values for the CP rate constants from fits to standard CP curves, since the CP rate constant is correlated to the scaling factor, the contribution from 29Si T1rho relaxation is ignored, and it is difficult to obtain reliable data at very long contact times. The use of a 29Si{1H} CP "drain" or "depolarization" experiment, which measures absolute values of the CP rate constants, is therefore proposed as being most appropriate for theses situations. To illustrate the importance of these observations, measurements of the 1H-29Si CP rate constants in the p-dichlorobenzene/ZSM-5 sorbate-zeolite complex by 29Si{1H} CP and CP drain magic-angle spinning (MAS) NMR experiments are presented and compared and used to determine the location of the guest sorbate molecules in the cavities of the host zeolite framework.     

Long-lived 1H singlet spin states originating from para-hydrogen in Cs-symmetric molecules stored for minutes in high magnetic fields

Nuclear magnetic resonance (NMR) is a very powerful tool in physics, chemistry, and life sciences, although limited by low sensitivity. This problem can be overcome by hyperpolarization techniques dramatically enhancing the NMR signal. However, this approach is restricted to relatively short time scales depending on the nuclear spin-lattice relaxation time T(1) in the range of seconds. This makes long-lived singlet states very useful as a way to extend the hyperpolarization lifetimes. Para-hydrogen induced polarization (PHIP) is particularly suitable, because para-H(2) possesses singlet symmetry. Most PHIP experiments, however, are performed on asymmetric molecules, and the initial singlet state is directly converted to a NMR observable triplet state decaying with T(1), in the order of seconds. We demonstrate that in symmetric molecules, a long-lived singlet state created by PHIP can be stored for several minutes on protons in high magnetic fields. Subsequently, it is converted into observable high nonthermal magnetization by controlled singlet-triplet conversion via level anticrossing.     

Dynamics of radiationless transitions: effects of displacement-distortion-rotation of potential energy surfaces on internal conversion decay rate constants

General expressions for calculating the internal conversion decay rate constants between two adiabatic electronic states and between two diabatic electronic states are derived. The expressions include the displacements, distortions, and rotations of potential energy surfaces as well as the temperature. For illustration, internal conversion rate constants between various singlet electronic states of ethylene and between the first excited S1 and the ground S0 singlet electronic states of azulene are calculated.     

The spin-unrestricted molecular Kohn-Sham solution and the analogue of Koopmans's theorem for open-shell molecules

Spin-unrestricted Kohn-Sham (KS) solutions are constructed from accurate ab initio spin densities for the prototype doublet molecules NO(2), ClO(2), and NF(2) with the iterative local updating procedure of van Leeuwen and Baerends (LB). A qualitative justification of the LB procedure is given with a "strong" form of the Hohenberg-Kohn theorem. The calculated energies epsilon(isigma) of the occupied KS spin orbitals provide numerical support to the analogue of Koopmans' theorem in spin-density functional theory. In particular, the energies -epsilon(ibeta) of the minor spin (beta) valence orbitals of the considered doublet molecules correspond fairly well to the experimental vertical ionization potentials (VIPs) I(i) (1) to the triplet cationic states. The energy -epsilon(Halpha) of the highest occupied (spin-unpaired) alpha orbital is equal to the first VIP I(H) (0) to the singlet cationic state. In turn, the energies -epsilon(ialpha) of the major spin (alpha) valence orbitals of the closed subshells correspond to a fifty-fifty average of the experimental VIPs I(i) (1) and I(i) (0) to the triplet and singlet states. For the Li atom we find that the exact spin densities are represented by a spin-polarized Kohn-Sham system which is not in its ground state, i.e., the orbital energy of the lowest unoccupied beta spin orbital is lower than that of the highest occupied alpha spin orbital ("a hole below the Fermi level"). The addition of a magnetic field in the -z direction will shift the beta levels up so as to restore the Aufbau principle. This is an example of the nonuniqueness of the mapping of the spin density on the KS spin-dependent potentials discussed recently in the literature. The KS potentials may no longer go to zero at infinity, and it is in general the differences nu(ssigma)( infinity )-epsilon(isigma) that can be interpreted as (averages of) ionization energies. In total, the present results suggest the spin-unrestricted KS theory as a natural one-electron independent-particle model for interpretation and assignment of the experimental photoelectron spectra of open-shell molecules.     

Relaxation-allowed nuclear magnetic resonance transitions by interference between the quadrupolar coupling and the paramagnetic interaction

Of the various ways in which nuclear spin systems can relax to their ground states, the processes involving an interference between different relaxation mechanisms, such as dipole-dipole coupling and chemical shift anisotropy, have become of great interest lately. The authors show here that the interference between the quadrupolar coupling and the paramagnetic interaction (cross-correlated relaxation) gives rise to nuclear spin transitions that would remain forbidden otherwise. In addition, frequency shifts arise. These would be reminiscent of residual anisotropic interactions when there are none. While interesting from a fundamental point of view, these processes may become relevant in magnetic resonance imaging experiments which involve quadrupolar spins, such as (23)Na, in the presence of contrast agents. Geometrical constraints in paramagnetic molecule structures may likewise be derived from these interference effects.