Effects of molecular size in solvation dynamics

The effects of molecular size on the dynamics of polar solvation are studied by using a microscopic theory which includes the translational relaxation modes of the solvent consistently. It is shown that while in the absence of the translational contribution the solvation rate increases with the size of the solute (in agreement with the conclusions of the nonequilibrium MSA theory),a complete reversal of the solute size dependence occurs when translational modes make a significant contribution to the solvent polarization relaxation.

Dielectric friction and solvation dynamics: Novel results on relaxation in dipolar liquids

In this article we present a new, general but simple, microscopic expression for time-dependent solvation energy of an ion. This expression is surprisingly similar to the expression for the time-dependent dielectric friction on a moving ion. We show that both the Chandra-Bagchi and the Fried-Mukamel formulations of solvation dynamics can be easily derived from this expression. This expression leads to an almost perfect agreement of the theory with all the available computer simulation results. Second, we show here for the first time that the mobility of a light solute ion can significantly accelerate its own solvation, specially in the underdamped limit. The latter result is also in excellent agreement with the computer simulations.

Microscopic theory of solvation of an ion in a binary dipolar liquid

A microscopic theory of the statics and the dynamics of solvation of an ion in a binary dipolar liquid is presented. The theory properly includes the different intermolecular correlations that are present in a binary mixture. As a result, the theory can explain several important aspects of both the statics and the dynamics of solvation that are observed in experiments. It provides a microscopic explanation of the preferential solvation of the more polar species by the solute ion. The dynamics of solvation is predicted to be highly non-exponential, in general. The average relaxation time is found to change nonlinearly with the composition of the mixture. These predictions are in qualitative agreement with the experimental results.

Molecular theory of ion solvation dynamics in water, acetonitrile and methanol: A unified microscopic description of collective dynamics in dipolar liquids

A recently developed microscopic theory of solvation dynamics in real dipolar liquids is used to calculate, for the first time, the solvation time correlation function in liquid acetonitrile, water and methanol. The calculated results are in excellent agreement with known experimental and computer simulation studies.

Solvation and axial ligation properties of (2,3,7,8,12,13,17,18-octabromo-5,10,15,20-tetraphenylporphyrinato)zinc(II)

he solvation of (2,3,7,8,12,13,17,18-octabromo-5,10,15,20-tetraphenylporphyrinato)zinc(II)[Zn(obtpp)], in twelve different solvents results in large red shifts of the B and Q bands of the porphyrin accompanied by enhanced absorbance ratios of the Q bands. These observations are ascribed to the destabilisation of the highest occupied molecular orbital a2u of the porphyrin arising from a flow of charge from the axial ligand to the porphyrin ring through the zinc(II) ion. The binding constants of adducts of [Zn(obtpp)] with neutral bases have been found to be an order of magnitude greater than those observed for the corresponding adducts of (5,10,15,20-tetraphenylporphyrinato)-zinc and vary in the order piperidine > imidazole > pyridine > 3-methylpyridine > pyridine-3-carbaldehyde. The enhanced binding constants and large spectral shifts are interpreted in terms of the electrophilicity of [Zn(obtpp)] induced by the electron-withdrawing bromine substituents in the porphyrin core. The structure of [Zn(obtpp)(PrCN)2] has been determined; it reveals six-co-ordinated zinc(II) with two long Zn–N distance [2.51(4), 2.59(3)Å]. The porphyrin is non-planar and displays a saddle-shaped conformation.

Solvation dynamics in a Brownian dipolar lattice. Comparison between computer simulation and various molecular theories of solvation dynamics

Several recent theoretical and computer simulation studies have considered solvation dynamics in a Brownian dipolar lattice which provides a simple model solvent for which detailed calculations can be carried out. In this article a fully microscopic calculation of the solvation dynamics of an ion in a Brownian dipolar lattice is presented. The calculation is based on the non‐Markovian molecular hydrodynamic theory developed recently. The main assumption of the present calculation is that the two‐particle orientational correlation functions of the solid can be replaced by those of the liquid state. It is shown that such a calculation provides an excellent agreement with the computer simulation results. More importantly, the present calculations clearly demonstrate that the frequency‐dependent dielectric friction plays an important role in the long time decay of the solvation time correlation function. We also find that the present calculation provides somewhat better agreement than either the dynamic mean spherical approximation (DMSA) or the Fried–Mukamel theory which use the simulated frequency‐dependent dielectric function. It is found that the dissipative kernels used in the molecular hydrodynamic approach and in the Fried–Mukamel theory are vastly different, especially at short times. However, in spite of this disagreement, the two theories still lead to comparable results in good agreement with computer simulation, which suggests that even a semiquantitatively accurate dissipative kernel may be sufficient to obtain a reliable solvation time correlation function. A new wave vector and frequency‐dependent dissipative kernel (or memory function) is proposed which correctly goes over to the appropriate expressions in both the single particle and the collective limits. This form is expected to lead to better results than all the existing descriptions.

Solvation dynamics in liquid water. A novel interplay between librational and diffusive modes

A microscopic calculation of the solvation dynamics of an ion in liquid water is presented. The calculated solvation time correlation function shows an ultrafast Gaussian decay which carries about 70%–90% of the strength followed by a biexponential decay with time constants equal to 250 fs and 1 ps. These results are in excellent agreement with the computer simulations of Maroncelli and Fleming and also with the experimental findings of Barbara and Jarzeba. In addition, we find that both the rotational librations and the intermolecular translational vibrational modes of water contribute significantly to the initial Gaussian decay.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.

Ionic and dipolar solvation dynamics in liquid water

The solvation time correlation function for solvation in liquid water was measured recently. The solvation was found to be very fast, with a time constant equal to 55 fs. In this article we present theoretical studies on solvation dynamics of ionic and dipolar solutes in liquid water, based on the molecular hydrodynamic approach developed earlier. The molecular hydrodynamic theory can successfully predict the ultrafast dynamics of solvation in liquid water as observed from recent experiments. The present study also reveals some interesting aspects of dipolar solvation dynamics, which differs significantly from that of ionic solvation.

Solvation dynamics, energy distribution and trapping of a light solute ion

In the theoretical treatments of the dynamics of solvation of a newly created ion in a dipolar solvent, the self-motion of the solute is usually ignored. Recently, it has been shown that for a light ion the translational motion of the ion can significantly enhance its own rate of solvation. Therefore, solvation itself may not be the rate determining step in the equilibration. Instead, the rate determining step is the search of the low energy configuration which serves to localize the light ion. In this article a microscopic calculation of the probability distribution of the interaction energy of the nascent charge with the dipolar solvent molecules is presented in order to address this problem of solute trapping. It is found that to a good approximation, this distribution is Gaussian and the second moment of this distribution is exactly equal to the half of its own solvation energy. It is shown that this is in excellent agreement with the simulation results that are available for the model Brownian dipolar lattice and for liquid acetonitrile. If the distortion of the solvent by the ion is negligible then the same relation gives the energy distribution for the solvated ion, with the average centered at the final equilibrium solvation energy. These results are expected to be useful in understanding various chemical processes in dipolar liquids. Another interesting outcome of the present study is a simple dynamic argument that supports Onsager's ''inverse snow-ball'' conjecture of solvation of a light ion. A simple derivation of the semi-phenomenological relation between the solvation time correlation function and the single particle orientation, reported recently by Maroncelli et al. (J. Phys. Chem. 97 (1993) 13), is also presented.

Self-consistent microscopic treatment of the effects of self-motion of the probe on ionic and dipolar solvation dynamics

A simple but self-consistent microscopic theory for the time dependent solvation energy of both ions and dipoles is presented which includes, for the first time, the details of the self-motion of the probe on its own solvation dynamics. The theory leads to several interesting predictions. The most important of them is that, for dipolar solvation, both the rotational and the translational motions of the dipolar solute probe can significantly accelerate the rate of solvation. In addition, the rotational self-motion of the solute can also give rise to an additional mechanism of nonexponentiality in solvation time correlation functions in otherwise slow liquids. A comparison between the present theoretical predictions and the recent experimental studies of Maroncelli et al. on solvation dynamics of aniline in l-propanol seems to indicate that the said experiments have missed the initial solvent response up to about 45 ps. After mapping the experimental results on the redefined time scale, the theoretical results can explain the experimental results for solvation of aniline in 1-propanol very well. For ionic solvation, the translational motion is significant for light solutes only. For example, for Li+ in water, translational motion speeds up the solvation by about 20%. The present theory demonstrates that in dipolar solvation the partial quenching of the self-motion due to the presence of specific solute-solvent interactions (such as H-bonding) may lead to a much slower solvation than that when the self-motion is present. This point has been discussed. In addition, we present the theoretical results for solvation of aniline in propylene carbonate, Here, the solvation is predicted to be complete within 15-20 ps.

Solvation dynamics in slow, viscous liquids: Application to amides

As the viscosity of a liquid increases rapidly in the supercooled regime, the nature of molecular relaxation can exhibit dynamics rather different from the fast dynamics observed in the normal regime. In this article, we present theoretical studies of solvation dynamics and orientational relaxation in slow liquids. As the local short-range correlations are important in the slow liquids, we have extended our previous theory to take into account the shea-range pair correlations between the polar solute and the dipolar solvent molecules. Application of the generalized theory To the study of solvation dynamics of amide systems gives nice agreement with the experimental results of Maroncelli and co-workers (J. Phys. Chem. 1990, 94, 4929). The theory also provides valuable insight into the orientational relaxation precesses in the viscous liquids.

Ultrafast solvation dynamics in water: Isotope effects and comparison with experimental results

A detailed theoretical study of solvation dynamics in water is presented. The motivation of the present study comes from the recent experimental observation that the dynamics of solvation of an ion in water is ultrafast and the solvation time correlation function decays with a time constant of about 55 fs. The slower decay in the long time can be described by a sum of two exponentials with time constants equal to 126 and 880 fs. The molecular theory (developed earlier) predicts a time constant equal to 52 fs for the initial Gaussian decay and time constants equal to 134 and 886 fs for the two exponential components at the long time. This nearly perfect agreement is obtained by using the most detailed dynamical information available in the literature. The present study emphasizes the importance of the intermolecular vibrational band originating from the O...O stretching mode of the O�H...O units in the initial dynamics and raises several interesting questions regarding the nature of the decay of this mode. We have also studied the effects of isotope substitution on solvation dynamics. It is predicted that a significant isotope effect may be observed in the long time. The experimental results have also been compared with the prediction of the dynamic mean spherical approximation (DMSA); the agreement is not satisfactory at the long time. It is further found that the molecular theory and the DMSA lead to virtually identical results if the translational modes of the solvent molecules are neglected in the former. DMSA has also been used to investigate the dynamics of solvation of a dipolar solute in water. It is found that the dynamics of dipolar solvation exhibit features rather different from those of ion solvation. © 1995 American Institute of Physics.