Research

• Theoretical techniques
• Photoisomerization in Proteins
• Phase Separation in Hydrocarbon-Alcohol-Water Systems at the Molecular Level

The goal of our research is to understand the fundamental laws that control chemistry in the condensed phase, using quantum chemistry tools. The environment can affect chemical processes in different ways. For example, a solvent may completely change the character of the electronic states of a solute and create new, so called charge transfer-to-solvent states (CTTS). This occurs, for example, when iodide anion is solvated in water. On the other hand, the protein environment does not create new electronic states in the retinal chromophore in visual rhodopsin, but modifies the potential energy surfaces (PESs) of the chromophore states and the coupling between them. In addition, coupling between a solute and an environment can also vary significantly. Whereas the electronic states of organic chromophores in non-polar solvents are essentially completely localized within the solute, the wave function of the electron solvated in water is more delocalized. Thus, it is often unclear if we can think about molecular electronic states as just being perturbed by the solvent, or if we need to completely depart from the gas phase picture even for a qualitative understanding. Additional complexity arises when dynamics comes into play, since solvent relaxation may occur in different time scales and by different pathways, often resulting in controversial spectroscopic signatures. While these are fundamental phenomena, their understanding can lead to practical ways of controlling chemistry in the condensed phase.

Figure 1. In the QM/MM approach, the system is separated into quantum (QM) and molecular mechanics (MM) parts.

Theoretical modeling of a chemical process in solution or on a surface is challenging due to the dramatic increase in the number of degrees of freedom of the combined system, exacerbated by the complexity and diversity of the underlying mechanisms and pathways. This makes computer simulations very demanding. The availability of a robust and predictive theoretical model that gives a clearer and more complete understanding of condensed-phase chemistry is very important. For example, the photoisomerization of rhodopsin has been reinvestigated many times as new theoretical tools have appeared, and every reinvestigation revealed new aspects of this mechanism. Therefore, our research focuses on developing and applying robust computational tools that will facilitate accurate and revealing investigations of chemical and biological processes in an environment.

Theoretical Techniques

Calculations in the condensed phase still remain a major challenge to the theoretical community. The increased number of nuclear and electronic degrees of freedom makes accurate ab initio calculations on a condensed phase system unfeasible long before the system can approach the bulk. One general approach to this type of problem is to separate a system into two parts, such that one (active) part is treated by quantum mechanical (QM) techniques, and the other, usually larger, part is calculated by using classical (molecular) mechanics (MM) (see Figure. 1). The Hamiltonian of the system then consists of three terms:

where H_QM/MM is a coupling term. Separation of the QM and MM subsystems, in principle, allows one to use any level of theory in both the QM and MM parts. For studying chemical reactions and the electronic excited states, the QM part should be described by the technique capable of describing electronci excitations and degeneracies. Thus, the method of choice for the QM region is the equation-of-motion coupled-cluster (EOM-CC) technique. EOM-CC is a single-reference black-box method for the excited states, which in a balanced fashion describes both dynamical and non-dynamical correlation. Several variants of EOM-CC, for example, Spin-Flip (SF) variant, can accurately target electronic degeneracies and multi-configurational electronic states.

Traditionally, the MM part in QM/MM is included through parameterized force fields. A drawback of such an approach is the dependence on fitted parameters for a chosen force field, such that different parameterizations may be optimal for different problems and the best parameters are often not well defined. There is also a concern regarding the absence of dispersion (and often polarization) coupling in the QM/MM term, although these issues have not been well studied. In order to overcome these drawbacks, we employ the effective fragment potential (EFP) method for the MM part. In the EFP, each solvent molecule is represented by an EFP with a set of parameters determined from a preparatory ab initio calculation. The uniqueness of the EFP method is that all EFP force field parameters are derived from first principles, i.e., the method is free of parameter fitting. Main features of the EFP method are summarized in Figure. 2. Through its force field, the EFP fragments can interact with each other and with ab initio components. The accuracy of an EFP depends on the analytic description of each energy term (electrostatic, polarization, dispersion, exchange-repulsion, and charge-transfer), and, to a lesser extent, on the quality of the ab initio calculation used to determine the EFP parameters. It has been recently shown that EFP reproduces structures and binding energies in hydrogen- and p-bonded systems with an accuracy similar or in some cases even better, than that of second order Moller-Plesset perturbation theory, MP2. Similar to other force-field methods, EFP fragments can be used in molecular dynamics and Monte Carlo simulations.

Using the EFP method results in an accurate and first-principles-based description of the MM part and in theoretically derived coupling between the QM and MM subsystems, i.e., with inclusion not only of electrostatic and polarization interactions, but also short-range and dispersion interaction terms.

Figure 2. Overview of the interaction terms present in the effective fragment potential (EFP) method.

One general approach to this type of problem is to separate a system into two parts, such that one (active) part is treated by quantum mechanical (QM) techniques, and the other, usually larger, part is calculated by using classical (molecular) mechanics (MM) (see Fig. 1). The Hamiltonian of the system then consists of three terms:

Photoisomerization in Proteins

Figure 3. Isomerization mechanisms in polyenes: one-bond-flip, bicycle-pedal, and Hula-twist. Different solvent environments favor different mechanisms of isomerization; however, understanding of these processes is still not complete.

Photoisomerization in organic compounds with a C=C double bond is a fundamental photochemical process. For example, photoisomerization in model polyenes, such as stilbenes, has been a topic of hot debate and controversy for more than seven decades. This is not surprising, since the mechanisms of photoinduced twisting around the C=C double bond are relevant to many photobiological phenomena, such as light-induced isomerization in visual rhodopsins, photoactive yellow protein, and green fluorescent proteins. However, despite numerous experimental and theoretical studies, the picture of the isomerization pathways of organic polyenes is not yet complete. For example, there is a competition among the one-bond-flip, bicycle-pedal, and Hila-twist isomerization mechanisms (see Fig. 3). However, it is unclear how this competition is affected by many external and internal factors, such as substitutions, sensitizers, temperature, viscosity and the character of solvent.

Photoisomerization mechanisms and pathways in photoactive yellow protein (PYP), bacterial photoreceptor, are schematically shown in Figure 4. Absorbing blue light, p-coumaric acid, the PYP chromophore, isomerizes, which initiates a cascade of events resulting in mechanical motion of bacteria. The initial event of the PYP photocycle, photoisomerization of p-coumaric acid, can be investigated with the QM/MM approach. The PYP protein (except the chromophore) is represented by a set of EFPs, and the p-coumaric acid is treated at the EOM-CC level. EOM-CC is an appealing method for studying excited states in the PYP chromophore, since it can in a balanced fashion describe both dynamical and non-dynamical correlation that are crucial for p-conjugated systems. Moreover, since EOM-CC can describe several excited states simultaneously, it is possible to study coupling between excited PESs, which is believed to dramatically affect the isomerization pathways in polyenes. Along the isomerization pathway, the C=C double bond in the PYP chromophore is broken; the molecule becomes a diradical and exhibits strong multi-configurational character, as shown schematically in Fig. 4. Several types of EOM-CC are able to treat these types of electronic degeneracies in a balanced way. For example, Spin-Flip (SF) EOM-CCSD accurately describes twisting around the double bond in ethylene.

Figure 4. Photocycle in PYP. Left: the key events in photocycle; right: the trigger of the photocycle – photoisomerization in the p-chromophore of PYP. Several electronic states of the chromophore are involved in the photoisomerization. The character of the chromophore wave function dramatically changes along the isomerization coordinate. Additional complexity may arise due to constraints imposed by the protein environment. The image of protein was adopted from www.scripps.edu/~ulrich/picture_gallery.html (created by Ulrich Genick based on coordinates reported in Borgstahl, G.E.O et al. Biochemistry 34, pp. 6278 - 6287)

Previous studies suggest that the protein environment changes the PESs of the electronic states of the PYP chromophore but does not create new states For example, barriers to rotation around the double bond are lower in the protein than in vacuum. However, it is unclear if the excited state PESs are affected mainly by the field of the protein or by a cavity effect. Another important problem to study is why the time-scale of the isomerization dynamics of the chromophore in vacuum is similar to that of the chromophore in protein, even though the isomerization in protein is constraint and involves twisting around several bonds.

Phase Separation in Hydrocarbon-Alcohol-Water Systems at the Molecular Level

Figure 5. Sample of fuel in which phase separation has occured. The upper phase is gasoline with a reduced level of ethanol. The lower phase is a mixture of ethanol and water. Water tolerance is temperature dependent and not linear with ethanol content, such that the commingling of gasolines of different ethanol content can result in unfavorable phase separation.

Broader use of bio-alcohols, i.e., alcohols produced from biomass rather than petroleum sources, as an addition or supplement to automotive fuels could result in energy security and lower emissions of green-house gases. Apart from the high production cost, a stumbling block for achieving the extensive use of alcohols is liquid-liquid phase separation in hydrocarbon-alcohol mixtures that becomes even more exacerbated by the presence of water (see Fig. 1). Understanding of the mechanisms and origins of phase-separation requires in-depth knowledge of the nature of intermolecular interactions in liquids. Unfortunately, accurate and reliable theoretical modeling of complex liquids imposes high computational costs because the prediction of macroscopic liquid properties, such as phase separation or heat of vaporization, requires nanosecond-long simulations, with hundreds or thousands of molecules. As a result, little is known about the molecular-level structure of alcohol-water-hydrocarbon systems, and even in binary water-alcohol, the extent of mixing is still under debate. Thus, creating a robust, predictive, and computationally-affordable theoretical model that can describe condensed phase processes will provide a major advance in the clearer understanding of fundamental interactions in liquids and solids. The objective of this project is to investigate mixtures of alcohols (methanol, ethanol, propanol, butanol) with hydrocarbons (alkanes and aromatic molecules) and water at the molecular level. Our goal is to identify (1) patterns of alcohol aggregation in water and hydrocarbons, (2) relations between microheterogeneity of water-alcohol-hydrocarbon mixtures and macroscopic phase separation, and (3) effects of water on phase-separation in these systems. To examine the structural characteristics (radial distribution functions and cross-correlation functions) of hydrocarbon-alcohol-water mixtures, we perform Monte Carlo (MC) and molecular dynamics (MD) simulations with the effective fragment potential method.