2. Molecules in different environments: Solvatochromic ...fig.if.usp.br/~kaline/Publicados_PDF/2009-Boudreaux-2-2-Final.pdf · those days ab initio quantum chemistry has seen an unprecedented

Transworld Research Network 37/661 (2), Fort P.O. Trivandrum-695 023 Kerala, India

Approximate Molecular Orbital Methods, 2010: 63-84 ISBN: 978-81-7895-466-0 Editor: Edward A. Boudreaux

2. Molecules in different environments: Solvatochromic effects using Monte Carlo

simulation and semi-empirical quantum mechanical calculations

Kaline Coutinho1, Tertius L. Fonseca2 and Sylvio Canuto1

1Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP Brazil 2Instituto de Física, Universidade Federal de Goiás, CP 131, 74001-970, Goiânia, GO, Brazil

Abstract. The sequential QM/MM methodology is used to describe the solvent effects on the electronic absorption spectra of organic molecules in solution. The structure of the liquid is generated by Monte Carlo computer simulation. Configurations composed by the solute and several solvent molecules are selected for a posteriori quantum mechanical calculations of the spectra. Situations are considered where a large number of solvent molecules are necessary to describe the solvation problem. The examples considered here involve super-molecular systems composed of ca. 1500-2000 valence electrons, justifying the need for a semi-empirical approach. The electronic spectrum is then calculated using the INDO/CIS method. The solvatochromic shifts of pyrimidine in water and of beta-carotene in acetone and isopentane are considered. These exemplify the situations of a polar molecule

Correspondence/Reprint request: Dr. Sylvio Canuto, Instituto de Física, Universidade de São Paulo, CP 66318 05315-970, São Paulo, SP Brazil. E-mail: [email protected]

Kaline Coutinho et al. 64

in a polar environment and of a non-polar molecule in both polar and non-polar environments. An additional example is considered where the absorption spectrum of acetone is analysed in a low-dense condition of a supercritical water environment. Good agreements with experimental shifts are obtained in all cases. The relative importance of the inner and outer solvation shells is analyzed. The case of beta-carotene is a persistent and difficult problem because the spectrum involves a π-π*excitation between two states of zero dipole moment. For the case of acetone in supercritical water analysis is made of the decrease in the solute-solvent hydrogen bonds and their role on the calculated solvatochromic shift. This solvatochromism is considered both in relation to the gas phase (blue shift) and the normal liquid water spectra (red shift). The success of the present approach emphasizes the importance of the combined use of quantum mechanics and statistical mechanics and the usefulness of the semi-empirical method employed. 1. Introduction Semi-empirical methods have been an important ally in the theoretical studies of ultra-violet-visible (UV-Vis) spectra [1]. Already in the early days of quantum chemistry, the very simple Hückel model [2] gave the first qualitative explanation of the complex UV-Vis absorption spectrum of the benzene molecule. Hückel model gives the correct picture: the nature of the π-π* transitions, the degeneracy of the molecular orbitals, the degeneracy of the intense and allowed 1E1u band and the origin of the three absorption transitions that are the characteristic signature of the benzene molecule. Since those days ab initio quantum chemistry has seen an unprecedented development [3]. But because of the enormous computational difficulties of ab initio methods to handle large molecular systems the semi-empirical techniques have been very important in elucidating many aspects and, in particular, absorption spectra. In spite of the extraordinary computer revolution semi-empirical methods are of great value and will certainly continue to be as the limit of interest is systematically moving forward. With the continuous developments of both computer hardware and software large molecular systems can be considered but then the interest is also slowly shifting towards larger systems, including bio-molecules, and semi-empirical methods thus remain of interest. The quantum chemistry horizon indicates that the interest in bio-molecular systems will be considerably increased in the coming years. But in addition to the increasing size of the molecular systems of interest one is also interested in situations where a molecule is not isolated from the environment. Including additional molecules similarly increases the complexity of the system and the necessity for a simple

Molecules in different environments 65

computational approach. This chapter deals with the application of semi-empirical methods, not to analyze a single large molecule but instead to analyze the UV-Vis absorption spectra of organic molecules in an explicit solvent environment. We are particularly focusing in the situations were the solvent effects on the solute molecule require consideration of the explicit solvent molecules. This is a situation where, even if the reference molecule is of a small size, amenable to ab initio procedures, the necessity of explicitly including the solvent molecules imposes severe limitations. First-principle calculations cannot be performed, at present, for a system surrounded by ca. 100 solvent molecules. Although there are indeed situations where the solvent effects are local, such as chemical shift in NMR shielding, for instance, there are also circumstances where solvent molecules, located far from the solute, can still affect the solute properties. This is the situation we report here. The solvatochromic shift of a polar molecule is one of the possible examples. Polar molecules in polar environment lead to an electronic polarization that extends over a large distance. But even the properties of non-polar molecules are influenced by explicit solvent molecules. This seems to be the case of the red shift of the absorption spectra of beta-carotene in different solvents. But using explicitly one beta-carotene molecule surrounded by the first solvation shell of acetone molecules leads to a problem involving more than 2000 valence electrons. This is a situation where semi-empirical methods can be of great value. The theoretical procedures to study solvent effects may be classified in two major categories. The first one is the so-called continuum dielectric methods. This is based in the ideas of Kirkwood [4] and Onsager [5] that has been developed into the self-consistent reaction field (SCRF) [6-10]. Further developments have been obtained leading to the conductor-like screening model (COSMO)[11] and the polarizable continuum method (PCM) [12] and some variants [13]. The second major category is composed by the combination of quantum mechanics and statistical mechanics leading to the QM/MM methods [14-17]. The use of molecular mechanics (MM) combined with quantum mechanics (QM) is an increasing and powerful technique to deal with the effects of the environment (generally treated by MM) into a reference molecule (treated by QM). However the partition between the QM and MM parts may not be so clear and may depend on the property of interest. This aspect led to the idea of carrying the QM/MM not at the same time but in two separate steps. In this sequential QM/MM (S-QM/MM) methodology [18-20] one first performs the molecular simulation to generate the solute-solvent configurations. Statistically uncorrelated configurations are then sampled for subsequent QM calculations. This is an efficient procedure that properly used ensures statistically converged results with a relatively


small number of QM calculations [18-26]. This procedure gives the additional advantage of flexibility in the size of the solute-solvent system to be submitted to QM calculations and also on the QM model to be used. This last is important because the determination of different molecular properties often requires different quantum chemical methods (the model and the basis set). The disadvantage is that uncoupling the MM and QM parts requires additional consideration of the solute polarization by the solvent. This has also been considered in the S-QM/MM methodology [21]. Sampling super-molecular structures signifies several configurations composed by the solute and the surrounding solvent molecules. Thus not only the system may be considerably large, but also the QM calculations have to be performed several times to give the ensemble average that characterizes the liquid properties. In some situations and for some molecular properties it is still possible to perform ab initio QM calculations [22-24] but in this chapter we reserve the examples where the use of semi-empirical methods is, at present, mandatory. In the following section we briefly describe how the solvent environment around the solute is generated in a specific liquid and in a specific thermodynamic condition. Next we also briefly discuss how the statistically uncorrelated configurations are sampled. And finally we discuss the solvatochromic shift in the UV-Vis absorption spectra of three molecules in solution. The first example is the case of pyrimidine in water [25], a polar molecule in a very polarizable solvent environment. We analyze the relative importance of the inner and outer solvent shell structures. As conventional QM/MM calculations often use solvent electrostatic contribution alone we also analyze the role of the electrostatic embedding around explicit solvent molecules. Next, we discuss the case of beta-carotene [26] in acetone and isopentane. A non-polar molecule immersed in polar and non-polar environments, respectively. Finally, we consider the case of acetone in supercritical water. This exemplifies a situation where the molecular absorption spectrum is modified by a low-dense supercritical fluid and thus can be a useful probe for the interesting physico-chemical properties of this fluid environment. 2. Method The structure of the liquid is obtained by Monte Carlo (MC) Metropolis simulation [27]. Periodic boundary conditions, with the minimum image method in a cubic box, are used. The simulations of the first two examples considered here are performed in the NVT ensemble, with a solute surrounded by N solvent molecules at room temperature (298 K). The system


is extremely diluted and the density is that of the solvent. For pyrimidine we use 900 water molecules. For beta-carotene we use 900 solvent molecules (acetone and isopentane). The corresponding densities of the simulated systems are 0.9966 g/cm3 (pyrimidine in water) and 0.7682 g/cm3 and 0.6001 g/cm3 (beta-carotene in acetone and isopentane, respectively). The intermolecular interactions are described by the standard Lennard-Jones plus Coulomb potential with 3 parameters for each site i (εi, σi and qi). For the water molecules we use the SPC potential [28]. For pyrimidine, beta-carotene, acetone and isopentane we use the OPLS [29]. Further details of the potential and geometries are described in previous publications [25,26]. After thermalization, the MC simulation is made with typically 108 MC steps. A new configuration is generated after N MC steps, i.e., after all solvent molecules are attempted to translate or rotate around a randomly chosen axis. As successive configurations do not give significant new statistical information we calculate the correlation interval using the auto-correlation function of the energy to sample statistically relevant configurations [18-20,30]. Configurations having less than 15% of statistical correlation are selected from the MC simulations for the subsequent QM calculations. An important point in this issue is that statistical convergence is obtained in all cases reported here. All the MC simulations were performed with the program DICE [31]. To select the size of the solute-solvent structures, the pair-wise distribution function [27] is used. For extended systems like beta-carotene the usual radial distribution is not appropriate and we use a minimum-distance distribution [26,32]. For each case considered we explicitly state the size and the number of solvent molecules used. The QM calculations of the absorption spectra are made using the ZINDO program [33] with the INDO/CIS parametrization suggested by Ridley and Zerner [34]. We first calculate the spectrum of the isolated molecule for the reference. Then the solvatochromic shift is obtained by calculating the spectrum of the solvated molecule including the explicit solvent molecules. These calculations lead to the average for L statistically uncorrelated configuration and the shift is thus obtained as the difference of this average and the result for the isolated situation. The wave function is anti-symmetric with respect to the entire solute-solvent system. This allows the delocalization of the wave function into the solvent region and gives some contribution to the dispersion interaction [35]. Dispersion interaction contributes to a red shift [36] and this is particularly important for non-polar solutes such as beta-carotene. Finally, we should also note that calculations with a varying number of molecules impose the use of size-extensive methods, as it is the case of singly excited configuration interaction (CIS) methods. As most low-lying excited states are


derived from single electron promotion the use of INDO/CIS is a natural choice for a semi-empirical method. 3. Results and discussions

3.1. Pyrimidine in water We first discuss the case of pyrimidine in water. This is an interesting case of a polar molecule in a polar environment that has attracted some theoretical interest [25, 37-42]. In pyrimidine there are two proton-acceptor sites for hydrogen bonds and their contribution to the total solvatochromic shift is still controversial [41]. The experimental n→ π* transition of pyrimidine in water has been well studied before [43-45]. The experimental transition has been reported at 36900 cm-1 in water. Baba et al. [44] reported n→ π* transition in isooctane [44,45] as 34250 cm-1 . This would correspond to an isooctane-water blue shift of 2650 cm−1. Because of the small polarity of isooctane the shift from the gas phase should be only slightly larger, close to 2700 cm-1. Indeed additional analysis [37] of several experimental results suggests a blue shift of 2700 ± 300 cm−1 for the n→π* transition of pyrimidine in water compared to gas phase. This is now our reference value for the experimental solvatochromic shift. On the theoretical side, some previous efforts have been made. Zeng et al. [37] performed a systematic study using different intermolecular pair potentials. They obtained a blue shift of 2450 cm-1, in good agreement with experiment. But they also concluded that hydrogen bonding accounts for half of the observed blue shift. This is an interesting aspect and suggests that the use of explicit solvent molecules is essential for a proper treatment. They have also noted that the pyrimidine-water hydrogen bonds may have long-range influences on the solvent shift. Karelson and Zerner [38], employing INDO/CIS calculations in the dielectric continuum approach, concluded that the blue shift could only be predicted with the inclusion of two explicit water molecules making hydrogen bonds to the two nitrogen atoms of pyrimidine. After this they estimate a blue shift of 2600 cm-1. Using DFT calculations Kongsted and Mennucci [42] also used a dielectric continuum around two explicit water molecules, hydrogen-bonded to pyrimidine, to find only a small solvatochromic shift of 1600 cm-1. They suggested that both specific and bulk effects are important. Gao and Byun [39] using hybrid QM/MM Monte Carlo simulations reported a value of 2275 ± 110 cm−1 for the n→π* blue shift of pyrimidine in water. The contribution of the hydrogen bond shell, in this case is found to be dominant. Recently, Liu et al [40] considered density-functional


theory within the self-consistent reaction field and obtained the shift of 2500 cm-1. To understand the role of the specific interaction and the influence of the outer solvent molecules we extend the theoretical analysis performing INDO/CIS calculations including the solvent as explicit molecules. Our results will discuss the influence of the different solvation shells in the solvatochromic blue shift. First, from the statistical distribution of MC configurations we find an average number of 1.3 hydrogen bonds. This is in agreement with ref [42] that reports 1.2 hydrogen bonds. A typical configuration is shown for illustration in Figure 1a. The solvatochromic shift obtained from the structures with hydrogen bonds only,

(a) (b)

(c) (d) Figure 1. Illustration of the (a) hydrogen bond and the hydration shells of pyrimidine in water. The (b) first, (c) second and (d) third shells are composed of 21, 71 and 213 water molecules, respectively. The solute-solvent center of mass distances are 5.5, 8.0 and 11.6 Å.


discarding all the other water molecules, is sizable (see below). Analyzing the hydrogen-bonded complexes of pyrimidine and water Cai and Reimers [41] suggest that the contribution of the inner shell is equivalent to that of the outer shells. This would attribute a large importance to the hydrogen bond shell. The previous theoretical studies all indicate that solvent molecules beyond the hydrogen bond shell are very important. Before discussing further our results including the inner and outer shells of explicit solvent molecules it is interesting to comment that the two nitrogen atoms giving two separate n→ π* transitions are not distinguished in solution. Previous studies [38,39] have noted that including the specific water molecules that make hydrogen bonds with pyrimidine joins the two n→ π* transitions allowing intensity borrowing and leading to band broadening. Hence the results reported here are the average between the two calculated n→ π* transitions. In this circumstance the contribution of the hydrogen bond shell is 1450 cm-1. Figure 1 illustrates the solvation shells of pyrimidine in explicit water molecules. Table 1 reports the calculated results for the blue shift. It is clear from this table that including only the first solvation shell is not enough to describe the solvatochromic shift. In fact including all solvent molecules up to a distance of 5.5 Å leads to a shift of only 1600 cm-1 that is a small value compared to the experimental shift of 2700 ± 300 cm-1. It is only after including 213 explicit water molecules, corresponding to all water molecules within a distance of 11.6 Å, that the shift of 2000 cm-1 is obtained. This corresponds to a 1734 valence-electron problem. Extending the results to the bulk limit gives a solvatochromic shift of 2400 cm-1, now in good agreement with the experimental result and in line with the previous theoretical estimates. It is clear that the water molecules located in the outer solvation shells can still influence the solute spectrum. The hydrogen bonds give an additional increase of the local dipole of the chromophore leading to a long-range polarization. The results are compatible with this picture and hence we conclude that the polarization effects of polar hydrogen-bond acceptor solutes in protic solvents extend to a long distance from the solute. This is further corroborated by noting that the calculated solvatochromic shift of pyrimidine in non-polar carbon tetrachloride, is converged with the first solvation shell only [25]. This conclusion is based on large QM calculations that required the explicit consideration of the CCl4 solvent molecules up to a distance of 13.3 Å and very large QM calculations involving nearly 2000 valence electrons [25]. Clearly these calculations with explicit solvent molecules could not be made outside the scope of semi-empirical methods. The role of the hydrogen bond and the inner shells to the total solvatochromic shift of pyrimidine in water is of interest [41]. The inner and


Table 1. Calculated blue shift of the n→ π* transition of pyrimidine in water. Shift is an average of the two n→ π* transitions. HB is the hydrogen-bond shell, NS is the number of explicit solvent water molecules in the solvation shell. M is the total number of valence electrons included in the quantum mechanical calculations. L is the number of MC configurations used for ensemble average. R is the radius of the solvation shell obtained from the radial distribution function. All calculations used the INDO/CIS method. Calculated uncertainty is the statistical error. Conversion: 1eV = 8067 cm-1.

the outer shells are important but the corresponding relative importance differs in different procedures. This has been pointed by Cai and Reimers [41] that noted that Gao and Byan [39] predicted larger contribution from the inner shell and a red shift for the dielectric contribution. This is the opposite to what we have obtained, up to this point. We obtained that increasing the number of solvent molecules increases systematically the blue shift of the n→ π* transition of pyrimidine in water. As discussed [41], other models


have obtained otherwise [39] with the outer solvent molecules decreasing the large result obtained for the inner shells. This has led to the belief that the solute-solvent hydrogen bond alone is sufficient, or gives the most significant contribution, to the total shift. To clarify this aspect we extend the calculation now to embed the explicit solvent molecules in the electrostatic field of the remaining water molecules. The role of the hydrogen bonds and the explicit inclusion of solvent molecules will be discussed. We have then selected from the configurations generated by the MC simulations the 500 water molecules that are nearest to pyrimidine. Initially these will be treated as simple point charges and gradually will be substituted by explicit water molecules. The results are also shown in Table 1. Using only point charges for the solvent molecules (electrostatic contribution only) leads to the large value of 2970 cm-1 for the solvatochromic shift. The electrostatic contribution alone, clearly overestimates the total shift. However, gradually increasing the number of explicit molecules then decreases the calculated shift. This should be compared with the results of ref [39]. Using explicitly only the solute and the hydrogen-bonded water molecules embedded in the electrostatic field of the remaining water molecules decreases this value to 2630 cm-1, in very good agreement with the experimental shift. But this is an artifact as it can be noted by further including the outer water molecules. Explicitly using all 21 water molecules of the first solvation shell embedded in the electrostatic field of the remaining (479 treated as point charges) gives a value of 2470 cm-1, which is also a good result. Proceeding further to the largest case of 213 explicit water molecules in the electrostatic field of the remaining 287 molecules treated as simple point charge gives the value of 2100 cm-1. These results explain the red shift of the dielectric contribution that has been noted before [39, 41]. Using only the electrostatic field of the solvent into the solute molecule overestimates the solvatochromic shift and inclusion of explicit molecules is necessary to obtain a proper description. In this case increasing the number of explicit molecules decreases the shift. Including a relatively large number of explicit solvent molecules in the electrostatic field of the outer shell is potentially a very good model. But using only the solute in the electrostatic field of the solvent seems to overestimate the solvatochromic shift. Including the solute polarization by the solvent may improve the results as seen in recent application [21,32]. 3.2. Beta-carotene in acetone and isopentane Carotenoids are very important in photosynthesis. The all-trans beta-carotene (Figure 2) is involved in the important mechanism of energy transfer with chlorophyll. Beta-carotene absorbs visible light in the region of 450 nm


Figure 2. The structure of all-trans beta-carotene. giving its characteristic colour. As beta-carotene is not soluble in water and also has very low volatility the absorption spectrum has not been recorded in either water or in gas phase. The study of the solvatochromic shifts of beta-carotene has then to rely on experimental results made on different solvents [46] or in ionic liquids [47]. The solvent effects on the visible spectrum of beta-carotene are a real challenge for theoretical methodologies for at least two aspects. First, the visible spectrum characterized by a strong π-π* absorption transition in the region of 450 nm suffers only small shifts in different solvents [46,48]. The shift from acetone to isopentane, for instance, is only 310 cm-1. The small magnitude of the shifts can be understood: the dipole moment is zero both in the ground and in the first excited state. The dominant dipolar interaction is then zero and the shift is dominated by dispersion interaction. As the dipole polarizability of the excited state is expected to be larger than in the ground state the dispersion will contribute to a better solvation of the excited state. This decreases the energy difference between the two states. This differential interaction is small for different solvents. Second, another difficulty is that beta-carotene is a relatively large molecule (ca. 30 Å long), composed of 216 valence electrons, with an elongated shape imposing the use of a non-spherical solvent shell. We have developed a minimum-distance distribution function [26,32] that follows the molecular shape and can be used for any molecule, no matter how elongated or distorted. The spectrum of beta-carotene has been analyzed by Applequist [49] using a cavity model, where the chromophore has been treated as classical point dipole oscillators. Myers and Birge [48] studied the change in oscillator strength of the absorption of beta-carotene in different solvents and found that the results depend on the cavity geometry. Zerner made an estimate of the shift of beta-carotene in cyclohexane [50] using SCRF. Abe and co-workers [46] analyzed solvent effects in 51 different solvents and made an empirical analysis in terms of reaction field models. Here, we use the results obtained with the S-MC/QM methodology, in a minimum-distance solvation


shell, to discuss the solvatochromic shift of beta-carotene in two different solvents; namely, isopentane and acetone. These two solvents are selected on the basis of their nature. Isopentane is non-polar and has a very low normalized polarity (0.006). Acetone is a polar molecule having a relatively large polarity (0.355). Using configurations obtained from the MC simulations, INDO/CIS calculations are performed on several super-molecular structures composed of one beta-carotene and NS surrounding molecules of solvent. The results are summarized in Table 2 that also gives some data pertaining to the solvents and the number NS of explicit molecules used. Figure 3 illustrates a typical configuration, extracted from the simulation, of one beta-carotene surrounded by the first shell of solvent acetone molecules. As discussed above the gas phase Table 2. Calculated absorption transitions (in cm-1) of beta-carotene in vacuum and in two different solvents. All calculations used the INDO/CIS method. NS is the total number of explicit solvent molecules and M is the total number of valence electrons included in the quantum mechanical calculations.

Solvent

Dielectric constant

Normalized

polarity

NS

M

Transition

Experiment [46]

Vacuum - - - 216 22230 -

Isopentane 1.828 0.006 59 2104 22180 22360

Acetone 21.36 0.355 77 2064 22070 22050

Figure 3. Illustration of one configuration obtained from the MC simulation. The system is composed of one beta-carotene molecules surrounded by nearest-neighbors acetone solvent molecules.


absorption transition is not known experimentally. The value calculated here for the gas phase π-π* transition is 22230 cm-1. In solvents of any polarity this transition suffers a red shift. The magnitude of the shift, of course, depends on the solvent. Using NS = 59 isopentanes solvent molecules the average transition of beta-carotene changes to 22180 cm-1, corresponding to a red shift of 50 cm-1. In acetone the transition is obtained at 22070 cm-1, in good agreement with the experimental value of 22050 cm-1. These transition energies are obtained using 40 INDO/CIS calculations on statistically uncorrelated configurations. In the case of acetone each calculation is made on beta-carotene surrounded by 77 acetone molecules, including the explicit consideration of 2064 valence electrons, in a wave function that is anti-symmetric with respect to the permutation of any two electrons. The wave function delocalization over the solvent region, followed by the CIS calculations, contributes to the differential dispersion interaction [35] and is the main responsible for the red shift. Table 2 shows that the calculated transition energy values are in good agreement with experiment and that the solvatochromic shifts have the correct trend. In both cases the correct sign (red shift) has been obtained. But the relative magnitude is more difficulty. The red shift of the π-π* absorption transition of beta-carotene from isopentane to acetone is calculated as –110 cm-1 compared to the corresponding experimental value of –310 cm-1. 3.3. Acetone in supercritical water It is well known that the coexistence line of the liquid and solid phases finishes at the so-called critical point. This is the point where the system becomes a supercritical fluid and exhibits physico-chemical properties that are markedly different from normal liquid systems [51,52]. Water becomes an exciting supercritical fluid at temperatures and pressures beyond the critical point located at Pc = 220 atm and Tc = 647 K. In this regime the dielectric constant is considerably decreased and water becomes an excellent solvent for many organic compounds. The density is also very much modified and under small variations of temperature and pressure it suffers intense changes. The situation is illustrated in Figure 4 that shows the density of water as a function of temperature and pressure and the location of the critical point. Understanding the properties of supercritical water (SCW) is of particular interest as water is the most important molecular system in nature. A direct approach can be made to understand the structural aspects of water by using X-ray and neutral diffraction experiments [53-57]. One aspect that emerges from experimental studies is the reduced number of hydrogen bonds as the density of water is decreased [53-58]. However the analysis of the electronic structure of supercritical water is conveniently made using a probe


Figure 4. The density of water as a function of temperature and pressure. The location of the critical point is shown. molecule and analyzing the change in the absorption spectrum compared to another thermodynamic situation, that is used as a reference. This reference could either be the condition of isolated molecule (gas phase situation) or the condition of normal liquid (P = 1 atm, T = 298 K). An important condition in this issue is, of course, that the probe molecule should be stable in SCW under different conditions of temperature and pressure. This is the case of acetone, where the n−π* transition in water has been studied in different supercritical conditions [59-61]. Bennett and Johnston [59] have made systematic experimental studies of different SCW conditions. From this work it is possible to characterize that for P = 340.2 atm and T = 673 K the n−π* transition of acetone suffers a blue shift of 500-700 cm-1, compared to the gas phase. In addition, there is indirect evidence [23,60,61] that the number of hydrogen bonds between acetone and water is reduced and that these are responsible for half of the total blue shift. Different thermodynamic conditions can be studied theoretically and in fact a recent theoretical analysis [23,61] of this blue shift can be found. In this section we now analyze the reduction in the number of solute-solvent hydrogen bonds, their participation in the spectral shift and, finally, the role of the inner and outer solvation shells for describing the total spectral blue shift. To obtain the solute-solvent configurations we use the MC simulation but now, as the pressure as well as the temperature are the important


thermodynamic parameters, we have used the NPT ensemble. To compare with the experimental condition described above the MC simulations are made using P = 340.2 atm and T = 673 K. The system consists of one acetone molecule surrounded by 700 water molecules. For water we now use the SPC/E potential [62], as it correctly describes the critical point of water [63,64]. The calculated density is 0.46 g/mL. Comparing with the density of water at the critical point (0.32 g/mL) shows that this corresponds to the near-critical regime (0.5 ≤ ρ/ρc ≤ 1.5). A density of 0.46 g/mL is expected to exhibit sizable changes in the number of hydrogen bonds. This is analyzed next. The identification of solute-solvent hydrogen bonds are normally made by considering the radial distribution function that characterizes the pair-wise atomic distances. Figure 5 show the calculated radial distribution function between the oxygen atom of acetone and the hydrogen atom of water. A clear structure is seen centered at 1.85 Å, starting at 1.50 Å and ending at 2.55 Å. This corresponds to the hydrogen-bond configurations between the acetone and water molecules. Although it is normally correct that the hydrogen bonds are found in this geometric region it cannot be assured that all water molecules located in this region are indeed hydrogen bonded to the solute. An additional consideration is made regarding the interaction energy between the solute and the solvent. Figure 6 shows the pair-wise energy distribution and

Figure 5. The pair-wise radial distribution between the O atom of acetone and the H atom of water for the supercritical condition.


Figure 6. The pair-wise interaction energy between acetone and water for the supercritical condition. the bump corresponding to the hydrogen bonding energies. Combining the results given in Figures 5 and 6 we obtain an average number of 0.7 hydrogen bonds between acetone and water. This number is indeed reduced compared to the case of water in normal thermodynamic condition that gives a value of 1.6 using the same type of analysis [23]. As it has been thoroughly discussed before one of the important aspects of SCW is the reduced number of hydrogen bonds. We now discuss the statistics of hydrogen bonds formed between acetone and SCW. The calculation indicates that 42.0% of the configurations make no hydrogen bonds. But 49.2% make one configuration. Proceeding, 8.5% of the configurations make 2 hydrogen bonds and a very small number (0.3%) make even 3 hydrogen bonds. The statistics thus implies that the most probable number of hydrogen bonds is simply one. But the average number is 0.7. Figure 7 shows in a single picture the superposition of all configurations that exhibit acetone-water hydrogen bonds. This superposition shows the configuration space that is spanned by the neighboring water molecules that are involved in hydrogen bonds (HB). We now analyze the contribution of the different hydration shells to the total calculated blue shift of the n−π* transition of acetone in supercritical water. First, we analyze the role of the HB shell. It has been indirectly estimated that this contributes to half of the total solvatochromic blue shift. Table 3 shows the results. As it can be seen using the configurations that make HB we obtain a solvatochromic shift of 330 cm-1, compared to the


Figure 7. Superposition of the configurations showing hydrogen bonds between acetone and supercritical water. The remaining water molecules are removed for clarity and for explicitly showing the configuration space spanned by hydrogen-bonded water molecules. Table 3. Calculated solvatochromic shift (cm-1) of the n→ π* transition of acetone in supercritical water (P = 340.2 atm, T = 673 K). Results show the calculated blue shift compared to the gas phase and the red shift compared to normal water. All calculations used the INDO/CIS method. HB is the hydrogen-bond shell, NS is the total number of explicit solvent molecules and M is the total number of valence electrons included in the quantum mechanical calculations. Solvatochromic shifts were obtained as averages over 100 uncorrelated configurations.

Solvation shell

NS

M

Blues shift (Gas phase)

Red shift

(Normal water)

HB (0,1,2,3)a - 330 450

First 30 264 630 570

Second 100 824 660 700

Third 170 1384 670 730

Experiment [57] 600 ± 100 800 ± 200

a) Average number of hydrogen bonds is 0.7. See text.


experimental result of 600 ± 100 cm-1. This is indeed in excellent agreement with the expectation that the HB shell contributes to half of the shift. The next shell gives an additional contribution and the total shift obtained using 30 explicit water molecules is 630 cm-1, showing that the first hydration shell is a good approximate model for obtaining the total shift. This is likely to be a consequence of the reduced density of water in this SC condition. Using next the second and third shells improves only slightly the result and gives our best estimate of 670 cm-1, in excellent agreement with the experimental result. The largest calculation, using explicitly 170 solvent water molecules involves a total of 1384 valence electrons. This situation is illustrated in Fig. 8, where all water molecules within the center of mass distance of 11.0 Å are explicitly included in the INDO/CIS calculations.

Figure 8. Illustration of acetone immersed in supercritical water. This corresponds to all 170 water molecules located within 11.0 Å.


In agreement with experiment the solvatochromic shift of the of the n−π* transition of acetone in supercritical water is calculated to suffer a blue shift of 670 cm-1 compared to isolated acetone, and a red shift of 730 cm-1 compared to normal water. As inferred experimentally, the blue shift from gas phase to water is reduced for the SCW condition from 1500 ± 200 cm-1 (normal water) to 600 ± 100 cm-1. This reduction is rationalized to be one consequence of the reduced number of hydrogen bonds. In fact, it can be noted that 50% of the total shift derives from the configurations that exhibit hydrogen bonds between the solute and the solvent. However, as derived from the results of our calculations, shown in Table 3, this is not peculiar to the SCW condition and in fact also happens for normal water. 4. Summary and conclusions

A combined use of Monte Carlo simulations and quantum mechanics calculations are made to analyze the absorption spectra of organic molecules in different solvent environments. The MC simulation generates the structure of the liquid to be used in QM calculations of the spectrum. We focus on the solvatochromic shifts associated to different solvents. Using super-molecular structures composed of the solute and several solvent molecules we have analyzed the role of the explicit consideration of the solvent molecules. This leads to fairly large systems imposing the consideration of semi-empirical approaches. Typically the systems considered here involve ca. 1500-2000 valence electrons. The spectrum is then calculated using the INDO/CIS method, with the spectroscopic parametrization proposed by Ridley and Zerner. The solvatochromic shifts of pyrimidine in water and of beta-carotene in acetone and isopentane are considered first. These exemplify the situations of a polar molecule in a polar environment and of a non-polar molecule in both polar and non-polar environments. Good agreements with experimental shifts are obtained in all cases. In the case of pyrimidine we analyze the relative importance of the different solvation shells and the role of the electrostatic embedding. Results are obtained using explicit solvent molecules with and without an electrostatic embedding. In the first case including the outer solvation shells increases the calculated shift, whereas in the latter it decreases. The solvatochromic shift of beta-carotene is a persistent and difficult problem because the spectrum involves a π-π*excitation between two states of zero dipole moment. The red shift of this transition is obtained both for isopentane and acetone. Finally, we have considered the absorption spectrum of acetone in supercritical water. The characteristic n−π* transition is calculated to suffer a blue shift of 670 cm-1 compared to the gas phase. This is in excellent agreement with the experimental result that places


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