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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
1
2
Kaline Coutinho1, Tertius L. Fonseca2 and Sylvio Canuto1
Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP Brazil
Instituto 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 supermolecular 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]
64
Kaline Coutinho et al.
in a polar environment and of a non-polar molecule in both polar and nonpolar 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 semiempirical 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
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Kaline Coutinho et al.
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 supermolecular 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
Molecules in different environments
67
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 [1820,30]. 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
68
Kaline Coutinho et al.
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
Molecules in different environments
69
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)
(c)
(b)
(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.
70
Kaline Coutinho et al.
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 longrange 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
Molecules in different environments
71
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
72
Kaline Coutinho et al.
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 betacarotene (Figure 2) is involved in the important mechanism of energy transfer
with chlorophyll. Beta-carotene absorbs visible light in the region of 450 nm
Molecules in different environments
73
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 betacarotene 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 coworkers [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
74
Kaline Coutinho et al.
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.
Molecules in different environments
75
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
76
Kaline Coutinho et al.
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
Molecules in different environments
77
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 nearcritical 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.
78
Kaline Coutinho et al.
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
Molecules in different environments
79
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 hydrogenbonded 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
600 ± 100
800 ± 200
Experiment [57]
a)
Average number of hydrogen bonds is 0.7. See text.
80
Kaline Coutinho et al.
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.
Molecules in different environments
81
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
82
Kaline Coutinho et al.
this solvatochromic shift in the interval 500-700 cm-1. Analysis of the
hydrogen bonds between the solute acetone and supercritical water indicates
that 44% of hydrogen bonds persist compared to water in normal
thermodynamic condition. This number correlates with the density of
supercritical water considered here where the density is 46% of that in
normal water. Compared to normal water the n−π* transition of acetone is
calculated to suffer a red shift of 730 cm-1.
The success of the present approach to study solvatochromic shifts of
organic molecules in solution corroborates the importance of the combined
use of quantum mechanics and statistical mechanics and exemplifies the
usefulness of the semi-empirical method employed.
Acknowledgments
We thank Dr. W. R. Rocha, Dr. H. C. Georg and Dr. D. Trzesniak for
discussions and collaboration. We also thank PhD candidate Rafael C. Barreto
for the illustration shown in Figure 4. The work reported here has been
partially supported by CNPq, CAPES and FAPESP (Brazil).
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