Molecular Property Investigations of an ortho-Hydroxy Schiff Base

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Molecular Property Investigations of an ortho-Hydroxy Schiff Base Type Compound with the First-Principle Molecular Dynamics Approach Aneta Jezierska-Mazzarello,*,†,‡ Rodolphe Vuilleumier,§,|,⊥ Jarosław J. Panek,† and Giovanni Ciccotti| UniVersity of Wrocław, Faculty of Chemistry, 14 F. Joliot-Curie, 50-383 Wrocław, Poland, National Institute of Chemistry, HajdrihoVa 19, SI-1001, Ljubljana, SloVenia, UniVersite´ Pierre et Marie Curie 4, Laboratoire de Physique Theórique de la Matie`re Condensee´, 4 Place Jussieu, 75005 Paris, France, and Dipartimento di Fisica, and CNISM unit 1, UniVersita` di Roma ‘La Sapienza’, Piazzale Aldo Moro 5, 00185 Roma, Italy ReceiVed: April 16, 2009; ReVised Manuscript ReceiVed: NoVember 24, 2009

The structure, proton transfer, and vibrational dynamics under ambient conditions of a selected ortho-hydroxy Schiff base type compound, 2-(N-methyl-R-iminoethyl)-4-chlorophenol, containing a very short intramolecular hydrogen bond, were investigated computationally in the gas phase and in the crystal by density functional theory (DFT) based first-principle molecular dynamics (FPMD). It is found that the proton is well localized on the nitrogen side of the O · · · H · · · N bridge in the crystal phase, in agreement with X-ray diffraction experiments, while a more labile proton is located most of the time on the oxygen side in a vacuum. Environmental effects on this very strong hydrogen bond thus appear crucial and lead to drastic changes of the infrared (IR) spectrum: The computed gas-phase IR spectrum shows a very broad absorption band that covers frequencies from about 1000 to 3000 cm-1 assigned to the labile proton. In mere contrast, a much more localized absorption band around 2600-2700 cm-1 is predicted in the crystal phase. Finally, effects of the quantization of the proton motion on the hydrogen bond structure were estimated in two ways. First, we constructed the one-dimensional (1D) potential energy surface (PES) for the proton along the O · · · H · · · N bridge in a vacuum. The 1D Schro¨dinger equation was then solved. Next, path integral molecular dynamics (PIMD) was performed in the solid state. Inclusion of quantum effects does not affect the observed change of the most probable tautomer, upon going from the gas phase to the crystal. 1. Introduction Imine type compounds with either aromatic or alkyl, but not hydrogen, substituents at the nitrogen atom are known in the literature as Schiff bases. This type of compounds is widely investigated because of their structural variety and molecular properties, such as intramolecular hydrogen bonding. The unique combination of an unsaturated carbon-nitrogen double bond and the formation of pseudoaromatic rings (six-membered rings with the presence of double bonds) enables this intramolecular bond to be exceptionally strong in some cases.1-3 The high mobility of the hydrogen-bonded proton of Schiff bases is important in many processes with biological relevance, e.g., the conversion of photons in the bacteriorhodopsin system4-7 and in biochemical catalysis.8,9 Schiff bases are also formed during the enzymatic processes of transamination and decarboxylation.10,11 Organometallic complexes containing Schiff bases are involved in many biochemical processes, e.g., the reaction pathways of enzyme cofactors.12 They have also been found as inhibitors of the enzymatic action of trypsin.13 Besides their biological importance, Schiff bases are interesting from the materials chemistry point of view as well. Metal complexes containing an imine group display potentially useful * Corresponding author. E-mail: [email protected]. Phone: +48 71 3757 224. Fax: +48 71 3282 348. † University of Wrocław. ‡ National Institute of Chemistry. § Universite´ Pierre et Marie Curie 4. | Universita` di Roma ‘La Sapienza’. ⊥ Present address: UMR PASTEUR, De´partement de Chimie de l’ENS, 24 rue Lhomond, 75005 Paris, France.

photophysical, magnetic, and conducting properties.14-16 New compounds related to the Schiff base family are still synthesized, and their properties, i.e., photochromism, thermochromism, and solvatochromism (dependence of a property on irradiation, temperature, and solvent presence) are investigated.17-20 A combination of biological knowledge with medicinal and industrial needs leads to the application of Schiff bases in biomimetic complexes with catalytic activity.21-23 The interand intramolecular hydrogen bonds are responsible for many of the above properties of Schiff bases. Investigations of such hydrogen bonds and related molecular features are interesting for understanding the various biologically and technically relevant properties at the microscopic level. Among Schiff bases, 2-(N-methyl-R-iminoethyl)-4-chlorophenol24 belongs to a class of compounds with very short and strong hydrogen bonds, which is formed between the nitrogen atom of the Schiff base moiety and the hydroxyl group from the ortho position of the aromatic ring (see Figure 1). The ortho-hydroxy Schiff bases are widely investigated using diffractometry and NMR and IR spectroscopies because of the interesting properties of their intramolecular hydrogen bridges formed between the oxygen and nitrogen atoms.1-3,24-33 In particular, proton position in the bridge depends on the substituents24,27 or solvent,26 making these compounds prototypes of “intramolecular switches”. The particular group of Schiff bases to which the studied compound belongs is unique,24 because these compounds contain substituents at the imine carbon atom (C4 in Figure 1). For the 2-(Nmethyl-R-iminoethyl)-4-chlorophenol, its very short and strong hydrogen bond is due to some extent to the chloro substitution of the phenol ring that increases the acidity of the enol but also

10.1021/jp903501m  2010 American Chemical Society Published on Web 12/17/2009

Molecular Property Investigations with FPMD

Figure 1. Molecular structure of both tautomers of the investigated Schiff base, 2-(N-methyl-R-iminoethyl)-4-chlorophenol, with the atom numbering scheme. Only selected atoms important in the discussion are marked. The labeling of the atoms in the compound studied is as follows: cyan, carbon atoms; green, chlorine atoms; white, hydrogen atoms; red, oxygen atoms; blue, nitrogen atoms. The molecular form on the left corresponds to the gas-phase tautomer, while the O · · · H-N form on the right is dominant in the solid state.

due to the presence of steric strain (repulsive interactions due to spatial constraints) between close-lying substituents at the nitrogen and carbon atoms of the Schiff moiety. This steric strain was found to increase the strength of the hydrogen bridge, not only in the ortho-hydroxy Schiff bases34,35 but also for related prototypic compounds with short, strong O-H · · · O hydrogen bonds, ortho-hydroxy acyls.36,37 There have recently been various X-ray diffraction studies of crystals of 2-(N-methyl-R-iminoethyl)-4-chlorophenol and related compounds24 and also various quantum chemistry calculations of the structure and electronic properties of these molecules in the gas phase.38,39 While gas-phase calculations, supported by IR experiments in liquids, point to labile protons or protons localized on the oxygen side of the O · · · H · · · N bridge for many of these compounds, X-ray diffraction puts them frequently on the nitrogen side.24 This is true not only for the cases with substituents at the C4 atom,24 which provide a steric strengthening effect. Even if the substituent at C4 is hydrogen, it often happens that in the solid state the proton is transferred to the nitrogen acceptor side,27 but this is not always the case.31 It is even possible that the crystal structure contains simultaneously both O-H · · · N and O · · · H-N forms of the same compound.30 It is then expected that environmental effects have a strong influence on the structure and proton transfer dynamics of these compounds. This is further suggested by the observation that even if the stability of the proton at the nitrogen site usually follows the expected change of basicity of the imine group,25 the contrary was found for a series of sterically strengthened Schiff bases with increasingly large aliphatic substituents at the nitrogen atom.24 It was suggested that large aliphatic groups screen the O · · · H · · · N bridge from the environment, leading to the observed unusual trend.24 A surrounding dielectric medium appears to slightly modulate the stability of the nitrogen site but does not lead to an inversion of stability;38 a full description of the environment found in the crystal is thus needed. In the current paper, we present density functional theory40 (DFT) based first-principle molecular dynamics41 (FPMD) of 2-(N-methyl-R-iminoethyl)-4-chlorophenol both in the gas phase and in the crystal phase in order to study the structure, proton transfer, and vibrational dynamics of the strong intramolecular hydrogen bond. DFT has known limitations for the description of hydrogen bonds42-44 but has nevertheless been applied with great success to the study of hydrogen-bonded complexes,45 hydrogen-bonded liquids46-48 or solids,49,50 and proton transfer

J. Phys. Chem. B, Vol. 114, No. 1, 2010 243 reactions.51-54 DFT also compares favorably to MP2 for Schiff bases in the gas phase.38 We have probed vibrational dynamics by means of the infrared (IR) spectra, also available experimentally.24 The signature of labile protons and strong hydrogen bonds is an absorption continuum in the IR spectrum that covers frequencies from about 1000 to 3000 cm-1. The proton potential energy surface inside the O · · · H · · · N bridge is very anharmonic, and it is further strongly modulated by the conformation of the rest of the molecule, as is usual for strong hydrogen bonds. Thus, static calculations based on the harmonic approximation are doomed to fail while a good sampling of the molecular conformations is needed. The FPMD approach, using molecular dynamics to explore the space of conformation, has been found useful even in the case of very anharmonic systems such as CH5+ cation,55 where large-amplitude vibrations and fast lightatom exchange processes make the use of static models inadequate. Many applications of FPMD in vibrational analysis have been performed, which involve the three states of matter: the gas phase, liquid or solution, and solid state. It thus allows for the study of the environmental influence on the behavior of molecular properties.56-58 Hydrogen bonding in particular has been much studied by FPMD, and a huge effort has been put into the study of the properties of water in the liquid46 and solid47 states. In addition, FPMD also found application in vibrational investigations of aqueous solutions59,60 and nonaqueous liquids.61 Finally, FPMD infrared spectra were calculated for crystals62,63 and enzymatic systems.64 Effects of the quantization of the proton motion on the hydrogen bond structure were estimated in two ways. We first constructed the potential energy surface (PES), which was then sampled to obtain proton potential functions (energy profiles for proton motion along a suitable path extending from the donor to the acceptor atom), for the two tautomers of the orthohydroxy Schiff base independently. These potential curves were used to solve the one-dimensional (1D) Schro¨dinger equation to obtain the first few vibrational states of the proton asymmetrical stretch along the O · · · H · · · N bridge. The PES for the proton transfer depends strongly on the tautomer considered, as does the electron density distribution throughout the molecule;39 the atoms in molecules (AIM) theory of R. F. W. Bader was then applied to analyze the intramolecular hydrogen bond and the topology of the electron density65 in order to rationalize these observations. Next, path integral molecular dynamics (PIMD)66-68 was performed in the solid state to investigate the quantum effects of nuclear motion. This enabled us to study the role of quantum effects on the structure of the strong hydrogen bond. The motivation of this study is not drawing general conclusions on the solid-state behavior of various Schiff bases. Rather, we would like to establish and test a protocol that should be able to describe gas-phase properties as well as capture the specific environmental effects of the solid state. The protocol is based on a thorough exploration of a single, well-described compound with interesting dynamical properties of the hydrogen bridge. The outline of the article is as follows: Section 2 contains details of the computational methodologies applied in the study. Results and discussion are presented in section 3 in the following order: static models, gas-phase and solidstate CPMD calculations, and PIMD simulation. Final remarks are given in section 4. 2. Computational Methodology Static gas-phase calculations were performed using density functional theory (DFT).40 The geometry of the studied Schiff

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base was optimized using the B3LYP hybrid functional69,70 for the exchange-correlation description, while double- (631+G(d,p))71 and triple- (6-311+G(d,p))72 zeta split-valence basis sets were used to represent the Kohn-Sham orbitals. Subsequently, a series of distorted structures was constructed by placing the hydrogen bridge proton (H2) on a set of points forming a circular arc defined by the O1-H2 · · · N3 atoms.73 The potential energy surface (PES) was sampled and proton potential functions (energy profiles for the movement of protons along the hydrogen bridge) were obtained. Next, the 1D Schro¨dinger equation was solved and the anharmonicity of the system was estimated.74 Atoms in molecules (AIM) theory65 was additionally applied to study the intramolecular hydrogen bond properties and atomic charges based on the wave function obtained from the DFT calculations at the B3LYP/6-311+G(d,p) level. DFT investigations were performed using the Gaussian 03 suite of programs,75 while the AIMPAC package was used for the AIM analysis.76 In a second part, first-principle molecular dynamics within the framework of Car-Parrinello (FPMD-CP)41 was performed in vacuo and in the solid state. We employed the exchange correlation functional proposed by J. P. Perdew, K. Burke, and M. Ernzerhof (PBE) coupled with the plane-wave basis set.77 A kinetic energy cutoff of 70 Ry was used throughout. The pseudopotentials proposed by N. Troullier and J. L. Martins78 were used for each type of atom in the analyzed Schiff base. Optimization of the structure was performed in both the gas phase and solid state to generate the initial condition for the MD runs. Gas-phase molecular dynamics was performed in a cubic cell of a ) 15 Å, and the scheme of Hockney79 was applied to remove interactions with periodic images of the cell. The molecular structure of the Schiff base studied and used for molecular dynamics in vacuo is presented in Figure 1. The simulations were performed at a temperature of 300 K. The fictitious electron mass µ was set to 400 au. The time-step value applied during the study was 2 au (0.0484 fs). Initially, the system was equilibrated and the data were collected for ca. 5 ps. The value of the dipole moment was calculated at each step of the MD run. The crystallographic data of the ortho-hydroxy Schiff base (2-(N-methyl-R-iminoethyl)-4-chlorophenol) for the solid-state calculations were taken from a study of Filarowski et al.24 The triclinic unit cell with a ) 6.411 Å, b ) 7.273 Å, c ) 10.251 Å, R ) 99.03°, β ) 95.57°, and γ ) 105.59° was used for the solid-state calculations. Molecular dynamics (MD) simulation was again performed at 300K. The fictitious electron mass was set to 400 au. A time step value of 2 au (0.0484 fs) was used for this part of the simulation. The dipole moments were collected for each step of the MD run. The periodic boundary conditions (PBCs) were applied in the calculations. Electrostatic interaction energy within the infinite periodic system was reproduced with the Ewald technique80 involving summations with eight images of the unit cell in each spatial direction. Molecular dynamics calculations were performed on the basis of the Γ-point approximation,81 while the convergence of Brillouin zone integration was tested during the geometry optimization using Γ-point, 2 × 2 × 2, and 4 × 4 × 4 Monkhorst-Pack k-point mesh.82 After the initial equilibration, the data collection time was ca. 14.5 ps. The trajectories obtained from the MD simulations were subsequently used for time evolution analysis of the interatomic distances of the atoms involved in the intramolecular hydrogen bond in both phases. Infrared spectra (IR) and vibrational density

Jezierska-Mazzarello et al. TABLE 1: Experimental and Calculated Interatomic Distances (in Å) between the Atoms Involved in the Intramolecular Hydrogen Bond of 2-(N-Methyl-riminoethyl)-4-chlorophenol in Vacuo for the Two Tautomeric Forms interatomic distances O1 · · · N3 O1-H2 H2 · · · N3 N3-C4 C4-C5 C5-C6 C6-O1 O1 · · · N3 O1 · · · H2 H2-N3 N3-C4 C4-C5 C5-C6 C6-O1 ∆E proton transfer energy (kcal/mol)

X-ray crystallography B3LYP/ B3LYP/ (ref 24) 6-31+G(d,p) 6-311+G(d,p) Tautomeric Form O-H · · · N 2.541 1.014 1.614 1.294 1.479 1.426 1.339

2.551 1.007 1.634 1.289 1.479 1.423 1.337

Tautomeric Form O · · · H-N 2.490 2.509 1.517 1.549 1.031 1.064 1.288 1.325 1.456 1.430 1.420 1.461 1.300 1.277 2.23

2.521 1.576 1.056 1.324 1.426 1.461 1.269 2.39

of states (VDOS) were generated using Fourier transformation of the time autocorrelation function of the dipole moment and atomic velocities obtained from MD simulations. For the IR spectra, the standard harmonic frequency dependent quantum correction was applied to the spectrum, as suggested in recent studies.60,83 Finally, path integral molecular dynamics (PIMD)66-68 simulation was carried out in the solid state. The calculations were performed at T ) 300 K controlled by a Nose´-Hoover thermostat.84-86 The fictitious electron mass µ was set to 400 au. The time-step applied for this part of the MD calculations was set to 3 au (0.0725 fs). The simulation was performed with periodic boundary conditions (PBCs) with the same settings as for the FPMD-CP run. Eight beads of the quantum polymer were used for imaginary time path integration. The staging of the path integral propagator was applied.68,87 Data were collected for 17.4 ps after the initial equilibration and further used to obtain a histogram for hydrogen (H2) position analysis in the intramolecular hydrogen bond. First-principle molecular dynamics (FPMD-CP and PIMD) simulations were performed using the CPMD program.88 To prepare the visualization of the investigated Schiff base, the VMD program was used89 for molecular structure presentation. The graphs of time series and simulated spectra were plotted with the Gnuplot program.90 3. Results and Discussion 3.1. Hydrogen Bond Study in Vacuo: DFT and AIM Approaches. The molecular structure of the studied Schiff base is presented in Figure 1. The intramolecular hydrogen bond, which is a determining factor for the preferred molecular conformation, is also indicated. The compound of interest contains a strong intramolecular hydrogen bond, commonly found among related compounds.24 The two possible tautomeric forms, with O1-H2 · · · N3 and O1 · · · H2-N3 hydrogen bridges, were analyzed via DFT theory, and the calculated interatomic distances for the atoms involved in the intramolecular hydrogen bonds are reported in Table 1. The isolated molecule calculations resulted in elongation of the hydrogen bridge with respect to


J. Phys. Chem. B, Vol. 114, No. 1, 2010 245 TABLE 2: Electron Density and Its Laplacian Evaluated at Bond Critical Points (BCPs) of the Hydrogen Bridge for the Molecular and Proton-Transferred Forms of the Studied Compound at the B3LYP/6-311+G(d,p) Level of Theorya Molecular Form

F (e*a0-3) ∇2(F) (e*a0-5)

O-H

H· · ·N

0.31474 –2.09787

0.06497 0.11306

Proton-Transferred Form

Figure 2. Topology maps of electron density obtained based on AIM theory at the B3LYP/6-311+G(d,p) level of theory for the orthohydroxy Schiff base (2-(N-methyl-R-iminoethyl)-4-chlorophenol)scross sections in the plane of the phenyl ring. Left, molecular (O1-H2 · · · N3) form; right, proton-transferred (O1 · · · H2-N3) tautomer. The red line marks the AIM interaction path for the intramolecular hydrogen bond.

the X-ray crystallographic measurement,24 with the proton located at the oxygen site (molecular form) rather than at the nitrogen site (proton transfer form) in the crystal. Furthermore, the proton transfer energy from the oxygen to the nitrogen side was calculated for the two split-valence basis sets employed in the study as the difference of electronic energies (corrected for the vibrational zero-point energy) between the two tautomers. The double-ζ split-valence basis set estimated the energy of proton transfer as 2.23 kcal/mol, while the triple-ζ split-valence basis set gave an energy equal to 2.39 kcal/mol. It is worth mentioning that, for similar compounds, Filarowski et al. reported values in the range 2.29-5.00 kcal/mol using the B3LYP/6-31G(d,p) level of theory.1 Such a low proton transfer energy suggests that the proton in the hydrogen bridge is strongly delocalized. The proton transfer is also connected with changes in the π skeleton of the molecule. This is indicated by selected bond lengths (Table 1); proton transfer to the acceptor side is accompanied by switching from double to single N3-C4 bonds. Simultaneously, the C6-O1 single bond is shortened and exhibits increased double character. Thus, the molecular form is a phenol-imine, while the proton-transferred form is a ketone-amine. These effects are accompanied by relevant changes of the C-C bond lengths involving the π-electron skeleton of the aromatic ring. The potential energy curves for the proton along the O · · · H · · · N bridge are shown in Figure 3 for the two tautomers. The two conformations differ by some bond length rearrangement inside the phenol ring, which are seen to strongly modulate the proton potential. The NH bond is however weaker than the OH bond with a lower barrier for proton transfer and a deeper minimum in the oxygen side for the NH tautomer than on the nitrogen site for the enol tautomer. Such modulation of the potential energy curves is correlated with changes in the electronic structure of the Schiff base. Atoms in molecules (AIM) theory was applied to study the topology of the electron density of this strongly hydrogen-bonded system. Topology maps of the electron density are presented in Figure 2, and they contain features common for the AIM description of the molecular electronic structure: critical points, which are stationary points of the electron density field (i.e., the density gradient is zero at the critical point). In the two-dimensional representation of Figure 2, these critical points are recognizable as maxima (nuclear positions), saddle points, and minima. A typical sixmember pseudoring is formed by the five interatomic bond paths

F (e*a0-3) ∇2(F) (e*a0-5) a

O· · ·H

H-N

0.06762 0.16193

0.29672 –1.51078

F ) electron density. ∇2(F) ) Laplacian of the electron density.

TABLE 3: AIM Charges Calculated for Selected Atoms of the Studied Compound at the B3LYP/6-311+G(d,p) Level of Theory atom

molecular form

proton-transferred form

O1 H2 N3 C4 C5 C6

–1.140 0.618 –1.123 0.640 –0.021 0.588

–1.135 0.520 –1.167 0.544 –0.035 0.811

corresponding to the covalent bonds and by the bond path of the hydrogen bridge. The presence of this ring is confirmed by the location of the ring critical point (RCP). The same picture holds for both tautomeric forms. Table 2 contains values of the electron density and its Laplacian for both tautomeric forms and both bond critical points (BCPs) of the hydrogen bridge. The electron density values at the hydrogen bridge BCPs reported in the current study are consistent with calculations of A. Filarowski and I. Majerz on o-hydroxy Schiff bases unsubstituted in the aromatic ring.39 These values are characteristics of very strong hydrogen bonds.91,92 The OH valence bond appears however stronger than the NH bond (higher density and modulus of the Laplacian at the BCP), while the H · · · O hydrogen bond is also stronger than the H · · · N one. This correlates with a deeper and more harmonic OH well for the enol tautomer and a more anharmonic potential with nearly equivalent wells for the NH tautomer, as observed in Figure 2. The values of the electron density and its Laplacian (Table 2) are, however, rather similar for the pairs: O-H with N-H and H · · · N with O · · · H. This suggests that the proton-transferred form is best described not as O- · · · +H-N but as simply O · · · H-N, in parallel with the molecular form O-H · · · N. In order to check this observation, we calculated AIM atomic charges for the relevant forms of the studied compound (see Table 3). The sum of atomic charges for the whole pseudoring of atoms from O1 to C6 (see Figure 1) decreases from -0.438 in the molecular form to -0.462 in the proton-transferred form. This change is not large. Moreover, the key atoms, O1, H2, and N3, also do not experience significant modifications of their electronic population. The hydrogen atom H2 becomes even less positively charged when it is transferred to the N3 acceptor. This indeed confirms that the +H-N notation does not reflect the details of the studied tautomerism. Interestingly, even if the local changes of the electron density seem small, they have an overall significant effect on the charge distribution of the molecule. The dipole moment calculated at the B3LYP/6311+G(d,p) level of theory is 3.56 D for the O-H · · · N form and 5.60 D for the O · · · H-N form.

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Figure 3. Proton potential and the first three vibrational eigenstates (0, 1, 2) together with the associated wave functions and transition energies (0 f 1, 1 f 2) obtained at the B3LYP/6-311+G(d,p) level of theory for the molecular (above) and the proton-transferred (below) forms of the ortho-hydroxy Schiff base (2-(N-methyl-R-iminoethyl)4-chlorophenol).

The potential energy curves (see Figure 3) suggest highly anharmonic dynamics of the proton. Vibrational frequencies were obtained by solving the 1D Schro¨dinger equations for both the O-H · · · N and O · · · H-N tautomeric forms at two theoretical levels. The results obtained at the B3LYP/6-311+G(d,p) level of theory are presented also in Figure 3. The O-H stretching 0 f 1 and 1 f 2 transition frequencies are 1718 and 807 cm-1, respectively, in the lowest energy form with the 6-31+G(d,p) basis set. The corresponding values obtained at the B3LYP/6-311+G(d,p) level of theory are 1918 and 727 cm-1, respectively. For the proton-transferred form, transition frequencies of 861 and 1089 cm-1, respectively, were obtained for the 0 f 1 and 1 f 2 transitions using the double-ζ splitvalence basis set. With the triple-ζ split-valence basis set, the two transitions were found at 1041 and 942 cm-1, respectively. The double-ζ split-valence basis set 0 f 1 transition frequencies appear systematically red-shifted by ca. 200 cm-1 with respect to the triple-ζ split-valence results. The net difference in the frequencies between the 0 f 1 and 1 f 2 transitions clearly indicates an anharmonic motion of the proton along the strong hydrogen bond. Indeed, the proton wave function can be seen in Figure 3 to be far from zero close to the top of the barrier for proton transfer. It is interesting to note that, although the 1 f 2 frequency is lower than the 0 f 1 frequency in the lowest energy (molecular) form, the contrary is found for the protontransferred form with the double-ζ split-valence basis set. In the proton-transferred form, the first excited state samples both

Jezierska-Mazzarello et al. wells nearly equally, correlating with a very low 0 f 1 frequency, below 1000 cm-1. On the other hand, the wave function of the second excited state, above the top of the barrier, is more strongly penetrating the repulsive wells at 0.9 and 1.7 Å, shifting the 1 f 2 transition to higher frequencies. Such change of anharmonicity of the asymmetrical proton motion in the O · · · H · · · N bridge is difficult to grasp from steady-state infrared spectroscopy but could be probed using infrared pump-probe techniques93 or two-dimensional IR spectroscopies.94 The strong dependence of the 0 f 1 transition on the tautomerism of the H2 proton suggests that a broad absorption from the O-H stretching mode can be anticipated when thermal fluctuations are taken into account. 3.2. Molecular Dynamics in Vacuo. Analysis of the Vibrational Model. Starting from the optimized molecular structure of the ortho-hydroxy Schiff base (2-(N-methyl-Riminoethyl)-4-chlorophenol) in vacuo displayed in Figure 1, a molecular dynamics simulation was performed at 300 K. The time evolution of the interatomic distances of the atoms involved in the hydrogen bridge is shown in Figure 4. It is evident that the O-H distance significantly fluctuates and the proton (H2) is very labile. Proton-transfer phenomena are observed a few times during the simulation, although the proton is localized most of the time in the vicinity of the (O1) atom. The average distance between the donor (O1) and acceptor (N3) obtained as a result of the MD simulation is 2.513 Å, which is considered to be a short H-bond and is consistent with the presence of the labile proton. There is not a clear correlation between the proton transfer events and O-N distance. This indicates that the reaction coordinate for the proton transfer involves other deformations of the molecule than just local O-N stretching. The proton is also able to stay for a short time (up to 0.2 ps) at the acceptor site, which is consistent with the model of double-well potential with the well shape modulated by vibrational modes involving other internal coordinates of the molecule. The predicted infrared (IR) spectrum obtained based on CPMD simulation in vacuo is presented in Figure 5. Continuous O-H absorption is visible in the range between 1600 and 3050 cm-1, but at both ends of this range, there is an overlap with C-H modes (ca. 3000 cm-1) and heavy atom vibrations below 1600 cm-1. The power spectrum of the atomic velocities is presented in Figure 6. The strongest O-H absorption is observed in ranges between 900 and 1050 cm-1 and 1400 and 1600 cm-1. This power spectrum for the O-H motion displays a continuous background between 900 and 2700 cm-1, the signature of a labile proton and a strong H-bond. This motion is then responsible for the broad infrared absorption predicted in the 1600-3050 cm-1 range (Figure 5). The atomic velocity power spectrum, which allows identification of individual contributions of atoms, indicates that the C-H modes form three distinct peaks: at 3000, 2900, and 2850 cm-1. Experimental positions of these bands are, respectively, 2980, 2920, and 2850 cm-1 (see Figure 5). Very good agreement of these values is an indication that the description of the system provided by the assumed FPMD protocol produces results of good quality. Because of relative chemical inertness of the carbon-bound hydrogen atoms, the C-H modes are rather not sensitive to the presence of solvent such as CCl4. Let us now return to the vibrational spectral signature of the proton in the O · · · N bridge. The broad O-H absorption is consistent with the large extent of proton delocalization in the bridge, and also with the experimental IR spectra of the studied Schiff base in CCl4 solution.24,95 The polarity of CCl4 is low enough to permit direct


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Figure 4. Evolution of the interatomic distances of the atoms involved in the hydrogen bridge. Results obtained from CPMD simulation in vacuo.

Figure 5. Predicted IR spectrum of the ortho-hydroxy Schiff base studied. Results obtained from the CPMD simulation in vacuo. Intensities, in arbitrary units, are proportional to the observable IR intensities. The thick line represents the experimental spectrum of the studied compound, redrawn from the data of ref 24.

comparison with the gas phase; it was found that the O-H stretching mode is red-shifted by this solvent by usually 100-150 cm-1 with respect to the measurements in the gas, which corresponds to an ∼1 kcal/mol increase in the hydrogen bond energy.96 The experimental IR spectrum of 2-(N-methylR-iminoethyl)-4-chlorophenol was recorded in the 1700-3500 cm-1 range,24 and the O-H stretching band is located between 1900 and 3100 cm-1 (see Figure 5); at both ends of this range, there is some overlap with the aromatic ring and C-H modes.24,95 The experimental maximum of absorption at 2580 cm-1 in CCl4 is reproduced in the gas-phase calculations as 2350

cm-1. Although carbon tetrachloride may be able to modify proton potential in the highly anharmonic bridge of the studied molecule, at least part of this computational red shift is, however, caused by the assumed theoretical model for reproducing the PES (a combination of the BLYP DFT functional with planewave basis set) as well as the effect of the finite fictitious electron mass used to propagate the Kohn-Sham determinant coefficients according to the Car-Parrinello scheme.60,97,98 The analysis of the accuracy of the vibrational model requires assessment of this artificial red shift on various modes. This can be carried out by comparison of the proton contribution to

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Figure 6. Atomic velocity power spectra obtained for all of the atoms (black line) and the H2 hydrogen bridge proton (gray line) of the orthohydroxy Schiff base (2-(N-methyl-R-iminoethyl)-4-chlorophenol) molecule. Results from the CPMD simulation in vacuo.

the vibrational power spectrum (Figure 6) with the experimental and computationally predicted IR spectra (Figure 5). The features in the 1600-1800 cm-1 window are not connected with the proton motion, and it is observed that they are reproduced with minimal (less than 50 cm-1) red shift. The distinct feature at 1850 cm-1 might contain contribution from the bridged proton (on the basis of Figure 6), but it is also reproduced without significant red-shifting. Harmonic but high-frequency C-H modes are predicted to lie at 3000, 2900, and 2850 cm-1, as mentioned above, and these positions match exactly the experimental positions, even if the relative intensities of these modes in the calculated spectrum in Figure 5 do not exactly match the experiment. Additionally, we can observe that the limits of the high-frequency signature of the hydrogen-bonded proton are also correctly reproduced. Thus, we can conclude that the computational model for reproduction of the spectra works very well for harmonic and heavy-atom modes. For the strongly anharmonic hydrogen bridge stretching, the shape of the spectral feature is reproduced correctly but with shifted position of the maximum. The increased red-shifting is a result of combination of the used DFT plane-wave approach and CPMD-related “orbital drag” effect (aggravated by strong anharmonicity of the PES for this mode). Particularly, insight into the dynamics of the bridge proton (Figure 4) shows that it is very labile and exhibits frequent jumps to the acceptor side. In such a case, even small modifications of the PES can have a large impact on the reproduced IR spectrum. The BLYP functional underestimates the proton-transfer barrier in some, but not all, cases,99,100 and in view of the very small red shift of the C-H modes, we consider this fact the main reason for the shift of the maximum of the bridged proton signature in our prediction. Potentially, the low-barrier hydrogen bond present in the analyzed case might also be influenced by the nuclear quantum effects. Overall, the developed model is satisfactory concerning the accuracy of the prediction for this strongly anharmonic system. 3.3. Solid-State Calculations. The molecular dynamics in the gas phase showed that the proton in the investigated hydrogen bridge is rather delocalized and exhibits large

amplitude motions. Such a labile proton is expected to be very sensitive to external perturbations, such as an applied electric field (e.g., Zundel polarization).101,102 This environmental influence on molecular properties was studied here by considering the solid state. It is believed that hydrogen bonding can affect thermochromic and photochromic properties of Schiff bases.27 However, direct structural observation of the temperature dependence of the proton position is difficult. It is worth mentioning here a neutron diffraction study for the intermolecular complex of p-methylpyridine with pentachlorophenol,103 where smooth transition from O · · · H-N at 20 K through O · · · H · · · N at 90 K to O-H · · · N at room temperature was observed. The experimental crystal unit cell24 was used as a model for the MD simulation. The fluctuations of the interatomic distances (O-H · · · N) as a function of time were analyzed for both molecules in the crystal cell. The obtained results are similar, and only data for one molecule are presented in Figure 7. They show that, contrary to the gas phase, the proton is now located on the nitrogen atom (N3) side. Also in the solid state, the proton-transfer phenomena were not observed during the MD run; however, there were fluctuations leading to short instantaneous equalization of the O-H and H-N distances. Environmental effects thus appear to play an important role in the proton localization for Schiff base crystals (see Figure 8 for a view of the studied crystal). This is most probably due to two effects: (i) the interaction between the labile protons and the chlorine atom in the vicinity (5.15 Å) of N3, which attracts the positively charged proton and (ii) the interaction between the intramolecular H-bonds due to the charge reorganization induced by the proton transfer that electrostatically couples the two protons in the unit cell (note the antiparallel arrangement of neighboring molecular dipoles, Figure 8). Indeed, movement of the proton in such short, strong hydrogen bridges leads to large changes of an instantaneous dipole moment, which in turn is visible in the intensities of the corresponding IR spectra. DFT calculations for isolated molecules (see section 3.1) estimate the dipole moment of the O-H · · · N form to be 3.56 D, and 5.60 D for the O · · · H-N form. This fact indicates also that the arrangement of molecules



Figure 7. Time evolution of the interatomic distances involved in the hydrogen bridge. Results obtained from CPMD simulation in the solid state.

TABLE 4: Influence of k-Points Sampling the Brillouin Zone on the Geometrical Parameters (in Å) of the Hydrogen Bridge in the Crystal of 2-(N-methyl-r-iminoethyl)-4chlorophenol, Results of the CPMD Geometry Optimization

Figure 8. View of the crystal of 2-(N-methyl-R-iminoethyl)-4chlorophenol along the b axis (data from ref 24). The unit cell is marked, chlorine atoms are presented as large spheres, and hydrogen atoms are omitted for clarity except for the protons of the N-H · · · O intramolecular bridges. Only one molecule of the bottom layer (in wireframe representation) is visualized.

in the crystal (Figure 8) provides more electrostatic stabilization for the proton-transferred form with its larger dipole moment. The k-point sampling of the Brillouin zone was performed to check the validity of the Γ-point approximation used in further molecular dynamics runs. The obtained results are presented in Table 4. The interatomic distances of the atoms involved in the intramolecular hydrogen bond are not changed significantly. The donor-acceptor distance is increased by ca. 0.009 Å when 2 × 2 × 2 and 4 × 4 × 4 k-point meshes are used. However, the location of the proton at the N3 atom is not changed. The results of the geometry optimization are practically identical for both meshes, which indicates that the properties of the crystal quickly

interatomic distances

Γ-point

2×2×2 mesh

4×4×4 mesh

O1 · · · N3 O1-H2 H2 · · · N3

2.534 1.572 1.074

2.543 1.586 1.071

2.543 1.585 1.071

converge. The very small effects of an increased k-point mesh allow us to be confident of the validity of the Γ-point approximation in the current study. The description of the vibrational properties of the studied molecular crystal was performed on the basis of the dipole moments and atomic velocities. The predicted IR spectrum (see Figure 9) shows strong N-H absorption between 2200 and 3100 cm-1, but the upper bound is not resolved because of overlap with C-H modes. The power spectrum of the atomic velocities offers the possibility of decomposing the vibrational features into a single atom contribution (see Figure 10). The strongest N-H motion intensity occurs between 900 and 1100 cm-1 and 1450 and 1600 cm-1. In addition, the high-wavenumber stretching region occurs between 2200 and 2900 cm-1. The increased localization of the proton leads to N-H vibrations which are more localized and at higher frequencies (centered at 2700 cm-1) compared with the gas-phase results for the O-H motion. This adds strength to our statement at the end of section 3.2. 3.4. Path Integral Molecular Dynamics. In order to enrich our study of the proton localization in the hydrogen bridge, path integral molecular dynamics (PIMD) in the solid state was performed for 2-(N-methyl-R-iminoethyl)-4-chlorophenol. Quantization of the nuclear motion is not included in the standard FPMD-CP calculation; therefore, the PIMD approach gave us insight into the behavior of light atoms with respect to the classical approximation for the nuclei. Since the path integral approach does not yield the real-time quantum dynamics of the

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Figure 9. Predicted IR spectrum of the ortho-hydroxy Schiff base (2-(N-methyl-R-iminoethyl)-4-chlorophenol) studied. Results obtained from CPMD simulation in the solid state. Intensities, in arbitrary units, are proportional to the observable IR intensities.

Figure 10. Atomic velocity power spectra obtained for all atoms (black line) and for the H2 hydrogen bridge proton (gray line) of the studied ortho-hydroxy Schiff base (2-(N-methyl-R-iminoethyl)-4-chlorophenol). Results obtained from the MD simulation in the solid state.

system but enables the calculation of ensemble averages only,67 the results are presented as a histogram of two distances defining the hydrogen bridge geometry: the O-N and N-H separations. Figure 11 presents this histogram for both the standard FPMDCP run and the PIMD simulation. Such a histogram describes the relationship of two statistical variables; if these variables are relatively uncorrelated, the joint probability density distribution P(X,Y) should be a product of the two marginal distributions P1(X)P2(Y), leading to a rectangular shape of the histogram contour lines. In the studied case, while classical nuclear dynamics (FPMD-CP) displays rather small coupling between the two investigated parameters (the respective isocontour is oval-shaped but oriented vertically), the PIMD results clearly

show that smaller O-N distances lead to a larger spread of the N-H bond lengths (the PIMD histogram is strongly flattened at the base). The effect of nuclear quantization of the proton motion is therefore more pronounced in instances of the shortened hydrogen bridge found in the simulation. Quantum effects also lead to changes in the structural parameters of the bridge. The values of the O-N distance lie in the range 2.39-2.73 Å for the FPMD-CP and 2.39-2.65 Å for the PIMD run. The N-H bond lies within the 1.0-1.2 Å range for the FPMD-CP and 0.97-1.3 Å for the PIMD. These values indicate that quantum effects for the nuclear motion lead to increased proton sharing and decreased bridge length. The latter phenomenon can be understood from the 1D vibrational states calculated



Figure 11. Two-dimensional histogram of H2 proton localization in the hydrogen bridge in the solid state obtained from path integral molecular dynamics (PIMD). Isoline values for the probability density plot are 5 and 15 Å-2 for the outer and inner contours, respectively.

in the gas phase (Figure 3). It can indeed be said that, for the tautomeric form, the probability density maximum of the ground-state wavepacket is situated at a larger N-H distance than the potential energy minimum. This is due to quantum penetration of the proton inside the barrier region. This is accompanied by an overall strengthening of the hydrogen bond in the investigated Schiff base. The increase in proton sharing will manifest as a broadening of the bridge proton vibrational signature in the IR spectrum with respect to our predictions based on the classical FPMD-CP trajectory. 4. Conclusions Computational investigations based on static and molecular dynamics approaches were performed for a compound of the Schiff base family. The studied Schiff base belongs to the class of systems exhibiting a low-barrier hydrogen bond. Static gasphase calculation locates the proton on the oxygen side, forming the enol tautomer, with a low barrier for proton transfer suggesting that the proton in the bridge is labile. Potential energy curves for the two accessible tautomers show very anharmonic potentials strongly modulated by the molecule conformation. A stronger hydrogen bond is formed when the hydrogen is transferred to the nitrogen side, but overall energy is lower for the molecular form in the static gas-phase model. AIM theory was used to correlate these observations with changes in the electronic density distribution. First-principle molecular dynamics in the Car-Parrinello framework in the gas phase showed a labile proton in the strong intramolecular H-bond, though mostly located on the oxygen side. It was found, however, that the proton is located on the nitrogen side in the crystal phase, confirming X-ray diffraction studies. This is thought to arise from interaction of the O-H · · · N groups in the crystal phase with one another and with a Cl substituent in the close vicinity of the nitrogen site in the crystal structure. Proton delocalization is also more important in the gas phase than in the crystal phase. This is reflected in the calculated IR spectra for both phases, where the gas-phase spectrum displays a very large absorption continuum between 850 and 2500 cm-1. This stabilization of the N-H tautomer is also confirmed in the crystal when quantum effects are included using path integral techniques.

Finally, the mechanism of proton transfer in the studied Schiff base does not appear to be governed simply by the O-N distance, since environmental effects were shown to play an important role on the proton localization. Static calculations indicate that the π electron skeleton is also involved in this process. Further studies are now in progress to determine the modes that are coupled to the proton-transfer reaction. Also, work is going on to study related compounds and describe systematically the effect of substitution both in the gas phase and in the crystalline phase. Acknowledgment. A.J.-M. and J.J.P. would like to thank Professor Aleksander Koll for a fruitful discussion. Additionally, A.J.-M. would like to thank Dr. Harald Forbert for the program for power spectrum/Fourier transform of the autocorrelation function. The work was performed within the Project HPCEUROPA (RII3-CT-2003-506079) with the support of European Community-Research Infrastructure Action under the FP6 ‘Structuring the European Research Area Program’. In addition, A.J.-M. and J.J.P. gratefully acknowledge the Wrocław Center for Networking and Supercomputing (WCSS), the Academic ´ W (Grants KBN/SGI/ Computer Center CYFRONET-KRAKO UWrocl/078/2001 and KBN/SGI/UWrocl/029/1998), and the Poznan´ Supercomputing and Networking Center for providing computer time and facilities. References and Notes (1) Filarowski, A.; Głowiak, T.; Koll, A. J. Mol. Struct. 1999, 484, 75–89. (2) Kro´l-Starzomska, I.; Filarowski, A.; Rospenk, M.; Koll, A.; Melikova, S. J. Phys. Chem. A 2004, 108, 2131–2138. (3) Filarowski, A. J. Phys. Org. Chem. 2005, 18, 686–698. (4) Bonder, A.-N.; Fischer, S.; Smth, J. C.; Elstner, M.; Suhai, S. J. Am. Chem. Soc. 2004, 126, 14668–14677. (5) Russell, T. S.; Coleman, M.; Rath, P.; Nilsson, A.; Rothschild, K. J. Biochemistry 1997, 36, 7490–7497. (6) Hayashi, S.; Ohmine, I. J. Phys. Chem. B 2000, 104, 10678–10691. (7) Baudry, J.; Tajkhorshid, E.; Molnar, F.; Phillips, J.; Schulten, K. J. Phys. Chem B 2001, 105, 905–918. (8) Osterman, A. L.; Brooks, H. B.; Jackson, L.; Abbott, J. J.; Phillips, M. A. Biochemistry 1999, 38, 11814–11826. (9) Islam, M. M.; Hayashi, H.; Mizuguchi, H.; Kagamiyama, H. Biochemistry 2000, 39, 15418–15428. (10) Sayer, J. M.; Conlon, P. J. Am. Chem. Soc. 1980, 102, 3592– 3600.

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JP903501M

Molecular Property Investigations of an ortho-Hydroxy Schiff Base

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