CarâParrinello and Path Integral Molecular Dynamics Study of the

Subscriber access provided by University of Sussex Library

B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Car-Parrinello and Path Integral Molecular Dynamics Study of the Proton Transfer in the Intramolecular Hydrogen Bonds in the Ketohydrazone-Azoenol System Piotr Durlak, and Zdzislaw Latajka J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b04883 • Publication Date (Web): 30 Jul 2018 Downloaded from http://pubs.acs.org on August 3, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Car-Parrinello and Path Integral Molecular Dynamics Study of the Proton Transfer in the Intramolecular Hydrogen Bonds in the Ketohydrazone-Azoenol System. Piotr Durlak*, Zdzisław Latajka Faculty of Chemistry, University of Wrocław, 14 F. Joliot-Curie Str., 50-383 Wrocław, Poland.

Abstract Car-Parrinello and path integrals molecular dynamics simulations were carried out for 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) (Sudan I) in vacuo and in the solid state at 298 K. The fast proton transfer (FPT) and tautomerism in the ketohydrazone-azoenol systems have been analyzed on the basis of CPMD and PIMD methods level. Two-dimensional free-energy landscape of reaction coordinate δ-parameter and RN...O distances shows that the NH tautomer to be more favorable as well as in the gas phase and solid state according respectively to the CP and PI results. The hydrogen between the nitrogen and the oxygen atoms adopts a starkly asymmetrical position in the double potential well. The molecular geometry and energy barrier for the intramolecular proton transference were calculated and the value found suggested a strong hydrogen bond with low barrier for FPT mechanism. These studies and the two-dimensional average index of π-delocalization 〈λ〉 landscape of time evolutions of RN1…O1 and RC1=O1 distances for the both crystals indicate that hydrogen bonds in the crystals of 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) have characteristic properties for the type of bonding model resonance-assisted hydrogen bonds (RAHB) and also low barrier hydrogen bonds (LBHB) without existing the equilibrium of the two tautomers. The infrared spectrum has been calculated, and a comparative vibrational analysis has been performed. The CPMD vibrational results appear to qualitatively agree with the experimental ones.

1. Introduction In the last year, for the first time ever, physicists have managed to directly detect a hydrogen bond within a single molecule.1 The hydrogen atom - the smallest and most abundant atom is of utmost importance in physics and chemistry.1 Hydrogen bond is the most important of all directional intermolecular interactions.2 Hydrogen bonded systems play also a very important role in many physical, chemical and biological processes.3-12 Most often we share hydrogen bonds on the three main classes: strong, moderate and weak. After many years of research 1318

and attempts to classify hydrogen bonds for parameters like: the length and angle of the

bond, the energy of the bond, the position of the proton in the hydrogen bridge, and the IR frequency shift of X-H stretching vibration, we know that the division of hydrogen bonds into three major classes is a significant simplification. During the recent years of structural and theoretical investigations 19-24 of hydrogen bonds focused on a group of strong and very strong hydrogen bonds, it was noted that some of them exhibited atypical structural and physicochemical anomalies caused by π-bond cooperativity phenomena. The first comprehensive classification of homonuclear O-H…O bonds, inclusive of very strong ones, is due to Gilli

25

and co-workers, who suggested, on the grounds of a large 1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 38

neutron and X-ray crystal structure evidence, that there can be only three classes of really strong H-bonds: (i) (-)CAHB: [O…H…O]-, negative-charge-assisted H-bonds; (ii) (+)CAHB: [O…H…O]+, positive-charge-assisted H-bonds; and (iii) RAHB: -O-H…O, resonance-assisted H-bonds or π-cooperative H-bonds, where the two oxygen atoms are connected by a π-conjugated system of single and double bonds.26 Gilli and co-workers have confirmed in a series of publications 27-33 on the validity of the theory on the new division of very strong hydrogen bonds. It should also be added that in the cited work 25, there are made classifications for moderate H-bonds and untypical, weak, isolated H-hydrogen bonds. Keto-enol tautomerism (KET) is very important in carbonyl chemistry (carbonyl specialty reactions) and also in several areas of biochemistry.34 In recent years, much attention has been paid to the experimental and theoretical studies of keto-enol tautomerism and proton transfer in enol tautomer of phenols 35, aldehydes 36-42, β-diketones 43-47 and hydrazones.48-50 Hydrogen-bonded systems, in the solid phase, have attracted considerable attention over the years. Especially interesting are those structures where hydrogens are transferred in a tautomeric change.50,51 In the professional literature, we can also find several important publications

52-54

in the subject of the proton dynamics in the solid state using dynamic

methods, but with a different approach to the implementation of quantum effects. These effective methods are QWAIMD or method proposed by Mavri and Panek for example, they give very good compatibility especially in terms of vibrational frequencies with the experiment and other methods that take into account quantum effects. But in our opinion the PIMD method formulated on Feynman’s description of quantum statistical mechanics in terms of path integrals

55

is one of the most efficient methods. Fast proton transfer between

donor and acceptor atoms is a paramount importance in many aspects of chemistry and biology. Applications are various and include many technological developments

56

such as

hydrogen fuel cells, electrochromic displays, gas/humidity sensors, electrochemical reactors, and even the basis of optical data storage devices.56,57 On the basis of quoted publications it appears that, the knowledge of processes of proton exchanges in solids is fundamental to an understanding of the structure and behavior of such solids and many other chemical interactions. In the present article, for the first time, we have described the structures, proton motion, the two-dimensional free-energy landscapes, the shapes of the N-H…O potential function and also the two-dimensional π-delocalization index landscapes in the 1(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) both in the vacuo and in the solid state. The studied compound belongs to the group of organic azo dyes suspected of 2 ACS Paragon Plus Environment

Page 3 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


carcinogenic properties. In trade is colloquially called Sudan I. We decided to use molecular dynamics approaches. From a theoretical perspective the accurate modeling of proton transfer dynamics in hydrogen bonded systems is a challenging problem. Therefore in this paper two types of molecular dynamics simulations were carried out. Firstly, the behavior of all atoms was treated classically within the Car-Parrinello (CPMD) formalism.58 Secondly, the path integrals molecular dynamics (PIMD) was applied.59-61 Within the PIMD approach it is possible to obtain more reliable description of nuclear motion due to the quantum effects incorporated in the simulations. It maps the problem of a quantum particle into one of a classical ring polymer model with N beads that interact through temperature and mass dependent spring forces. In practice, the representation of each atom in the system as a group of N beads requires N electronic structure calculations, and therefore requires much larger computational expense than CPMD. The organization of the paper after introduction section is as follows: in section 2, the applied computational methods are presented; section 3 contains results and discussion, whereas the final conclusions are given in the last paragraph.

2. Computational details 2.1. Static calculations in the crystal phase. A series of full geometry and cell optimizations with the London-type empirical correction for dispersion interactions as proposed by Grimme

62

, together with the vibrational harmonic

frequency calculations, were undertaken to localize the key stationary points on the potential energy surface (PES) of the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) in the solid state. For the crystal the structural data was taken from the X-ray Crystallographic study by Gilli

48,49

and co-workers and Olivieri.50 Calculations were

performed using the CRYSTAL09 program functional

65,66

63,64

, utilizing the DFT method with PBE

with the two shrinking factors (8, 8) to generate a commensurate grid of k-

points in reciprocal space, following Monkhorst-Pack method.67 Calculations were carried out with the consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations (pob_TZVP_2012) as proposed by Peintinger, Vilela Oliveira, and Bredow.68 For the both crystals (I) and (II) vibrational frequencies calculations in CRYSTAL09 were performed at the Γ-point.63,64

3 ACS Paragon Plus Environment


Page 4 of 38

2.2. Dynamic and quantum dynamic simulations in the crystal phase. Molecular dynamics calculations were carried out using the CPMD program version 3.15.3. 69 The initial molecular configuration for the 1-(Phenylazo)-2-naphthol (I) and 1-(4-FPhenylazo)-2-naphthol (II) crystals was optimized by the preconditioned conjugate gradient (PCG) method with the London-type empirical correction for dispersion interactions as proposed by Grimme

62

also with Periodic Boundary Conditions (PBCs) employed for the

solid state calculations. In these cases, the real space Ewald summation of electrostatic interactions was carried out taking into account 8 cell replicas in each direction. We also generated the Monkhorst-Pack mesh (3,3,3) for calculated k-points in reciprocal space in each direction. The crystals data from the X-ray Crystallographic study by Olivieri workers for the crystal (I) and Gilli and co-workers

48, 49

50

and co-

for the crystal (II) respectively were

selected as starting points. The crystals are monoclinic, 1-(Phenylazo)-2-naphthol (C2/c) with cell dimensions a = 14.928, b = 27.875, c = 6.082 Å, and α = γ = 90°, β = 103.57° with eight formula units in the unit cell (Z=8) and 1-(4-F-Phenylazo)-2-naphthol (P21/c) with cell dimensions a = 3.982, b = 27.146, c = 11.669Å, and α = γ = 90°, β = 97.6° with four formula units in the unit cell (Z=4). Molecular dynamics (NVT ensemble) were carried out at 298 K respectively with a time step of 3.0 a.u. (0.072566 fs), coupled to a Nosé-Hoover chains thermostat

70

at a frequency of 3200 cm−1. The experimental values of unit cell parameters

were used in the CPMD and PIMD simulations. An electronic mass parameter of 400 a.u. was employed. An electronic exchange and correlation have been modeled using the gradientcorrected functional of Perdew, Burke and Ernzerhof (PBE).65,66 Core electrons were treated using the norm-conserving atomic pseudopotentials (PP) of Troullier and Martins

71

, while

valence electrons were represented in a plane-wave basis set truncated at an extended energy cut-off of 80 Ry. Following the initial equilibration period (5 ps), data was accrued for further 60 ps for crystals (I) and (II) Car-Parrinello and for the both crystals imaginary-time (60 ps) for the path integral dynamics simulation, carried out at 298 K, respectively for eight (PI8) Trotter replicas (polymer-beads) using the normal mode variable transformation. The data was visualized using the VMD

72

and Gnuplot

73

programs; with the path integral data first

processed using a script by Kohlmeyer to calculate the centroid position of each set of polymer-beads. 74 The vibrational spectrum was also calculated using the Fourier transformation of the dipole autocorrelation function obtained from dipole trajectories generated by the CPMD simulation facilitated by the scripts of Forbert and Kohlmeyer.75 It is important to point out that this approach includes anharmonic effects and all of the vibrational modes for molecules 4 ACS Paragon Plus Environment

Page 5 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


in crystals. The lattice vibrations were not received because fixed experimental values of unit cell were used.

2.3. Dynamic and quantum dynamic simulations in the gas phase. A series of molecular dynamics simulations, together with calculations of changes in dipole moment have been performed for the isolated systems: 1-(Phenylazo)-2-naphthol (I), 1-(4-FPhenylazo)-2-naphthol (II). For the simulations conducted for isolated molecules at the CPMD and PIMD method levels we have used the same physical parameters settings like those used for the solid state calculations, except for the below described. The isolated molecules were placed in the simple cubic boxes of dimensions a = 20 Å. Following the initial equilibration period (3ps), data was accrued for further 60 ps for CP simulations and for (60 ps) imaginary-time for the path integral dynamics simulation (PI), carried out at 298 K, respectively for sixteen (PI16) Trotter replicas (polymer-beads) using the normal mode variable transformation.

3. Results and discussion 3.1. Chemical bonding and molecular structure. The molecular geometry and atoms labeling of 1-(Phenylazo)-2-naphthol (I) and 1-(4-FPhenylazo)-2-naphthol (II) in the gas phase are shown in Fig. 1. We have also presented on the Fig. 2 and Fig.3 structures of the studied crystals (I) and (II) respectively. For the sake of simplicity in the solid state molecular structure (in the unit cell) have the same description of the number of atoms as in the case of compounds in the gas phase.

Fig. 1 Molecular structure and selected atoms labeling of 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2naphthol (II) in the gas phase.



Page 6 of 38

In Table 1, the calculated selected interatomic distances and angles after optimization compared with the average geometrical parameters from CPMD (standard deviation in brackets) and with the existing experimental data for both the crystals and additionally the molecules (I) and (II) in the gas phase are presented. As can be inferred from Table 1, distances between heavy atoms in the hydrogen bond (N1–O1) in the studied crystals are very short and have a similar length regardless of the method of analysis. However, in both cases, it should be noted that the lengths of hydrogen bonds, derived from calculations at the CPMD method level are closer to the experimental values than to the static calculations. The comparison of the CP calculated values versus experimental for the length of the hydrogen bridge in the studied crystals is as follows: (I) 2.550 vs. 2.552 Å and (II) 2.532 vs. 2.535 Å. It should also be noted that the calculations reproduce the correct trend relative to the experiment for a small difference in the hydrogen bridge lengths between crystal (I) and (II). The experimental difference in the length of hydrogen bridges is 0.017 Å. For the computational methods, static and molecular dynamics these differences are exactly the same for the both crystals and are about 0.018 Å. It shows very good agreement of computed MD geometrical parameters with the X-ray diffraction experiment.48-50 The very large nonlinearity of the hydrogen bond is noteworthy. Each of the methods of calculation indicates that the angle values of the hydrogen bridge are between 136 and 143 degrees, which are close to the experimental data. 48-50 Similar trends are maintained in the results of calculations for molecular geometry also for the gas phase presented comparatively in Table 1. As we can see in the Table 1 the lengths of the remaining bonds of studies molecular systems are reproduced during the calculation with very good accuracy in relation to the experiment, and the average error of calculation is about 6%. The results of static and dynamic calculations are very similar. This fact and the geometric analysis carried out in Table 1 allow us to believe that the assumptions we used and the parameters adopted for quantum methods were correct. At this point, the presented comparison of selected calculated geometric parameters with experimental data, in our opinion confirms the need to implement the currently available extensions and new techniques during calculations based on the quantum chemistry computational methods. We want to emphasize that these very good and concurrent results correlate directly with the application of additional parameters to our calculations, such as: analytical corrections to the total energy of the system resulting from the occurrence of dispersion interactions as proposed by Grimme, the use of k-points, quantum effects incorporated in the simulations and the use of relatively large functional basis sets. In the precalculations tests, we noticed that the use of Grimme correction significantly affects to the 6 ACS Paragon Plus Environment

Page 7 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 1 Calculated selected geometrical parameters after optimization from the gas phase and the solid state compared with the average geometrical parameters from CPMD (standard deviation in brackets) and the existing experimental data for the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) (bond lengths and unit cell parameters are in Å, angles are in degrees).

Gas phase Parameter

N1-H1 H1...O1 N1...O1 C1-O1 N1-N2 N2-C2 C1-C2 C2-C3 C3-C4 C4-C5 C5-C6 C1-C6 N1-C7 ∠ N1-H1...O1 ∠ H1-N1-N2 ∠ O1-C1-C2 a b c α β γ

Static PCG/PBE/ 80Ry I II 1.058 1.062 1.638 1.606 2.540 2.521 1.270 1.272 1.307 1.308 1.338 1.339 1.472 1.470 1.459 1.459 1.423 1.423 1.438 1.437 1.362 1.362 1.447 1.445 1.399 1.399 139.9 140.9 115.0 114.6 121.5 121.4

Solid state

CPMD avg. PBE/80Ry I 1.115 (0.152) 1.582 (0.213) 2.537 (0.081) 1.279 (0.301) 1.312 (0.026) 1.346 (0.028) 1.471 (0.035) 1.461 (0.030) 1.427 (0.027) 1.441 (0.028) 1.365 (0.024) 1.448 (0.031) 1.407 (0.029) 141.2 (1.032) 115.8 (0.988) 121.6 (1.026)

II 1.202 (0.227) 1.464 (0.271) 2.523 (0.079) 1.291 (0.037) 1.308 (0.027) 1.353 (0.032) 1.462 (0.038) 1.459 (0.031) 1.429 (0.028) 1.438 (0.029) 1.368( 0.024) 1.442 (0.032) 1.406 (0.030) 141.1 (1.033) 114.8 (0.882) 121.7 (1.023)

Static PBE/pob_TZVP _2012 I II 1.047 1.048 1.716 1.686 2.582 2.564 1.279 1.281 1.337 1.336 1.339 1.338 1.471 1.434 1.459 1.459 1.424 1.422 1.435 1.434 1.360 1.359 1.443 1.440 1.403 1.401 136.8 138.0 115.9 115.3 121.5 121.4 27.254 3.875 6.031 27.227 14.731 11.527 90.0 90.0 102.8 98.1 90.0 90.0

CPMD avg. PBE/80Ry I 1.180 (0.231) 1.546 (1.296) 2.550 (0.093) 1.282 (0.036) 1.306 (0.028) 1.348 (0.031) 1.459 (0.037) 1.447 (0.029) 1.422 (0.028) 1.436 (0.029) 1.367 (0.025) 1.440 (0.032) 1.407 (0.029) 135.2 (1.320) 118.4 (0.888) 121.1 (1.035)

II 0.934 (0.128) 1.620 (0.246) 2.532 (0.081) 1.256 (0.026) 1.289 (0.025) 1.365 (0.029) 1.440 (0.033) 1.443 (0.028) 1.449 (0.029) 1.411 (0.027) 1.353 (0.024) 1.431 (0.031) 1.407 (0.032) 143.8 (1.290) 122.3 (0.325) 122.3 (1.485)

Exptl. 48-50 I 1.030 1.735 2.552 1.262 1.309 1.339 1.455 1.455 1.410 1.443 1.343 1.436 1.408 133.2 119.2 121.5 27.875 6.028 14.928 90.0 103.6 90.0

II 0.887 1.861 2.535 1.293 1.294 1.353 1.433 1.453 1.412 1.431 1.344 1.426 1.404 131.3 124.7 121.9 3.982 27.146 11.668 90.0 97.6 90.0

7

ACS Paragon Plus Environment


Page 8 of 38

Fig. 2 Unit cell and selected atoms labelling of 1-(Phenylazo)-2-naphthol crystal (I).

Fig. 3 Unit cell and selected atoms labeling of 1-(4-F-Phenylazo)-2-naphthol crystal (II).


Page 9 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


quality of restored cell parameters of crystals. Using pure DFT method level for calculations usually quite overestimates these quantities. Geometry analysis is not only a tool to confirm the correctness of molecular dynamics simulations, but also allows us to analyze subtle molecular effects for atypical hydrogen bonds, where every smallest deviation can have consequences in the formulated conclusions. Geometric analysis carried out at this stage allows us to initially conclude on the classification of the hydrogen bond occurring in the studied crystals. For analyzing the geometric structure of the molecule in terms of the prevalence of characteristics model RAHB we should carefully consider the length of the four bonds in the keto-enol parts of the molecule.

19,27

In the molecular systems of the

ketohydrazone-azoenol type, especially when we analyze heteronuclear hydrogen bonding NH...O, the matter of classification of this bond becomes a bit more complicated. The studied crystals (I) and (II) are classified as ketohydrazone-azoenol molecular systems with a heteronuclear hydrogen bond N-H...O therefore nine bonds will be used for the calculating πdelocalization index. 48 In this cited article Gilli and co-workers 48, based on Pauling equation, proposed a new formula (1) to calculate the π-Delocalization Parameters 〈λ〉. The average index of π-delocalization 〈λ〉 is calculated:

〈λ〉 = ∑ λ /4

(1)

where: λ1=n1-1; λ2=2-n2; λ3=1/2[n3+(n5+n6+n7+n8+n9)/5]-1; λ4=2-n4 and where n1 to n9 these are the lengths of the respective bonds. In our studies, the π-delocalization parameters for (I) and (II) crystals were described by relevant molecular distances n1=N1-N2; n2=N2=C2; n3=C1-C2; n4=C1=O1; n5=C2-C3; n6=C3=C4; n7=C4-C5; n8=C5=C6; n9=C1-C6. The resulting values from static calculation in the gas phase and in the solid state are presented in order: 〈λ〉(I)gas = 0.787; 〈λ〉(II)gas = 0.785; 〈λ〉(I)solid = 0.792; 〈λ〉(II)solid = 0.784. It can be concluded that the calculated values of 〈λ〉 parameter is typical for the ketohydrazone-azoenol molecular systems

48

with a heteronuclear hydrogen bond N-H...O and we have a relatively short

hydrogen bridge, so all of these features fit well in the assumptions of the RAHB model proposed by Gilli.

27

It should also be added that the statically calculated values of the 〈λ〉

parameter differ slightly from each other and regardless of whether they were calculated in the gas phase or in the solid state. They are also in good agreement with 〈λ〉 parameters calculated at the dynamic methods level, which will be presented in the following paragraphs.



Page 10 of 38

3.2. Molecular dynamics simulation. Using the CPMD and PIMD approach, the time evolution of the interatomic distances, single fast proton transfer free-energy profiles, two-dimensional free-energy landscapes, twodimensional average index of π-delocalization 〈λ〉 landscape and spectroscopic features were investigated on the basis of simulated gas phase in vacuo and solid state trajectories. All simulations were conducted at normal temperature for thermodynamic calculations at 298 K. It should be added that PIMD simulations are not standard calculations and due to a very high computational cost. Fig. 4 presents the distribution functions (δ-parameter) of proton position along the reaction coordinate on the basis of our results from the CP and PI method for studied molecules (I) and (II). As expected on the basis of previous experimental and theoretical reports

48-50

during simulation, in both cases a fast single proton transfer within the

heteronuclear hydrogen bridge N-H...O was observed. As we could imagine the simulation image of CP and PI is significantly different when analyzing Fig. 4 in terms of the mobility and location of the proton in the hydrogen bridge. First of all, it is clear that the proton is more mobile in the case of the crystalline phase for the both compounds (see Fig.4 c,d), and secondly the proton is much more mobile and delocalized in the case of the second compound (see Fig.4 b,d). However, it should be verified that the proton in both compound (I) and (II), whether in the gas or crystalline phase, occupies an asymmetrical position in the hydrogen bridge, more often staying on the nitrogen atom side. By integrating the surfaces under the curve of the diagram of distribution functions (δ-parameter) from CP and PI simulations, the so-called position ratio parameter of proton can be calculated. The resulting values of ratio parameter from dynamic calculation are presented in order in the gas phase: RCP(I)gas=0.904/0.095; RPI(I)gas=0.783/0.216; RCP(II)gas=0.737/0.262; RPI(II)gas=0.677/0.322; and in the solid state: RCP(I)solid=0.786/0.214; RPI(I)solid=0.644/0.356; RCP(II)solid=0.608/0.392; RPI(II)solid=0.544/0.456. The presented series of ratio parameter data confirms in full the above conclusions on the location of the proton in the hydrogen bridge and the occurrence of the phenomenon of non-equilibrium tautomerism in the both compounds. In addition the calculated ratio parameters (R) for the crystal of 1-(4-F-Phenylazo)-2-naphthol (II) results appear to qualitatively agree with the experimental ones from X-ray diffraction (64:36). 49 Fig. 5 show the free energy profiles for proton motion obtained from the CP and PI results. Free energy profiles were calculated following the equation:

∆F = −kT lnPδ

(2)


Page 11 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where k is the Boltzmann constant, T is the simulation temperature, and P(δ) is the proton distribution as a function of δ (the reaction coordinate), which is defined as the difference between the distances (rN1–H1- rH1–O1) and is a measure of the proton transfer degree in the hydrogen bond. The value of zero indicated the midpoint of the hydrogen position in H-bond. The profiles of free energy in Fig. 5 demonstrate a very low effective barrier for proton transfer even without an inclusion of quantum effects for the CPMD simulation. Calculations show that the quantity of the barrier for proton transfer in the crystal (I) and (II) from CP calculation is about 2.21 and 1.25 kcal*mol-1 and PI calculation decreases values to 0.58 and 0.51 kcal*mol-1 respectively.

Fig. 4 Comparison of the distribution functions (δ-parameter) from CPMD and PIMD simulations for the intramolecular H-bonds for the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) at 298 K in the gas phase (a,b) and in the solid state (c,d) respectively.



Page 12 of 38

Fig. 5 Comparison of the single proton transfer free-energy ∆F profiles from CPMD and PIMD simulations for the intramolecular H-bonds for the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) at 298 K in the gas phase (a,b) and in the solid state (c,d) respectively.

The above ∆F values for crystals (I) and (II) allow classifying the studied hydrogen bonds into the group of bonds called low-barrier hydrogen bonds (LBHB).

76

The profiles of free energy

in Fig. 5c,d demonstrate practically the absence of an effective barrier for proton transfer in the crystals (I) and (II) and the results for the gas phase seem to confirm this trend (see Fig. 5a,b). However, it should be noted, that the barrier for fast proton transfer (FPT) is slightly lower in the case of the second compound in both examined phases. Probably this behavior of the molecular system (II) results from the presence in the structure as a substituent of the fluorine atom. Our theoretical research also shows that in both cases it occurs during proton transfer we observed the potentials slightly asymmetrical wells with a double minimum. In addition the results of CP and PI simulations (the double well potential) are very similar to the experimental results and static DFT calculations from earlier Gilli’s studies. 48,49 For a meaningful analysis of proton mobility in the studied intramolecular H-bonds, we constructed two-dimensional free-energy landscapes from two-dimensional distribution of δ-parameter and N1...O1 distances, as illustrated in Fig. 6 and Fig. 7, for hydrogen bridge in the gas phase and crystal units respectively, for further analysis of the proton transfer.


Page 13 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 6 Two-dimensional free-energy landscape of δ-parameter (reaction coordinate) and N1…O1 distances for the 1-(Phenylazo)-2-naphthol (I) for CPMD (a) and PIMD (b) simulation in the gas phase at 289 K and the 1-(4F-Phenylazo)-2-naphthol (II) for CPMD (c) and PIMD (d) simulation in the gas phase at 289 K. The unit of ∆F free energy (potential of mean force) is kcal*mol-1.

Fig. 7 Two-dimensional free-energy landscape of δ-parameter (reaction coordinate) and N1…O1 distances for the 1-(Phenylazo)-2-naphthol (I) for CPMD (a) and PIMD (b) simulation in the solid state at 289 K and for the 1-(4-F-Phenylazo)-2-naphthol (II) for CPMD (c) and PIMD (d) simulation in the solid state at 289 K. The unit of ∆F free energy (potential of mean force) is kcal*mol-1.



Page 14 of 38

As shown in the Fig. 6, the panels (a) and (b) presented the free energy surfaces obtained for the 1-(Phenylazo)-2-naphthol (I) in the gas phase from (a) CPMD and (b) PIMD simulations. Similarly, the sections (c) and (d) of figures 6 were obtained for second compound 1-(4-FPhenylazo)-2-naphthol (II) also at the CP and PI method level. Fig. 7 has the same layout, but for calculations of compounds (I) and (II) carried out in the crystalline phase. Figures 6 and 7 are a development and supplement to the discussion on the value of the barrier and shape of the well potential for the mechanism of fast proton transfer in the studied crystals. Let us now briefly discuss the subtle effects from the shown abovementioned landscapes. During their analysis, several important conclusions can be drawn. First of all, our research indicates that the proton is more mobile in the second compound, regardless of the state of aggregation. At second, the proton is more mobile and delocalized in the crystalline phase for both compounds tested. Finally, it can be clearly seen that the proton in each examined situation occupies an asymmetrical position in the hydrogen bridge on the nitrogen side. As shown in sections a, c of figures 6,7, the free energy surfaces obtained from CP simulations have two minima while sections (b) and (d) obtained from PIMD simulations have also two minima, very subtle defined in each case. In addition, two-dimensional free-energy landscape of reaction coordinate δ-parameter and RN...O distances also shows that the NH isomer to be more favorable as well as in the gas phase and solid state according respectively to the CP and PI results. Chart analysis also confirms our suggestion that we have a strong hydrogen bond with very low barrier for FPT mechanism. According to Gilli and Gilli

12,27,48,49

for the description resonance assisted hydrogen

bonded systems, the very important so-called π-delocalization 〈λ〉 index is defined by the equation (1). In the previous paragraph of our publication, we calculated the theoretical values of π-delocalization 〈λ〉 index, using static optimized and average lengths of appropriate bonds. These index values are in very good agreement with the experimental and theoretical parameters studies by Gilli and co-workers.

48

In their cited publication for the two studied

crystals (I) and (II), the π-delocalization 〈λ〉 index values are 0.44, 0.63 and 0.78 for N-H...O tautomer, transition state N...H...O and N...H-O tautomer, respectively.

48

For a deeper

analysis of the nature of the studied intramolecular H-bonds, we constructed the twodimensional average index of π-delocalization 〈λ〉 landscape of time evolutions of RN1…O1 and RC1=O1

distances for the both crystals of 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-

2-naphthol (II). Fig. 8 shows the changes in average index of π-delocalization 〈λ〉 in time against changes in the length of the bonds in the keto-enol parts of the molecule. The section


Page 15 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) of the Fig. 8 corresponds to the crystal (I) while section (b) representative the crystal (II).

Fig. 8 Two-dimensional average index of π-delocalization 〈λ〉 landscape of time evolutions of RN1…O1 and RC1=O1 distances for the crystal of 1-(Phenylazo)-2-naphthol (a) and for the crystal of 1-(4-F-Phenylazo)-2naphthol (b), both from PIMD simulation at 298 K.

The data to prepare these landscapes comes from dynamics simulations taking in the account the quantum effects (PI). As we can see in Fig. 8a,b, the value of the index of π-delocalization 〈λ〉 is very similar for both studied crystals, although for the second one it is slightly larger. The acquired landscapes allow additionally following the time-evolution in the length of bonds (N1-O1; C1=O1) in the keto-enol part of the molecule. During the entire simulation and changes in the length of bonds in a representative the keto-enol part of the molecule, the 〈λ〉 index takes values in the range from 0.512 to 0.534. The obtained theoretical values of the 〈λ〉 index form PIMD simulations fit the previous research

48

and allow recognizing that we

are dealing with molecular systems in which the hydrogen bond exhibits the characteristics of resonance assisted hydrogen bonds. However, it should be noted that in this disordered molecular system there are two forms with slightly more contribution from the π-localized Ketohydrazone-azoenol (KA) form than π-localized Azoenol-ketohydrazone (AK) form. There are not many papers in the literature where CPMD or PIMD were applied to RAHB systems. Therefore we believe that our results are shed new light on the problem of RAHB phenomena and we are presenting the new perspective to ongoing discussions in this subject. We apply the other approach and admit new research methods. The main goal of this



Page 16 of 38

paper was the systematic theoretical studies of properties and hydrogen bonds dynamics in the Ketohydrazone-azoenol systems in the solid state. The standard ‘static’ ab initio calculations are very useful to obtain the information of the localization of critical points (minima and transition state structures) on the potential energy surface (PES). However, hydrogen bonded systems are not static but fluctuate in the femtosecond ultra-short time scale. Therefore, to summarize this paragraph of the publication, we would like to briefly compare the final results from the simulation at the dynamics method levels. Comparing the four main physical parameters, such as: distribution function, ratio parameter, free energy and π-delocalization index 〈λ〉, which were calculated on the basis of dynamic simulations, one should notice goodly differences between the image of results from CP and PI simulations. After incorporating quantum effects into the simulation, the distribution of the proton positions are different in comparison to the CP dynamics. The proton is subject to greater delocalization and more often stays in the middle area of the hydrogen bond, though maintaining asymmetry. This tendency can be seen especially in the previously presented differences in the value of the ratio parameter. Secondly, we have observed noticeably lower value of the potential energy barrier for the proton transfer mechanism. Finally the π-delocalization index are more precisely in proportion to value from CP simulation and indicate that in this disordered molecular system there are two forms with slightly more contribution from the πlocalized ketohydrazone-azoenol (KA) form than π-localized azoenol-ketohydrazone (AK) form. In summary, we can say that the only methods like CPMD and PIMD (where quantum effects are included) give realistic description of H-bonded systems. It is worth mentioning that the presence of fluorine substituent in 1-(4-F-Phenylazo)-2-naphthol due to the πconjugated double bond skeleton has relatively large influence on the shape the proton transfer free energy profiles on both levels of simulations as is presented in Fig. 5. The curves are more symmetrical indicating on increase role of the N…H-O hydrogen bond form in comparison with not substituted system. Also on this basis, one can strongly suggest the RAHB character of the hydrogen bond in studied systems.

3.3. IR spectra. As we know from earlier studies

77-79

the IR spectroscopy is a very useful experimental

method for studying the strength of the hydrogen bond and it is also very important because it confirms that the results of molecular dynamics simulation are correct. For the crystal 1(Phenylazo)-2-naphthol (I), selected characteristics of vibrational frequencies from CPMD, together with harmonic frequencies from static calculations and available experimental data, 16 ACS Paragon Plus Environment

Page 17 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


are presented in Table 2. Fig. 9 presents the graphical comparison between the experimental and theoretical spectrums from CPMD and static simulations in harmonic approximation. It is worth adding that the vibrational spectrum was also calculated using the Fourier transformation of the dipole autocorrelation function obtained from dipole trajectories generated by the CPMD simulation. It is also important to point out that this approach includes anharmonic effects and all of the vibrational modes for molecules in crystals. However, it is clearly visible already in the comparison of the spectra and in Table 2 that the spectrum derived from the CPMD simulation is slightly shifted towards higher frequencies, about 70-90 cm-1 or less, depending on the band. The frequency shift observed on the CPMD spectrum is most likely the result of using the PBE density functional in the computational processes. As we know from the literature, density functionals in this type of calculations have a tendency to overestimate both the barriers on the potential energy curve and the harmonic and anharmonic infrared frequencies. 77 However, this is not so problematic because the shape of the bands has been very well reproduced (see Fig.9). Even applied the harmonic approximation does not prevent proper band assignment. As normally expected, the frequencies calculated at the CPMD method level and static harmonic approximations are somewhat higher than experimental data. The infrared spectrum is very sensitive to structural changes during simulation especially for molecular systems with hydrogen bonds. Comparison of the experimental frequencies and those calculated at the CPMD and the DFT method levels with the harmonic approximation shows only small differences for the characteristic molecular group; please see Table 2. It should also be added that conducted theoretical simulations were extremely helpful in identifying individual vibration contributions in the experimental spectrum and in the assigning bands. On the harmonic spectrum derived from static calculations for a molecular system in the solid state, we do not observe the frequency for the -OH stretching vibrations. The broad band coming from the stretching vibration of the -OH group is located on the experimental spectrum around 3458/3430 cm-1

81,82

, however, the CMPD method reproduces this band at the level of 3570

cm-1. The νOH band is not visible on the harmonic spectrum because it has been static calculated for the structure of the dominant NH tautomer. On the other hand, the molecular dynamics at CP level reproduces the proton transfer phenomena and illustrates the contribution to the spectrum from the second …HO tautomer and shows the -OH vibration.



Page 18 of 38

Fig. 9 Comparison of the experimental 77 (Exptl.) and simulated (CPMD, CRYSTAL09; harm. approx.) IR spectra for 1-(Phenylazo)-2-naphthol in the solid state.

As for the position of the stretching band of the –NH group, it is located on the experimental spectrum 81,82 at the value of 3020 cm-1 and is well reproduced by both calculation methods at the level about 3096/3015 cm-1 CP and DFT method respectively. The N-H...O stretching mode for crystal (I) in the experiment is not observed but according to our static and CP calculations, these modes are very characteristic and are located at about 223/220 cm-1. As can be seen in the attached Table 2, the other frequencies also connect very well with the experimental data. 81,82 In addition the total infrared spectrum presents a typical image for a system with strong hydrogen bonds and confirms the occurrence of fast proton transfer (FPT) and tautomerism in these studied molecular systems.


Page 19 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2 Comparison of the experimental and calculated selected vibrational frequencies in (cm-1) for the crystal of 1-(Phenylazo)-2-naphthol.

Assignment frequencies νOH νaCHring νsCHring νNH δNH + νC=Cring + δCH δNH + νC=Cring+ δCH δNH + νC=O δNH + νC=N δCH νC=N + νC=Cring + δCH νC=Cring + δCH νN=N + δNH νC=Cring + δCH νC-NH νC=Cring + δCH δC=C-Cring ωNH ωCH νN-H...O

PBE/pob_TZVP_2012 3200 3180 3096 1702 1696 1642 1584 1526 1481 1404 1340 1320 1290 1218 1076 922 832 223

CPMD/PBE/80Ry 3570 3080 3070 3015 1680 1640 1580 1510 1460 1420 1340 1270 1230 1210 1160 1000 850 760 220

Exptl.81,82 3458/3430 3060 3035 3020 1660 1620/1618 1560 1500 1448 1400 1323 1255/1269 1228 1207 1143 985 842 752 -

Conclusion We have presented the results of theoretical studies on the intramolecular hydrogen bonds in 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) in the solid state and in the gas phase using static as well as ab initio molecular dynamics methods. The main purpose of the following publication was an attempt to classify the hydrogen bond occurring in the crystals (I) and (II), based on theoretical studies carried out at the level of molecular dynamics methods with the support of static methods. According to the definition proposed by Gilli and Gilli

12

RAHB is a synergistic reinforcement between H-bond strengthening and π-

delocalization enhancement occurring when the donor (acid) and the acceptor (base) are connected by a short π-conjugated fragment such as [...O=C-OH...] or [...O=C-C=C-OH...]. In addition to the main definition, there are basically several criteria that allow us to classify hydrogen bonding in a given compound to a group of RAHB-type bonds. We have focused on the determination of these criteria in the following work. A summary of our theoretical research will be presented below in a few important points. The tautomeric between fragments (...O=C-C=N-NH...↔...HO-C=C-N=N...) in ketohydrazone-azoenol system form strong N-H...O/N...H-O intramolecular resonanceassisted H-bonds (RAHBs) which are of the low-barrier H-bond type (LBHB) with dynamic



Page 20 of 38

exchange of the proton in the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) in the solid state. The confirmation of this thesis is our geometric analysis of the nature of the bonds and the value of energy barriers for proton transfer determined at the level about 0.58 and 0.51 kcal*mol-1. We also showed the NH tautomer to be more favorable as well as in the gas phase and solid state according respectively to the CP and PI results. The hydrogen between the nitrogen and the oxygen atoms adopts a starkly asymmetrical position in the double potential well. The proof of the tautomerism occurring in this molecular system is also the shape of the infrared spectrum, simulated for crystal (I). The analysis of average distances in the geometric structure of the eight bonds in the keto-enol parts of the molecule indicated that the equivalence of the bond lengths may be attributed to delocalization over a conjugated π-bonded system in the ketohydrazone-azoenol group. We also calculated the average πdelocalization index (which is equal to 〈λ〉(I)solid = 0.792; 〈λ〉(II)solid = 0.784 and 〈λ〉(I,II) = 0.512 to 0.534) for the both crystals taking as the basis for calculating the average bond lengths from CPMD and PIMD simulations. In addition, the calculated ratio parameters and average π-delocalization index as well as the length of the hydrogen bridge throughout the simulation shows that the system is characterized by the type of strong π-delocalized structure (ketohydrazone-azoenol) with visible bigger contribution from the π-localized ketohydrazoneazoenol (KA) form than π-localized azoenol-ketohydrazone (AK) form. In summary, all the arguments considered above in publication: occurrence of the compounds in the crystalline phase, short hydrogen bridge, occurrence of a tautomeric fragment in a molecule, asymmetrical position of the proton, the shape of the potential function of proton, very low barrier of proton transfer, the correlation between π-delocalization index 〈λ〉 and the timeevolution in the length of bonds in the keto-enol part of the molecule and typical total infrared spectrum indicate, shows that the hydrogen bonds in the crystals (I) and (II) have properties characteristic of the type of bonding model resonance-assisted hydrogen bonds without the existing equilibrium of the two tautomers. A detailed analysis of the calculations allows emphasizing the huge impact of the implementation of quantum effects in the calculation on the obtained image of proton transfer processes and tautomerization phenomena. In summary, our CP and PI calculations suggest that proton tunneling though the potential barrier has a significant contribution to the movement of the proton and its position in the hydrogen bridges of the studied crystals. In addition, the introduction of quantum effects to the calculations significantly reduced the value of the estimated potential proton transfer barrier and increased the frequency of proton jumps (hops) and the rate of tautomerization changes throughout the molecular system. 20 ACS Paragon Plus Environment

Page 21 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Finally the information presented in this paper are important because it shows that the quantum effects (PIMD) simulations are very important not only for the proton motion in the H-bridge but also have influence on dynamics “heavy” atoms.

Author information *Corresponding author Email: [email protected] Phone: +48 71 375 7279 Website: http://kwanty.wchuwr.pl/?q=durlak

Acknowledgement The authors would like to gratefully acknowledge the Academic Computer Centre in Gdansk (CI TASK) for the use of the Tryton Cluster and the Wroclaw Centre for Networking and Supercomputing (WCSS) for the use of the BEM Cluster. The calculations also were performed at the Interdisciplinary Centre for Mathematical and Computational Modeling (ICM), Warsaw University under a grant No G60-18. Dr Andrzej Bil, Ph.D. is acknowledged for helpful discussion and suggestion. References (1) Kawai, S.; Nishiuchi, T.; Kodama, T.; Spijker, P.; Pawlak, R.; Meier, T.; Tracey, J.; Kubo, T.; Meyer, E.; Foster, A. S. Direct Quantitative Measurement of the C=O…H–C Bond by Atomic Force Microscopy. Sci. Adv. 2017, 3, 1603258–1603263. (2) Steiner, T. The Hydrogen Bond in the Solid State. Angew. Chem., Int. Ed. 2002, 41, 48– 76. (3) Scheiner, S. Intermolecular Interactions – From van der Waals to Strongly Bound Complexes, Scheiner, S. Ed.; Wiley-Blackwell: New York, 1997. (4) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond in Structural Chemistry and Biology, Oxford University Press: New York, 1999. (5) Perrin, C. L.; Nielson, J. B. "Strong" Hydrogen Bonds in Chemistry and Biology. Annu. Rev. Phys. Chem. 1997, 48, 511–544. (6) Theoretical Treatment of Hydrogen Bonding, Hadži, D. Ed.; Wiley: Chichester, 1997. (7) Desiraju, G. R. Hydrogen Bridges in Crystal Engineering: Interactions without Borders. Acc. Chem. Res. 2002, 35, 565–573.



Page 22 of 38

(8) Elsaesser, T.; Bakker, H. J. Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Kluwer Academic Publishers: Dordrecht, 2002. (9) Sobczyk, L.; Grabowski, S. J.; Krygowski, T. M. Interrelation between H-bond and PiElectron Delocalization. Chem. Rev. 2005, 105, 3513–3560. (10) Hydrogen–Transfer Reactions, Hynes, J. T.; Klinman, J. P.; Limbach, H.-H.; Schowen, R. L. Eds.; Wiley: Weinheim, 2006. (11) Maréchal, Y. The Hydrogen Bond and the Water Molecule. The Physics and Chemistry of Water, Aqueous and Bio Media, Elsevier: Amsterdam, 2007. (12) Gilli, G.; Gilli, P. The Nature of the Hydrogen Bond: Outline of a Comprehensive Hydrogen Bond Theory, Oxford University Press: Oxford, 2009. (13) Speakman, J. C. Acid Salts of Carboxylic Acids, Crystals with Some “Very Short” Hydrogen Bonds. Struct. Bond. 1972, 12, 141–199. (14) Huggins, M. L. 50 Years of Hydrogen Bond Theory. Angew. Chem. Int. Ed. Engl. 1971, 10, 147–152. (15) Emsley, J. Very Strong Hydrogen Bonding. Chem. Soc. Rev. 1980, 9, 91–124. (16) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures, Springer-Verlag: Berlin, 1991. (17) Jeffrey G. A. An Introduction to Hydrogen Bonding, Oxford University Press: New York, 1997. (18) Jeffrey, G. A. Hydrogen-Bonding: An Update. Cryst. Rev. 1995, 4, 213–254. (19) Desiraju, G. R.; Steiner T. in The Weak Hydrogen Bond: in Structural Chemistry and Biology.( International Union of Crystallography Monographs on Crystallography; no. 23), Oxford University Press: USA, 1997. (20) Durlak, P.; Mierzwicki, K.; Latajka, Z. Investigations of the Very Short Hydrogen Bond in the Crystal of Nitromalonamide via Car-Parrinello and Path Integral Molecular Dynamics. J. Phys. Chem. B 2013, 117, 5430–5440. (21) Sanz, P.; Mó, O.; Yáñez, M.; Elguero, J. Resonance-Assisted Hydrogen Bonds: A Critical Examination. Structure and Stability of the Enols of Beta-Diketones and BetaEnaminones. J. Phys. Chem. A 2007, 111, 3585–3591. (22) Singh, R. N.; Kumar, A.; Tiwari, R. K.; Rawat, P.; Baboo, V.; Verma, D. Molecular Structure, Heteronuclear Resonance Assisted Hydrogen Bond Analysis, Chemical Reactivity and First Hyperpolarizability of a Novel Ethyl-4-{[(2,4-Dinitrophenyl)-Hydrazono]-Ethyl}3,5-Dimethyl-1H-Pyrrole-2-Carboxylate: A Combined DFT and AIM Approach. Spectrochim. Acta A 2012, 92, 295–304.


Page 23 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(23) Karabıyık, H.; Sevinçek, R.; Petek, H.; Aygün, M. Aromaticity Balance, Π-Electron Cooperativity and H-Bonding Properties in Tautomerism of Salicylideneaniline: The Quantum Theory of Atoms in Molecules (QTAIM) Approach. J. Mol. Model. 2011, 7, 1295– 1309. (24) Rick, S. W.; Stuart S. J. in Potentials and Algorithms for Incorporating Polarizability in Computer Simulations., Lipkowitz, K. B.; Cundari T. R.; Gillet, V. J.; Boyd, D. B. Eds.; vol. 18, in Reviews in Computational Chemistry, Wiley-VCH: Hoboken, New Jersey, 2002; pp. 89–146. (25) Gilli, P.; Bertolasi, V.; Ferretti, V.; Gilli, G. Evidence for Resonance-Assisted Hydrogen Bonding. 4. Covalent Nature of the Strong Homonuclear Hydrogen Bond. Study of the O-H-O System by Crystal Structure Correlation Methods J. Am. Chem. Soc. 1994, 116, 909–915. (26) Gilli, P.; Bertolasi, V.; Ferretti, V.; Gilli, G. Evidence for Intramolecular N−H···O Resonance-Assisted Hydrogen Bonding in β-Enaminones and Related Heterodienes. A Combined Crystal-Structural, IR and NMR Spectroscopic, and Quantum-Mechanical Investigation. J. Am. Chem. Soc. 2000, 122, 10405–10417. (27) Gilli, G.; Bellucci, F.; Ferretti, V.; Bertolasi, V. Evidence for Resonance-Assisted Hydrogen Bonding from Crystal-Structure Correlations on the Enol Form of the β-Diketone Fragment. J. Am. Chem. Soc. 1989, 111, 1023–1028. (28) Bertolasi, V.; Gilli, P.; Ferretti, V.; Gilli, G. Evidence for Resonance-Assisted Hydrogen Bonding. 2. Intercorrelation between Crystal Structure and Spectroscopic Parameters in Eight Intramolecularly Hydrogen Bonded 1,3-Diaryl-1,3-Propanedione Enols. J. Am. Chem. Soc. 1991, 113, 4917. (29) Gilli, P.; Ferretti, V.; Bertolasi, V.; Gilli, G. Advances in Molecular Structure Research, Hargittai, I.; Hargittai, M. Eds.; JAI Press, Inc.: Greenwich, 1996, vol. 2, pp. 67. (30) Gilli, G.; Bertolasi, V.; Ferretti, V.; Gilli, P. Resonance-Assisted Hydrogen Bonding. III. Formation of Intermolecular Hydrogen-Bonded Chains in Crystals of β-Diketone Enols and Its Relevance to Molecular Association. Acta Crystallogr. 1993, B49, 564–576. (31) Bertolasi, V.; Gilli, P.; Ferretti, V.; Gilli, G. Resonance‐Assisted O‐H...O Hydrogen Bonding: Its Role in the Crystalline Self‐Recognition of β‐Diketone Enols and its Structural and IR Characterization. Chem. Eur. J. 1996, 2, 925–934. (32) Gilli, P.; Ferretti, V.; Gilli, G. Fundamental Principles of Molecular Modeling, Gans, W.; Amann, A.; Boeyens, J. C. A., Eds.; Plenum Press: New York, 1996. (33) Gilli, G.; Gilli, P. Towards an Unified Hydrogen-Bond Theory. J. Mol. Struct. 2000, 552, 1–15. (34) Wang, W.; Hellinga, H. W.; Beese, L. S. Structural Evidence for the Rare Tautomer Hypothesis of Spontaneous Mutagenesis. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 17644– 17648.



Page 24 of 38

(35) Karabıyık, H.; Sevinçek, R.; Karabıyık, H. Effects of Pnictogen and Chalcogen Bonds on the Aromaticities of Carbazole‐Like and Dibenzofuran‐Like Molecular Skeletons: Cambridge Crystallographic Data Centre (CCDC) Study. J. Phys. Org. Chem. 2015, 28, 490–496. (36) Hayashi, T.; Mukamel, S. Multidimensional Infrared Signatures of Intramolecular Hydrogen Bonding in Malonaldehyde. J. Phys. Chem., Sect. A 2003, 107, 9113–9131. (37) Fillaux, F.; Nicolai, B. Proton Transfer in Malonaldehyde: From Reaction Path to Schrödinger’s Cat. Chem. Phys. Lett., 2005, 415, 357–361. (38) Caminati, W.; Grabow, J. U. The C2v Structure of Enolic Acetylacetone. J. Am. Chem. Soc. 2006, 128, 854–857. (39) Zhao, X.; Rossi, P.; Barsegov, V.; Zhou, J.; Woodford, J. N.; Harbison, G. S. Temperature Dependent Deuterium Quadrupole Coupling Constants of Short Hydrogen Bonds. J. Mol. Struct. 2006, 790, 152–159. (40) Bertolasi, V.; Ferretti, V.; Gilli, P.; Yao, X.; Li, C. –J. Substituent Effects on Keto–Enol Tautomerization of β-Diketones from X-ray Structural Data and DFT Calculations. New J. Chem. 2008, 32, 694–704. (41) Zarycz, N.; Aucar, G.A.; Vedova, C. O. D. NMR Spectroscopic Parameters of Molecular Systems with Strong Hydrogen Bonds. J. Phys. Chem., Sect. A 2010, 114, 7162–7172. (42) Belova, N.V.; Girichev, G. V.; Oberhammer, H.; Hoang, T. N.; Shlykov, S. A. Tautomeric and Conformational Properties of Benzoylacetone, CH3–C(O)–CH2–C(O)–C6H5: Gas-Phase Electron Diffraction and Quantum Chemical Study. J. Phys. Chem. A 2012, 116, 3428–3435. (43) Belova, N. V.; Sliznev, V. V.; Oberhammer, H.; Girichev, G. V. Tautomeric and Conformational Properties of β-Diketones. J. Mol. Struct. 2010, 978, 282–293. (44) Gomez-Garibay, F.; Calderon, J. S.; Quijano, L.; Tellez, O.; Soccoro-Olivares, M.; Rios, T. An Unusual Prenyl Biflavanol from Tephrosia Tepicana. Phytochemistry 2001, 46, 1285– 1287. (45) Wetz, F.; Routaboul, C.; Lavabre, D.; Garrigues, J. C.; Rico-Latters, I.; Pernet, I.; Denis, A. Photochemical Behavior of a New Long‐Chain UV Absorber Drived from 4‐Tert‐Butyl‐4′‐ Methoxydibenzoylmethane. Photochem. Photobiol. 2004, 80, 316–321. (46) Silvernail, C. M.; Yap, G.; Sommer, R. D.; Rheingold, A. L.; Day, V. W.; Belot, J. A. An Effective Synthesis of Alkyl β-Cyano-α,γ-Diketones Using Chlorosulfonylisocyanate and a Representative Cu(II) Complex. Polyhedron 2001, 20, 3113–3117. (47) Belot, J. A.; Clark, J.; Cowan, J. A.; Harbison, G. S.; Kolesnikov, A. I. Y.; Kye, –S.; Schultz, A. J.; Silvernail, C.; Zhao, X. The Shortest Symmetrical O−H···O Hydrogen Bond Has a Low-Barrier Double-Well Potential. J. Phys. Chem. B 2004, 108, 6922–6926. (48) Gilli, P.; Bertolasi, V.; Pretto, L.; Lyĉka, A.; Gilli, G. The Nature of Solid-State N−H…O/O−H…N Tautomeric Competition in Resonant Systems. Intramolecular Proton 24 ACS Paragon Plus Environment

Page 25 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Transfer in Low-Barrier Hydrogen Bonds Formed by the …OC−CN−NH… ⇄…HO−CC−NN… Ketohydrazone−Azoenol System. A Variable-Temperature X-ray Crystallographic and DFT Computational Study. J. Am. Chem. Soc. 2002, 124, 13554–13567. (49) Gilli, P.; Bertolasi, V.; Pretto, L.; Antonov, L.; Gilli, G. Variable-Temperature X-ray Crystallographic and DFT Computational Study of the NH…O/N…HO Tautomeric Competition in 1-(Arylazo)-2-naphthols. Outline of a Transiton-State Hydrogen-Bond Theory J. Am. Chem. Soc. 2005, 127, 4943–4953. (50) Shiau, W.; Duesler, E. N.; Paul, I. C.; Curtin, D. Y.; Blann, W. G.; Fyfe, C. A. Investigation of Crystalline Naphthazarin B by 13C NMR Spectroscopy Using "Magic Angle" Spinning Techniques and by X-ray Diffraction: Evidence for a Dynamic Disordered Structure. J. Am. Chem. Soc. 1980, 102, 4546–4548. (51) Frydman, L.; Olivieri, A. C.; Diaz, L. E.; Frydman, B.; Morin, F. G.; Mayne, C. L.; Grant, D. M.; Adler, A. D. High-Resolution Solid-State 13C NMR Spectra of Porphine and 5,10,15-20-Tetraalkylporphyrins: Implications for the N-H Tautomerization Process. J. Am. Chem. Soc. 1988, 110, 336–342. (52) Stare, J.; Panek, J.; Eckert, J.; Grdadolnik, J.; Mavri, J.; Hadži, D. Proton Dynamics in the Strong Chelate Hydrogen Bond of Crystalline Picolinic Acid N-Oxide. A New Computational Approach and Infrared, Raman and INS Study. J. Phys. Chem. A 2008, 112, 1576–1586. (53) Sumner, I.; Iyengar, S. S. Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects. J. Phys. Chem. A 2007, 111, 10313–10324. (54) Brela, M. Z.; Wojcik, M. J.; Witek, Ł. J.; Boczar, M.; Wrona, E.; Hashim, R.; Ozaki, Y. Born−Oppenheimer Molecular Dynamics Study on Proton Dynamics of Strong Hydrogen Bonds in Aspirin Crystals, with Emphasis on Differences between Two Crystal Forms. J. Phys. Chem. B 2016, 120, 3854–3862. (55) Feynman, R.P.; Hibbs, A.R. Quantum Mechanics and Path Integrals, McGraw-Hill College: New York, 1965. (56) Olivieri, A. C.; Wilson, R. B.; Paul, I. C.; Curtin, D. Y. 13C NMR and X-ray Structure Determination of 1-(Arylazo)-2-Naphthols. Intramolecular Proton Transfer Between Nitrogen and Oxygen Atoms in the Solid State. J. Am. Chem. Soc. 1989, 111, 5525–5532. (57) Kreuer, K. D. Proton Conductivity: Materials and Applications. Chem. Matter. 1996, 8, 610–641. (58) Car, R.; Parrinello, M. Unified Approach for Molecular Dynamics and DensityFunctional Theory. Phys. Rev. Lett. 1985, 55, 2471–2474. (59) Marx, D.; Parrinello, M. Ab Initio Path Integral Molecular Dynamics. Z. Phys. B: Condens. Matter. 1994, 95, 143−144.



Page 26 of 38

(60) Marx, D.; Parrinello, M. Ab Initio Path Integral Molecular Dynamics: Basic Ideas. J. Chem. Phys. 1996, 104, 4077–4082. (61) Tuckerman, M.; Marx, D.; Klein, M. L.; Parrinello, M. Efficient and General Algorithms for Path Integral Car–Parrinello Molecular Dynamics. J. Chem. Phys. 1996, 104, 5579–5588. (62) Grimme, S. J. Semiempirical GGA-type Density Functional Constructed with a LongRange Dispersion Correction. J. Comput. Chem. 2006, 27, 1787–1799. (63) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, Ph.; Llunell, M. CRYSTAL09 User’s Manual; University of Torino, Torino, 2009. (64) Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V. R.; Zicovich-Wilson, C. M. CRYSTAL: A Computational Tool for the Ab Initio Study of the Electronic Properties of Crystals. Z. Kristallogr. 2005, 220, 571–573. (65) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett., 1996, 77, 3865–3868. (66) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 1997, 78, 1396–1396. (67) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188–5192. (68) Peintinger, M. F.; Vilela Oliveira, D.; Bredow, T. Consistent Gaussian Basis Sets of Triple‐Zeta Valence with Polarization Quality for Solid‐State Calculations. J. Comput. Chem. 2013, 34, 451–459. (69) CPMD, version 3.15.3; Copyright IBM Corp 1990-2008, Copyright MPI für Festkörperforschung Stuttgart 1997-2001; http://www.cpmd.org. (70) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé–Hoover chains: The Canonical Ensemble via Continuous Dynamics. J. Chem. Phys. 1992, 97, 2635–2643. (71) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B 1991, 43, 1993–2006. (72) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Molec. Graphics. 1996, 14, 33–38. (73) Williams, T.; Kelley, C. Gnuplot 5.0; http://www.gnuplot.info, 2015. (74) Kohlmeyer, A.; Forbert, H. traj2xyz.pl, version 1.4., 2004. (75) Forbert, H.; Kohlmeyer, A. Fourier, version 2, 2002-05. (76) Cleland, W. W. Low-Barrier Hydrogen Bonds and Low Fractionation Factor Bases in Enzymic Reactions. Biochemistry 1992, 31, 317–319. 26 ACS Paragon Plus Environment

Page 27 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(77) Durlak, P.; Latajka, Z. Car–Parrinello Molecular Dynamics and Density Functional Theory Simulations of Infrared Spectra for Acetic Acid Monomers and Cyclic Dimers. Chem. Phys. Lett. 2009, 477, 249–254. (78) Kwiendacz, J.; Boczar, M.; Wójcik, M. J. Car–Parrinello Molecular Dynamics Simulations of Infrared Spectra of Crystalline Imidazole. Chem. Phys. Lett. 2011, 501, 623– 627. (79) Brela, M.; Stare, J.; Pirc, G.; Sollner-Dolenc, M.; Boczar, M.; Wojcik, M. J.; Mavri, J. Car–Parrinello Simulation of the Vibrational Spectrum of a Medium Strong Hydrogen Bond by Two-Dimensional Quantization of the Nuclear Motion: Application to 2-Hydroxy-5nitrobenzamide. J. Phys.Chem. B 2012, 116, 4510–4518. (80) Smith, A. L. The Coblentz Society Desk Book of Infrared Spectra in Carver, C.D., Ed., The Coblentz Society Desk Book of Infrared Spectra, Second Edition, The Coblentz Society: Kirkwood, MO, 1982; pp. 1-24. (81) Almeida, M. R.; Stephani, R.; Dos Santos, H. F.; de Oliveira, L. F. C. Spectroscopic and Theoretical Study of the “Azo”-Dye E124 in Condensate Phase: Evidence of a Dominant Hydrazo Form. J. Phys. Chem. A 2010, 114, 526–534. (82) Ferreira, G. R.; Costa Garcia, H.; Couri, M. R. C.; Dos Santos, H. F.; de Oliveira L. F. C. On the Azo/Hydrazo Equilibrium in Sudan I Azo Dye Derivatives. J. Phys. Chem. A 2013, 117, 642–649.



Page 28 of 38

TOC Graphic


Page 29 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 1 Molecular structure and selected atoms labelling of 1-(Phenylazo)-2-naphthol (I) and 1-(4-FPhenylazo)-2-naphthol (II) in the gas phase. 262x142mm (72 x 72 DPI)



Fig. 2 Unit cell and selected atoms labelling of 1-(Phenylazo)-2-naphthol crystal (I). 280x336mm (72 x 72 DPI)


Page 30 of 38

Page 31 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 3 Unit cell and selected atoms labelling of 1-(4-F-Phenylazo)-2-naphthol crystal (II). 226x330mm (72 x 72 DPI)



Fig. 4 Comparison of the distribution functions (δ-parameter) from CPMD and PIMD simulations for the intramolecular H-bonds for the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) at 298 K in the gas phase (a,b) and in the solid state (c,d) respectively. 211x158mm (96 x 96 DPI)


Page 32 of 38

Page 33 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 5 Comparison of the single proton transfer free-energy ∆F profiles from CPMD and PIMD simulations for the intramolecular H-bonds for the 1-(Phenylazo)-2-naphthol (I) and 1-(4-F-Phenylazo)-2-naphthol (II) at 298 K in the gas phase (a,b) and in the solid state (c,d) respectively. 211x158mm (96 x 96 DPI)



Fig. 6 Two-dimensional free-energy landscape of δ-parameter (reaction coordinate) and N1…O1 distances for the 1-(Phenylazo)-2-naphthol (I) for CPMD (a) and PIMD (b) simulation in the gas phase at 289 K and the 1-(4-F-Phenylazo)-2-naphthol (II) for CPMD (c) and PIMD (d) simulation in the gas phase at 289 K. The unit of ∆F free energy (potential of mean force) is kcal*mol-1. 370x264mm (96 x 96 DPI)


Page 34 of 38

Page 35 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 7 Two-dimensional free-energy landscape of δ-parameter (reaction coordinate) and N1…O1 distances for the 1-(Phenylazo)-2-naphthol (I) for CPMD (a) and PIMD (b) simulation in the solid state at 289 K and for the 1-(4-F-Phenylazo)-2-naphthol (II) for CPMD (c) and PIMD (d) simulation in the solid state at 289 K. The unit of ∆F free energy (potential of mean force) is kcal*mol-1. 370x264mm (96 x 96 DPI)



Fig. 8 Two-dimensional average index of π-delocalisation 〈λ〉 landscape of time evolutions of RN1…O1 and RC1=O1 distances for the crystal of 1-(Phenylazo)-2-naphthol (a) and for the crystal of 1-(4-F-Phenylazo)2-naphthol (b), both from PIMD simulation at 298 K. 317x211mm (96 x 96 DPI)


Page 36 of 38

Page 37 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 9 Comparison of the experimental 76 (Exptl.) and simulated (CPMD, CRYSTAL09; harm. approx.) IR spectra for 1-(Phenylazo)-2-naphthol in the solid state. 317x211mm (96 x 96 DPI)



TOC Graphic 82x44mm (300 x 300 DPI)


Page 38 of 38

CarâParrinello and Path Integral Molecular Dynamics Study of the

Recommend Documents

CarâParrinello and Path Integral Molecular Dynamics Study of the