Quantum-Mechanical Prediction of the Averaged Structure

Article pubs.acs.org/JPCA

Quantum-Mechanical Prediction of the Averaged Structure, Anharmonic Vibrational Frequencies, and Intensities of the H2O···trans-HONO Complex and Comparison with the Experiment Published as part of The Journal of Physical Chemistry virtual special issue “W. Lester S. Andrews Festschrift”. V. P. Bulychev, M. V. Buturlimova, and K. G. Tokhadze* Department of Physics, St. Petersburg State University, 7/9 Universitetskaya Nab., St. Petersburg 199034, Russian Federation ABSTRACT: The geometrical parameters, the frequencies, and absolute intensities of vibrational transitions of H2O···trans-HONO hydrogenbonded complex are calculated using the approach earlier tested in calculations of isolated molecules of nitrous acid and complexes of this acid with ammonia. The equilibrium nuclear configuration and potential energy and dipole moment surfaces are calculated by the MP2/aug-ccpVTZ method with the basis set superposition error taken into account. The fundamental transition frequencies and intensities of the complex are first obtained in the harmonic approximation, and then the energy values, vibrational wave functions, and transition frequencies and intensities are determined from variational solutions of one- to four-dimensional anharmonic equations. The results obtained are compared with the data calculated in the same approximation for an isolated trans-HONO molecule and the NH3···trans-HONO complex. The average discrepancy between the anharmonic frequency values and five available experimental data is 15 cm−1. Three absorption bands of trans-HONO with the highest intensity are recommended for detecting the presence of H2O···trans-HONO.

1. INTRODUCTION The fruitful ideas put forth by L. Andrews for matrix-isolation investigation of unstable species1−3 were applied in numerous studies of hydrogen-bonded complexes. Among such compounds the complexes formed by nitrous acid molecules HONO with molecules present in the Earth’s atmosphere NH3,4 N2 and CO,5 CS2 and CO2,6 HF and HCl,7 CH4,8 and H2O9 are undoubtedly of special interest. These complexes are important objects for spectroscopic studies because of the specific properties of nitrous acid. There exist two stable cis and trans isomers of this compound, which can transform into one another. As a source of the hydroxyl radical, HONO is involved in the photochemical process associated with the generation of tropospheric ozone.10 Remote sensing of the presence of the complexes formed by HONO with other atmospheric molecules requires the knowledge of absolute intensity values and frequencies of spectral transitions. Recording of the absorption spectra of strong H3N···HONO complexes in an argon matrix4 was supplemented with an ab initio calculation of their equilibrium geometries and transition frequencies and intensities in the harmonic approximation. In the experiment five HONO modes and one NH3 bending mode of the H3N···trans-HONO complex were identified, and their relative intensities were determined. It was found that the O−H stretching mode and the HON in-plane bending mode of this complex are, respectively, red-shifted by 800 cm−1 and blue-shifted by 190 cm−1 relative to the trans-HONO monomeric bands. The doublet structure observed in the O− © XXXX American Chemical Society

H stretching region of the H3N···trans-HONO complex was ascribed to a resonance between the first excited O−H stretching state and the second excited HON bending state. For the H3N···cis-HONO complex, only one band was assigned to the ν4(N−O) stretch of cis-HONO and one band to a bending mode of NH3. Subsequently,11−13 the structural and spectroscopic parameters of H-bonded complexes of cis- and trans-HONO (DONO) with ammonia were calculated using a more accurate ab initio theory for determining the equilibrium geometry and potential energy surfaces (PESs) and dipole moment surfaces (DMSs) and a variational method for solving anharmonic vibrational equations in one to four dimensions. Anharmonic values of transition frequencies and absolute intensities were obtained for six internal vibrations of nitrous acid molecules and the H-bond stretching vibration. The calculated frequencies are in good agreement with the available experimental data. The calculations confirmed the presence of the ν(O−H)/2ν(HON) resonance in H3N···trans-HONO and the relative intensities of bands measured for this complex.4 It was found that the form of internal vibrations of nitrous acid molecules and, consequently, the assignment of these vibrations, can significantly change upon complexation. With the results obtained in the same approximation for the complexes of different isomers and isotopologues of nitrous Received: July 4, 2017 Revised: August 25, 2017 Published: September 5, 2017 A

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functions, and transition frequencies and intensities will be obtained using the variational method with the PESs and DMSs calculated in the approximation used in our previous studies.11−13 Of the spectroscopic parameters to be considered, the absolute values of transition intensities are most important. On the one hand, this information is crucial for understanding the mechanisms of formation of the complicated band shapes,18 but, on the other hand, the absolute values of this quantity are difficult to measure in experiments.19 In the following section we discuss the calculation methods adopted to obtain the equilibrium geometry and the binding energy of H2O···trans-HONO and to perform harmonic and anharmonic calculations. The third section presents the most important numerical results, which are discussed in detail in the fourth section. In the concluding section we briefly outline the computational approaches, analyze the changes in the spectroscopic parameters of trans-HONO upon formation of the complex in question, and recommend the frequency and intensity values for the most intense absorption bands of the H2O···trans-HONO complex.

acid, the changes in the spectroscopic and structural characteristics upon trans−cis transition, isotope substitution, and Hbond formation were revealed. Nitrous acid can form H-bonded complexes with water molecules, which are also abundant in the Earth’s atmosphere. It is known that water complexes can serve as catalysts in atmospheric chemistry.14 This topic was discussed in detail in the excellent review by V. Vaida.15 Molecular complexes of water may influence the nitrous acid content in the atmosphere and may act as sites for water condensation. Hydrogen-bonded complexes of trans and cis isomers of HONO with water molecules were calculated at the DFT (B3LYP)/6-311+ +G(3df,3dp) level of theory.16 The basis set superposition error (BSSE) was taken into account using the counterpoise method.17 It was found that both HONO isomers form a strong H-bond with water in which the acid acts as the hydrogen bond donor. The binding energies De = −29.9 and −29.6 kJ mol−1 were predicted for H2O···trans-HONO and H2O···cis-HONO, respectively. In addition, there exist some weaker complexes with the water molecule acting as the hydrogen bond donor. The structure, binding energies, harmonic frequencies, and intensities, as well as relative atmospheric abundances of the 1:1 complexes, were calculated with a reasonable accuracy, although the assignment reported in Table 7 of the DFT calculation17 for the H bond and N−O stretching modes is incorrect. Absorption spectra of H-bonded complexes of HONO with water were recorded in argon matrixes.9 The experimental study was supplemented with MP2 and DFT (B3LYP)/6-311+ +G(2d,2p) calculations of stable nuclear configurations, binding energies, and harmonic vibrational frequencies and intensities. The calculated results were corrected for the BSSE by the standard procedure.17 In the experiment five fundamental bands of internal vibrations of trans-HONO (excepting for the OH torsional motion) and two stretching bands of H2O were identified for H2O···trans-HONO. For H2O···cis-HONO, three bands of nitrous acid (O−H, NO, and HON) and the antisymmetric OH stretch of water were measured. In addition, three bands of the H2O···H2O···trans-HONO trimer were recorded. For H2O···trans-HONO, the largest in magnitude frequency shifts upon complexation were observed for the O− H stretching (−247.5 cm−1) and HON bending (103 cm−1) modes. For H2O···cis-HONO, the O−H stretching frequency shift equals −227 cm−1. These frequency shifts are indicative of hydrogen bonds of moderate strength. The harmonic frequency values calculated in this paper for these complexes with the DFT method are higher than the experimental values, especially for three OH stretching bands. Nonetheless, the frequency shifts upon formation of complexes are reproduced rather well. The fundamental transition intensities are, in general, reasonable; however, the value for the NO mode is overestimated, while the value for the N−O mode is underestimated. The purpose of this paper is to calculate the most stable configuration of the H2O···trans-HONO complex at a higher level of theory than in earlier studies,9,16 to obtain more correct harmonic values of transition frequencies and intensities, and, what is the main objective, to perform anharmonic calculations of vibrational spectral parameters and vibrationally averaged geometrical parameters. The calculated results will be compared with the experimental data,9 and the analogous results derived with the same method for the related H3N··· trans-HONO complex.11 Vibrational energy levels, wave

2. COMPUTATIONAL DETAILS The equilibrium geometry of H2O···trans-HONO was calculated in the CCSD/aug-cc-pVTZ approximation using the Gaussian 09 package of codes.20 The BSSE was corrected by the counterpoise method.17 With the electronic energies of isolated H2O and trans-HONO molecules computed in the same approximation, the binding energy of the H2O···transHONO complex was found to be −29.6 kJ mol−1. In view of the necessity of computing the PESs and DMSs of H2O···transHONO for anharmonic calculations at many points in the space of nuclear coordinates, the equilibrium nuclear configuration, as well as the harmonic vibrational fundamental frequencies and intensities of H2O···trans-HONO, were also calculated in the MP2/aug-cc-pVTZ approximation with the BSSE corrected by the counterpoise method using the same package of codes.20 The equilibrium geometry of the H2O··· trans-HONO complex corresponding to the global minimum is shown in Figure 1. This geometry is in accordance with an

Figure 1. Equilibrium geometry of the H2O···trans-HONO complex.

approximate sp3 hybridization of valence electron orbitals of the oxygen atom of water. The MP2/aug-cc-pVTZ binding energy of H2O···trans-HONO in this configuration equals −29.8 kJ mol−1, which is close to the above CCSD value of −29.6 kJ mol−1 and the values of −26.4 and −29.9 kJ mol−1 obtained earlier.9,16 The MP2/aug-cc-pVTZ binding energy of H2O··· trans-HONO is 13.5 kJ mol−1 lower in magnitude than the binding energy of H3N···trans-HONO11 calculated with the same method. For the H2O···trans-HONO complex in the equilibrium configuration, the dipole moment value is 4.782 D, and the rotational constants are 28.82, 2.77, and 2.54 GHz. It is extremely difficult to perform an anharmonic calculation of a seven-atom polyatomic system with all interactions B

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internuclear separations and angles of HONO upon formation of a complex with H2O have the same signs but are smaller in magnitude than in the case of formation of H3N···trans-HONO. For example, upon complexation the H−O bond length becomes longer by 0.013 Å in H2O···trans-HONO and by 0.031 Å in H3N···trans-HONO. The bond length r(O1−N) decreases by 0.038 and 0.046 Å upon formation of a complex with water and ammonia, respectively. The H-bond length r(O1···O3) is 0.012 Å longer than the H-bond length in H3N··· trans-HONO. Note that the atoms O2, N, O1, H1, O3, and H3 of H2O···trans-HONO lie virtually in one plane. This fact is confirmed by the dihedral angles NO1O3H3 = 2.64°, O2NO1H1 = 179.9°, and O1H1O3H3 = 1.56°. The harmonic frequencies and intensities for fundamental vibrational transitions of the H2O···trans-HONO complex calculated in the MP2/aug-cc-pVTZ approximation are listed in Table 2. The frequencies and intensities computed for the trans-HONO monomer21 are shown in parentheses. The assignment of normal vibrations in Table 2 is approximate, except for three internal vibrations of water and the H−O stretch of nitrous acid, which are characteristic. All nuclei of water take part in low-frequency vibrations of the complex and also in the N = O2 stretching vibration, because the frequency of the internal bending mode of water is close to the N = O2 frequency. The normal vibrations at 80 and 327 cm−1 are torsional vibrations of the water molecule about the direction of one of two electron lone pairs of the oxygen atom. In all intermolecular vibrations, except for that at 327 cm−1, the water molecule vibrates so that the corresponding electron lone pair of O3 is always directed to the hydrogen atom of HONO. In this study we first solved 1D anharmonic equations for all vibrations of interest to us with other vibrational coordinates fixed at their equilibrium values to estimate the intramode anharmonic effects and then solved 2D anharmonic equations for all pairs of such vibrations to examine the intermode anharmonic coupling. These data are summarized in Table 3, where, because of space limitations, the pairwise effects are shown only for pairs including the H1−O1 mode. In this table, along with the structural assignment of vibrations, we use the conventional notation for six HONO modes, ν1−ν6, denote the H-bond stretch as ν7 and the H2O torsional vibration at 327 cm−1 as ν8. The third and fourth columns of Table 3 contain the frequencies and intensities for the eight considered vibrations derived from solutions of 1D anharmonic equations. The fifth column shows the difference between the 2D frequency value of the ν1(O−H) vibration calculated for the 2D subsystem (ν1, νk) and its 1D frequency value. In the parentheses, analogous changes in the fundamental transition

between different vibrational degrees of freedom taken into account. A realistic way out of this situation is to choose a certain number of degrees of freedom that are associated with a definite spectral region and strongly interact with one another. Ignoring their weak interaction with remaining vibrational coordinates, it is possible to formulate an anharmonic problem with a small number of dimensions. It was shown11,21 that, for HONO and its H-bonded complexes, it is advisable to choose the mass-weighted normal coordinates qi of the whole system as the vibrational variables for anharmonic calculations. In the variational method adopted for solving anharmonic Schrödinger equations we expanded the one-dimensional (1D) wave functions in harmonic-oscillator eigenfunctions χk(ξi) with ξi = qi√ωi/ℏ, where ωi is the cyclic frequency of a harmonic oscillator, and ℏ is the Planck constant. Multidimensional anharmonic wave functions were expanded in products of 1D basis functions. The expansion coefficients for each anharmonic solution and the energy eigenvalues were obtained from secular equations. The quantum states of multidimensional systems were assigned judging by the basis function with a maximum weight and by the nodal structure of 1D and two-dimensional (2D) sections of wave functions. Transition intensities were expressed in terms of matrix elements of dipole moment components between the vibrational wave functions of combining states. The construction of Hamiltonian matrices and other details of variational calculations are discussed in our previous papers.11,13,21

3. RESULTS The most important geometrical parameters of the MP2/augcc-pVTZ equilibrium configuration are presented in Table 1. Table 1. Optimized Structural Parameters of the H2O···transHONO Complex r(H1−O1)

r(O1−N)

0.9831

1.3891

H1O1N 101.59

O1NO2 111.62

distances (Å) r(N = O2) r(O1··· O3) 1.1885 2.7939 angles (deg) O1H1O3 H2O3H3 170.34 104.97

r(O3−H2)

r(O3−H3)

0.9621

0.9630

NO1O3H3 2.64

NO1O3H2 −117.61

These structural parameters are rather close to the values obtained in the DFT calculation.9 A value of 1.809 Å reported earlier16 for r(H1···O3) almost coincides with our value of 1.820 Å. Comparison of the data of Table 1 with the analogous parameters calculated for the trans-HONO monomer21 and the H3N···trans-HONO complex11 shows that the changes in the

Table 2. Harmonic Frequencies (cm−1) and Intensities (km mol−1) for the Fundamental Transitions of the H2O···trans-HONO Complexa

a

assignment

frequency

intensity

assignment

frequency

intensity

H-bond rock. H2O tors. H-bond rock. H-bond str. H2O wag. H2O tors. O1NO2 bend. H1−O1 tors.

43 80 136 197 246 327 692 (614)a 854 (577)a

5.7 44 5.5 11 210 28 70 (194)a 100 (99)a

N−O1 str. H1O1N bend. H2O3H3 bend. N = O2 str. H1−O1 str. H2O symm. str. H2O antis. str.

895 (819)a 1420 (1291)a 1629 1639 (1658)a 3504 (3774)a 3809 3930

274 (161)a 170 (175)a 92 67 (107)a 788 (91)a 17 108

Values of transition frequencies and intensities for the free trans-HONO isomer21 are shown for comparison in parentheses. C

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Table 3. Experimental9 Frequencies (cm−1), the Frequencies (cm−1) and Intensities (km mol−1) of Eight Modes of H2O···transHONO Obtained from 1D Anharmonic Equations, and the Frequency and Intensity Shifts Due to Interactions in Pairs (ν1,νk) with k > 1 mode νk

experiment9

1D frequency

1D intensity

ν1(2D)−ν1(1D)

νk(2D)−νk(1D)

ν1(O−H) ν2(NO) ν3(NOH) ν4(N−O) ν5(ONO) ν6(OH tors) ν7(H-bond str) ν8(H2O tors)

3323 1653 1368 873 672

3291 1635 1436 882 689 965 201 567

923 90 230 240 52 122 9 30

0 −3 (−160) 3 (−53) 1 (−8) −3 (6) 13 (−70) −19 (17) 9 (−8)

0 −9 (4) −40 (−5) 3 (9) −6 (−1) −137 (0) 5 (3) 5 (3)

intensity of the ν1(O−H) vibration are shown. For example, the frequency of the ν1(O−H) mode decreases by 19 cm−1, and the intensity of this mode increases by 17 km mol−1 due to the interaction of ν1 with ν7. The sixth column of this table shows analogous changes for the νk vibrations (k > 1) caused by their coupling to the ν1 vibration.

HONO complex. These absorption bands can be used to detect the presence of H2O···trans-HONO complexes in the gas phase. Therefore, their spectroscopic parameters deserve a more careful calculation with the anharmonic effects taken into account. The influence of intramode and intermode anharmonicities on the transition frequencies and intensities is seen from comparison of the results of harmonic (Table 2) and 1D and 2D anharmonic calculations (Table 3). The intramode anharmonicity decreases the frequencies of the ν1 and ν7 stretches and makes stiffer the torsional ν6 vibration. The last effect has been observed and explained earlier.11,21 The small differences between the harmonic and 1D anharmonic frequencies of the ν2−ν5 modes are indicative of insignificant mechanical anharmonicity of these vibrations. In the case of the ν1, ν4, and ν5 modes, the 1D anharmonic frequency values are in better agreement with the experimental data9 than the harmonic frequencies. As for the anharmonic 1D intensities, they are appreciably higher than the harmonic values for the ν1−ν3 and ν6 modes. These calculations predict that, as in the case of the H3N···trans-HONO complex,11 the ν5(ONO) band should be the weakest band among those ascribed to the internal vibrations of nitrous acid in the H2O···trans-HONO complex. Inspection of the data presented in Table 3 shows that, of the intermolecular modes, the modes ν6, ν7, and ν8 have the largest anharmonic effect on the ν1(O−H) frequency. Consequently, to refine the anharmonic frequency value of ν1, as well as the values of ν6−ν8, it is necessary to consider a four-dimensional (4D) vibrational problem for the subsystem (ν1, ν6, ν7, ν8). As for the anharmonic coupling within the pairs of modes not presented in Table 3, it is significant only in the (ν4, ν5) pair, where the anharmonic coupling decreases the frequency values by 15 and 11 cm−1 for ν4 and ν5, respectively. Thus, to improve the 1D anharmonic frequencies ν3, ν4, and ν5, it is necessary to consider the pairwise interactions within the 2D subsystems (ν1, ν3) and (ν4, ν5). Solutions of the problems (ν1, ν3) and (ν4, ν5) yield the values 1396 cm−1 and 225 km mol−1 (ν3), 867 cm−1 and 221 km mol−1 (ν4), and 678 cm−1 and 69 km mol−1 (ν5). It suffices to restrict the anharmonic calculation of the ν2 mode to the 1D case (Table 3), the more so that, as has been indicated,22 it is necessary to use a higher ab initio level to describe the double NO bond. The too-high 1D anharmonic frequency value of the ν8(H2O tors) vibration shows that this mode is strongly coupled to other bending modes of the complex, interaction with which should be taken into account to improve the ν8 frequency. However, this problem is beyond the scope of our paper.

4. DISCUSSION Because of the dynamic and kinematic effects, the harmonic characteristics of some vibrations of monomers experience diverse changes upon formation of the complex. The H−O stretching frequency of HONO is lowered by 270 cm−1, and the fundamental intensity of this mode is increased by a factor of 8.76. In the H3N···trans-HONO complex11 the frequency of this mode was decreased by 598 cm−1, and the intensity was increased by a factor of 17. This vibration remains characteristic, and its reduced mass does not virtually change. In contrast, the NO vibration changes its form, its reduced mass becomes a factor of 2.74 smaller, and its intensity is lowered by a factor of 1.62, while the frequency remains virtually unchanged. The frequencies of the remaining four vibrations of HONO are increased by 90−267 cm−1. The frequency of the OH torsional motion experiences the maximum increase, because the H1···O3 bond hinders this motion. Upon formation of the complex, the HON bending vibration increases its frequency by 129 cm−1, while its form and intensity almost do not change. The reduced masses of the N−O stretching and ONO bending vibrations are increased by a factor of 1.23 and 1.19, respectively, while the N−O intensity becomes a factor of 1.71 higher, and the ONO intensity is lowered by a factor of 2.8. Except for the OH torsional vibration and the HON bending vibration, the relative changes in the transition intensities are considerably larger than the changes in the frequencies. The changes in stretching vibration frequencies are in agreement with the changes in the corresponding bond lengths. With the sole exception of the OH torsional vibration intensity, the changes in the transition frequencies and intensities of all internal modes of trans-HONO on formation of H2O···trans-HONO have the same signs as on formation of H3N···trans-HONO, but they are considerably smaller in magnitude. As for the modes of H2O, their frequencies change insignificantly upon complexation, while the transition intensities are increased by factors of 1.28, 3.0, and 1.43 for the bending, symmetric stretching, and antisymmetric stretching vibrations, respectively. One can see from these data that the absorption bands associated with the O−H and N−O stretching vibrations and the HON bending vibration of HONO have the highest intensities in the absorption spectrum of the H2O···transD

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wave functions. These data demonstrate that excitations of the OH torsional and H-bond stretching vibrations weaken the Hbond, while excitation of the O−H stretching vibration of HONO makes the H-bond stronger. The signs and magnitudes of these effects are similar to those predicted for H3N··· transHONO.11 Because the trans-HONO molecule almost retains its planar equilibrium structure upon complexation, the OH torsional vibration can be approximately considered as an out-of-plane motion. Then, the root-mean-square deviation of the H atom of trans-HONO perpendicular to the equilibrium position of the NO1H1 plane equals 0.135 and 0.236 Å in the ground 4D state and in the (0,1,0,0) state, respectively.

As in the consideration of H3N···trans(cis)-HONO complexes,11−13 the most accurate spectral parameters of the ν1(O−H) stretching band of HONO are obtained from a 4D vibrational Schrödinger equation. For H2O···trans-HONO, these parameters were obtained by the variational method with the PES and DMS calculated in the space of coordinates q1, q6, q7, and q8 discussed above. We considered 11 grid points corresponding to the roots of Hermite polynomial H11 for each variable. The Hamiltonian matrix was constructed with 4900 4D basis functions composed of 70 2D solutions for pairs (q1, q7) and (q6, q8). The following frequency and intensity values were obtained for the fundamental transitions: 3306 cm−1 and 827 km mol−1 (ν1), 816 cm−1 and 122 km mol−1 (ν6), and 209 cm−1 and 9 km mol−1 (ν7). The values obtained for the hot transition (ν1 + ν7) − ν7 are 3316 cm−1 and 717 km mol−1. The 4D and 2D frequency values are in better agreement with the experimental data presented in Table 3 than our 1D anharmonic and harmonic values and the DFT harmonic values.9 For example, our 4D value of the ν1(O−H) frequency is only 17 cm−1 lower than the experimental value. We believe that this calculation also improved the absolute transition intensity values. In view of the special importance of spectral parameters of the ν1(O−H) stretching band, we performed additional calculations of its frequency and intensity using another form of vibrational coordinates. The ν1(O−H) stretch was described by the corresponding normal coordinate of an isolated HONO molecule, the H-bond stretch was represented as a normal vibration of two centers of mass, and rotations of H2O in two planes and rotation of HONO in its plane were described by angular variables. Variational solutions of 1D to three-dimensional (3D) problems for different combinations of ν1(O−H) with the low-frequency motions showed that the resulting values of the ν1(O−H) frequency is close to 3300 cm−1 and that the corresponding intensity is ∼870 km mol−1, which are close to the 4D values discussed above. Because the calculation using the normal coordinates of the whole complex is more consistent, the 4D values 3306 cm−1 and 827 km mol−1 should be recommended for the ν1(O−H) mode. Using the above frequency values for ν1 and ν3 and the values of these frequencies calculated for free trans-HONO,21 we obtain the frequency shifts −281 and 136 cm−1 for ν1 and ν3 upon formation of H2O···trans-HONO. Both these shifts are lower in magnitude by 33 cm−1 than the shifts observed in the argon matrix.9 It is conceivable that this discrepancy may be attributed to the matrix solvation effect. Of interest is the dependence of internuclear separations r(H1−O1), r(O1···O3), and r(H1···O3) on vibrational states of the H2O···trans-HONO complex. Table 4 presents the equilibrium values of these parameters and their values calculated for several states (v1,v6,v7,v8) using 4D vibrational

5. CONCLUSIONS The hydrogen-bonded H2O···trans-HONO complex of atmospheric significance was calculated using the approach earlier tested in calculations of isolated HONO molecules21 and the H3N···trans-HONO complex.11 The equilibrium geometry and the binding energy were calculated in the CCSD/aug-cc-pVTZ approximation with the BSSE correction taken into account. The MP2/aug-cc-pVTZ approximation was used to calculate the most stable nuclear configuration, the harmonic vibrational frequencies, and intensities and to determine the PESs and DMSs necessary for anharmonic calculations. The changes in the form of normal coordinates and in spectral parameters of trans-HONO upon formation of the complex were analyzed. Anharmonic values of frequencies and absolute intensities were derived for six internal vibrations of trans-HONO in the complex and the H-bond stretching vibration from variational solutions of 1D−4D vibrational Schrödinger equations. The importance of taking into account the intramode and intermode anharmonicities in calculating the spectral parameters was analyzed by comparing the results of 1D, 2D, and 4D calculations. Vibrationally averaged values of r(H1−O1) of trans-HONO and H-bond distances r(O1···O3) and r(H1···O3) were obtained for the ground state and several excited states using 4D vibrational wave functions. The results obtained were compared with the experimental findings in argon matrixes9 and the results calculated for the related H3N···trans-HONO complex.11 The anharmonic frequency values obtained in this study for ν1−ν5 trans-HONO vibrations in the H2O···transHONO complex differ from the experimental values9 by −17, −18, 28, −6, and 6 cm−1, respectively, which can be considered to be good agreement in view of possible matrix effects on the vibrations of different nature. The 2D and 4D calculations predict that the fundamental absorption modes ν1(OH), ν3(NOH), and ν4(N−O) are most strong of the H2O···transHONO modes with the absolute intensities 827, 225, and 221 km mol−1, respectively. These bands can be used to detect the presence of these complexes. The ν5(ONO) band should be the weakest band. Note that the hydrogen-bonding effect on spectral parameters of trans-HONO is weaker in H2O···transHONO than in H3N···trans-HONO. For example, the frequency shifts of ν1(OH), ν3(NOH), and ν4(N−O) upon complexation are approximately a factor of 2 smaller, and the increase of their intensities is a factor of 1.5 lower.

Table 4. Equilibrium and Vibrationally Averaged Values of r(H1−O1), r(O1···O3), and r(H1···O3) (Å) in the (v1,v6,v7, v8) States of the H2O···trans-HONO Complex state

r(H1−O1)

r(O1···O3)

r(H1···O3)

equilibrium (0,0,0,0) (0,0,1,0) (0,0,2,0) (0,1,0,0) (1,0,0,0)

0.9831 0.9971 0.9966 0.9963 0.9765 1.0381

2.7939 2.8074 2.8345 2.8582 2.8297 2.7733

1.8199 1.8289 1.8586 1.8846 1.8728 1.7528

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AUTHOR INFORMATION

Corresponding Author

*Phone: +7 812 4287419. E-mail: [email protected]. ORCID

K. G. Tokhadze: 0000-0003-1131-8535 E

DOI: 10.1021/acs.jpca.7b06517 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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(18) Bulychev, V. P.; Gromova, E. I.; Tokhadze, K. G. Study of the H−F Stretching Band in the Absorption Spectrum of (CH3)2O···HF in the Gas Phase. J. Phys. Chem. A 2008, 112, 1251−1260. (19) Keefe, C. D.; Wilcox, T.; Campbell, E. Measurement and Application of Absolute Infrared Intensities. J. Mol. Struct. 2012, 1009, 111−122. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 09, Revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (21) Bulychev, V. P.; Tokhadze, K. G. Multidimensional Anharmonic Calculation of the Vibrational Frequencies and Intensities for the trans and cis Isomers of HONO with the Use of Normal Coordinates. J. Mol. Struct. 2004, 708, 47−54. (22) Bulychev, V. P.; Buturlimova, M. V.; Tokhadze, K. G. Anharmonic Calculation of Structural and Spectroscopic Parameters of the cis-DONO Molecule. J. Phys. Chem. A 2015, 119, 9910−9916.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Russian Foundation for Basic Research, Grant No. 15-03-04605.

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DEDICATION This work is dedicated to Prof. Lester Andrews for his many valuable contributions to molecular spectroscopy.

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REFERENCES

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DOI: 10.1021/acs.jpca.7b06517 J. Phys. Chem. A XXXX, XXX, XXX−XXX