Anharmonic Calculation of the Structure, Vibrational Frequencies, and

Article pubs.acs.org/JPCA

Anharmonic Calculation of the Structure, Vibrational Frequencies, and Intensities of the NH3···cis-HONO and NH3···cis-DONO Complexes 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 for transitions between vibrational states of NH3···cis-HONO and NH3···cis-DONO hydrogen-bonded complexes are calculated using the approach earlier tested in calculations of isolated molecules of nitrous acid and the NH3···trans-HONO and NH3·· trans-DONO complexes. Vibrational wave functions and energy values of the complexes are derived from variational solutions of anharmonic equations in one to four dimensions. The equilibrium nuclear configuration and potential energy surfaces are calculated by the MP2/aug-cc-pVTZ method with the basis set superposition error taken into account. Comparison of the obtained results with the analogous data calculated in the same approximation for isolated cis- and trans-HONO (DONO) molecules and the NH3···trans-HONO (DONO) complexes provides information about the changes in the spectroscopic and geometrical parameters of nitrous acid upon cis− trans transition, H/D substitution, and H-bond formation.

1. INTRODUCTION The nitrous acid molecule HONO is a prototypical system for studying kinetic, structural, and spectroscopic properties of molecules. Nitrous acid is one of the simplest systems that possess different stable, trans and cis, isomers, the absorption spectra of which significantly differ in both the frequency and absolute intensity of vibrational bands. Nitrous acid is present in the upper Earth’s atmosphere and is involved in generation of tropospheric ozone. Its molecules can form complexes, in particular, H-bonded complexes, with other compounds. Of interest is the investigation of structural, energetic, and spectroscopic parameters of the complexes formed by nitrous acid with many important atmospheric species. Remote sensing of the presence of these compounds requires the knowledge of absolute intensity values for spectral transitions, which are difficult to obtain experimentally. The nitrous acid molecule has been the object of many experimental1−13 and theoretical spectroscopic studies.14−19 The fundamental vibrational frequencies were obtained from absorption spectra in the gas phase1−7 and low-temperature matrixes8−10 for all transitions of trans and cis isomers of HONO and DONO except for the ν3 band of cis-HONO and cis-DONO. However, the experimental determinations of absolute values of absorption band intensities are not numerous. In the gas phase the band strengths for the ν1, ν2, ν3, and ν4 bands of trans-HONO and the ν1, ν2, and ν4 bands of cis-HONO were determined11 from the FTIR absorption spectra, and the integrated band intensities were measured12,13 for the ν3 and ν4 trans-HONO bands and the ν4 cis-HONO band. The vibrational spectra of the trans-HONO and cis-HONO molecules were calculated14 with a six-dimensional (6D) DFT potential energy surface (PES) and dipole moment surface (DMS) using the discrete variable representation. The © XXXX American Chemical Society

variational method was employed to obtain the transition frequencies and intensities of trans-HONO (DONO) and cisHONO (DONO) from anharmonic solutions of 3D and 4D vibrational problems in the space of normal vibrational coordinates with the PESs and DMSs calculated in the MP2/ aug-cc-pVTZ approximation.15−17 The frequencies and intensities of the fundamental and some combination transitions are in good agreement with the available experimental data. The sole exception is the ν2 frequency ascribed to the NO vibration. Both the harmonic and anharmonic frequencies were somewhat lower than the experimental frequency values. It was shown17 that the reason for this discrepancy lies in the inability of the MP2/aug-cc-pVTZ approximation to correctly describe the NO double bond. The use of the CCSD(T)/aug-ccpVQZ approach led to the calculated ν2 value almost equal to the experimental result. The most accurate theoretical values of vibrational transition frequencies were derived from the variational (for trans- and cis-HONO) and perturbative (for trans- and cis-DONO) calculations with a 6D CCSD(T) PES using a full 6D Hamiltonian in internal coordinates.18 With this 6D PES, the values of transition frequencies and intensities were determined in the time-dependent wave packet study on trans−cis isomerization of HONO.19 More detailed review of experimental and theoretical studies of HONO can be found elsewhere.17,20,21 Nitrous acid can form molecular complexes with different compounds. Of special interest are H-bonded complexes with molecules present in the Earth’s atmosphere. The bibliography on the experimental studies of these complexes was presented in our earlier paper.21 Experimental studies of such complexes Received: May 27, 2016 Revised: July 29, 2016

A

DOI: 10.1021/acs.jpca.6b05346 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

substitution and trans−cis transition in HONO on the spectroscopic and structural parameters of the complexes of nitrous acid with ammonia.

were often accompanied by quantum-chemical calculations of structural parameters and harmonic frequencies and intensities. The absorption spectra of the H3N···HONO complexes containing the cis and trans isomers of HONO were recorded in argon matrixes.22 The equilibrium geometries and the harmonic frequencies and intensities were calculated in the MP2/6-31+G(d,p) approximation. Values of 40.13 and 36.39 kJ mol−1 for the binding energies of complexes formed by transHONO and cis-HONO, respectively, were obtained with a wider basis set 6-311+G(2d,2p). In the recorded spectra five HONO vibrations and one NH3 bending vibration were identified for the NH3···trans-HONO complex, and their relative intensities were measured. For the NH3···cis-HONO complex, it was possible to assign only one band at 947.5 cm−1 to the ν4(N−O) stretch of cis-HONO and a band at 1076.8 cm−1 to a bending mode of NH3. Structural and spectroscopic parameters of the strong NH3···trans-HONO complex were calculated21 using the variational procedures and ab initio approximation tested on monomeric nitrous acid.15 The fundamental transition frequencies and intensities were derived from variational solutions of anharmonic Schrödinger equations for 1D−4D vibrational subsystems. The calculated results were compared with the experimental data.22 The calculation confirmed the assumption22 that the doublet observed at about 2750 cm−1 can be explained by a strong ν1/2ν3 resonance. To within reasonable matrix effects, the theoretical frequencies are in good agreement with the experimental findings, and the ratios of absolute intensities almost coincide with the observed relative intensities. The analogous calculation was performed on the NH3···trans-DONO complex.16 The purpose of this paper is to calculate the structure and vibrational spectroscopic parameters of the H-bonded complexes NH3···cis-HONO and NH3···cis-DONO using the approaches already employed in our calculations of equilibrium geometries and vibrations of isolated trans- and cis-HONO (DONO) molecules and NH3 ···trans-HONO (DONO) complexes.15−17,21 This fact will facilitate analysis of changes in parameter values upon trans−cis transition and H/D substitution and due to the H-bond formation. The frequencies and intensities of absorption bands assigned to the HONO (DONO) subunit and the H-bond stretching vibration will be derived from anharmonic variational solutions of vibrational 1D−4D Schrödinger equations with ab initio potential energy surfaces (PESs). Consecutive consideration of 1D, 2D, and 3D subsystems in the space of the normal coordinates will allow us to estimate the strength of intermode coupling and to make the optimal choice of a 4D subsystem of modes most strongly coupled to one another. The results predicted for the complex will be compared with the available experimental findings22 and will be useful in assignment of future experimental spectra. In the following section we discuss the method of our calculation and the main results obtained. First, we outline the calculation of the equilibrium geometry and discuss the harmonic frequencies and intensities of the complexes in question. In the second subsection, the variational method for solving anharmonic vibrational problems is briefly considered and the results of 1D and 2D calculations are analyzed. In subsection 2.3 the results of more accurate 3D and 4D calculations of the NH3···cis-HONO and NH3···cis-DONO complexes are discussed and compared with the analogous characteristics of the complexes formed by trans-HONO (DONO). In the concluding section we briefly outline the computational approaches and analyze the influence of H/D

2. METHOD OF CALCULATION AND DISCUSSION OF THE RESULTS 2.1. Calculation of the Equilibrium Geometry and Harmonic Spectral Parameters. The electronic structure, equilibrium configuration, and harmonic vibrational frequencies and intensities of NH3···cis-HONO and NH3···cis-DONO were calculated in the MP2/aug-cc-pVTZ approximation using the GAUSSIAN 09 package of codes.23 The basis set superposition error (BSSE) was corrected by the counterpoise method. The equilibrium nuclear configuration of NH3···cis-HONO corresponding to the global minimum is shown in Figure 1. The

Figure 1. Equilibrium geometry of the NH3···cis-HONO complex.

binding energy of NH3···cis-HONO in this configuration equals 39.7 kJ mol−1, which is 3.6 kJ mol−1 lower than the binding energy of NH3···trans-HONO.21 The NH3···cis-DONO complex has an analogous equilibrium configuration. This configuration possesses the symmetry properties of the Cs point group. All atoms of HONO and the N atom and one of the H atoms of NH3 lie in the symmetry plane. The dihedral angle N 1 O 1 N 2 H 2 is zero. There exists a saddlepoint configuration with the dihedral angle N1O1N2H2 equal to 180°, the total energy of which is 33 cm−1 higher than the global minimum. The most important geometrical parameters of the global minimum configuration are presented in Table 1. Table 1. Optimized Structural Parameters of the NH3···cisHONO Complex Distances (Å) r(H1 O1)

r(O1 N1)

r(N1 O2)

r(N2··· O1)

r(N2 H2)

r(N2 H3)

1.0097

1.3575

1.2042 2.8002 Angles (deg)

1.0136

1.0127

H1O1N1

O1N1O2

N2H1O1

H2N2H1

H3N2H1

N1O1N2H3

108.09

114.17

176.35

102.00

116.21

116.84

These structural parameters and the binding energies are rather close to the values obtained earlier.22 Comparison of the data of Table 1 with the analogous parameters calculated for the transand cis-HONO monomers17 and NH3···trans-HONO21 shows that the changes in the internuclear separations and angles of HONO on formation of a complex with NH3 are virtually the same for trans- and cis-HONO. For example, the H−O bond length becomes longer by about 0.03 Å. The intermolecular separation r(N2···O1) is longer by 0.0187 Å in the weaker B


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increase in the ν1 intensity of cis-HONO (DONO) is twice as high. Except for the ν2 stretch, the signs of changes in the intensities for all other internal modes of trans- and cis-HONO (DONO) upon complexation do not depend on the isotopic composition and the type of an isomer. But the magnitudes of changes can be quite different. For example, the ν3 intensity increases by a factor of 1.23 in the case of trans-HONO and a factor of 3.86 for cis-HONO, and the ν5 intensity decreases upon complexation by a factor of 4.62 for trans-HONO and only by a factor of 2.25 for cis-HONO. The ν2 intensity slightly increases upon complexation of cis-HONO (DONO) and trans-DONO but drops in the case of trans-HONO. The last fact is explained by the difference in the form of the ν2 normal coordinates of NH3···trans-HONO and NH3···trans-DONO due to distinctions in the kinematic interactions, which is not the case for the complexes formed by cis-HONO (DONO). Intensities of all six intermolecular modes do not change on H/ D and cis−trans transitions. The frequency of the ν7 H-bond stretch slightly decreases on trans-to-cis transition and on H/D substitution. The H-bond twisting and bending modes associated with libration of HONO do not depend on the isotopic composition and are increased by 10−25% on trans-tocis transition. As expected, the frequencies of fundamental transitions ascribed to internal vibrations of NH3 are almost the same in all the four complexes, whereas the transition intensities can slightly differ. 2.2. Method of the Anharmonic Calculations. Results of 1D and 2D Calculations. Anharmonic calculations were carried out for the vibrational modes of NH3···cis-HONO and NH3···cis-DONO assigned to the nitrous acid subunit and the H-bond stretching mode. The frequencies and intensities of these vibrations are of particular interest in an analysis of experimental spectra. The anharmonic vibrational Schrödinger equations were solved in 1D−4D spaces of mass-weighted normal coordinates qi by the variational method. It was shown in our earlier papers21 that with this choice of vibrational coordinates the frequencies and intensities of monomeric nitrous acid and its complexes with NH3 can be obtained with good accuracy. One of the advantages of these coordinates is that in calculations of different isotopologues the changes in the reduced masses and forms of vibrations are automatically taken into account. The region of variation of each variable qi was sufficiently wide to describe the ground state and a number of excited vibrational states. The 1D wave functions were expanded 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. For example, in solving a 2D Schrödinger equation, the vibrational wave functions ψk(2)(ξ1,ξ2) were represented as

NH3···cis-HONO complex than in NH3···trans-HONO. The structure of NH3 is practically the same in both complexes. For the NH3···cis-HONO complex in the equilibrium configuration, the dipole moment value is 4.225 D, and the rotational constants are 13.31, 3.98, and 3.11 GHz. Harmonic frequencies and intensities for fundamental vibrational transitions of the complexes considered were computed using the GAUSSIAN 09 package23 and are listed in Table 2. Given the analogous parameters calculated in the Table 2. Harmonic Frequencies (cm−1) and Intensities (km mol−1) for the Fundamental Transitions of the NH3···cisHONO and NH3···cis-DONO Complexesa NH3···cis-HONO assignment H-bond twist., A″ H-bond bend., A′ H-bond bend., A″ H-bond stretch., A′ H-bond bend., A″ H-bond bend., A′ O1N1O2 bend., A′ O1−N1 stretch., A′ O1−H1 tors, A″ NH3 bend., A′ H1O1N1 bend., A′ N1O2 stretch., A′ NH3 bend., A″ NH3 bend., A′ H1−O1 stretch., A′ NH3 stretch., A′ NH3 stretch., A′ NH3 stretch., A″

frequency

intensity

NH3···cis-DONO frequency

intensity

42

0.006

47

0.006

94

4.2

94

4.3

152

1.4

149

1.2

224

29

220

28

310

19

309

19

363

19

361

19

707 (634)

15 (36)

666 (582)

8 (15)

1007 (884)

365 (359)

987 (846)

373 (358)

1058 (694)

82 (98)

789 (546)

50 (46)

1119

159

1118

137

1437 (1320)

27 (7)

1148 (1092)

40 (16)

1588 (1611)

169 (142)

1544 (1591)

142 (127)

1666

8

1664

17

1669

16

1669

17

3031 (3592)

1220 (38)

2212 (2612)

628 (22)

3494

0.7

3494

0.04

3635

24

3635

23

3642

22

3642

22

a

Values of transition frequencies and intensities for free cis-HONO and cis-DONO are shown for comparison in parentheses.

same approximation for four monomeric nitrous acid molecules17 and the complexes of ammonia with transHONO21 and trans-DONO,16 the trends in the changes of spectroscopic parameters upon complexation, on passing from trans to cis isomers, and on H/D substitution can be analyzed. Irrespective of the isotopic composition, the ν1 and ν2 frequencies of both HONO isomers decrease upon complexation, while the ν3, ν4, ν5, and ν6 frequencies are increased by 10−40%. The behavior of fundamental transition intensities is more complicated. Their relative changes are larger in magnitude and can have different signs. The ν1(H−O) stretching intensity of trans-HONO (DONO) becomes a factor of about 15 higher upon complexation. The analogous

10

ψk(2)(ξ1 ,ξ2) =

∑ μ,ν=1

Akμν χμ (ξ1) χν (ξ2) (1)

The PESs necessary in variational calculations were computed by the MP2 method used above to determine the equilibrium nuclear configuration. The DMSs required for evaluating the transition intensities were calculated in the selfconsistent field (SCF) approximation. It was demonstrated21 that such calculation of the dipole moment increases the absolute intensity values by several percent as compared to the C


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Table 3. Fundamental Frequencies (cm−1) and Intensities (km mol−1) of Modes νk of NH3···cis-HONO and NH3···cis-DONO Obtained from 1D Anharmonic Equations and the Frequency Shifts (cm−1) Due to Interactions in Pairs (ν1, νk) mode νk

1D frequency

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

2696 1586 1444 995 702 1122 219

ν1(OD) ν2(NO) ν3(NOD) ν4(NO) ν5(ONO) ν6(OD tors) ν7(H-bond str)

2051 1531 1148 977 664 819 216

1D intensity NH3···cis-HONO 1517 208 51 353 11 111 27 NH3···cis-DONO 745 193 46 352 8 69 26

8π 3 1 · ν[⟨i|μx |f⟩2 + ⟨i|μy |f⟩2 + ⟨i|μz |f⟩2 ] 3hc 4πε0

νk(2D) − νk(1D)

0 −21 −34 −2 4 56 −145

0 −15 −23 4 4 −80 12

0 −11 −14 4 2 25 −66

0 −6 −13 0 1 −40 7

mechanical anharmonicity of these vibrations is small. The anharmonic value of 995 cm−1 for ν4(N−O) of NH3···cisHONO is in good agreement, to within a possible matrix effect, with the experimental value22 of 947.5 cm−1, which is the only experimentally observed band frequency for a complex formed by the cis-HONO isomer. As for the anharmonic intensities, they are higher than the harmonic values for the ν1−ν3 and ν6 modes. These calculations predict that the ν5(ONO) band should be the weakest band among those ascribed to the internal vibrations of nitrous acid in the NH3···cis-HONO (DONO) complex. The changes in the frequency values caused by taking into account the intramode anharmonicity are in conformity with the changes in the calculated geometrical parameters. For example, r(H−O) and r(D−O) increase by 0.055 and 0.038 Å, respectively, and r(N···O) increases by 0.044 Å in both isotopologues due to the anharmonic zeropoint vibrations. Analysis of solutions of 2D problems shows that the frequencies and intensities of the ν2(NO), ν4(NO), and ν5(ONO) bands are very weakly perturbed by pairwise anharmonic interactions. The other four modes considered in Table 3 are strongly coupled to one another. The changes in the 1D frequency value of the ν1(O−H) band caused by the interaction with a νk vibration are presented in column 4 of Table 3, and the analogous changes in the 1D frequency value of the νk band caused by its interaction with the ν1 vibration are shown in column 5. The pairwise interactions of the ν1 mode with ν2, ν3, and ν7 lower the ν1 frequency, the largest decrease of ν1 being caused by the ν7 vibration. The last fact agrees with the shorter average value of r(N···O) (2.777 Å) obtained for the pair (ν1, ν7) as compared to the corresponding 1D value (2.846 Å). The more energetic ν1 mode wins in competition of these two anharmonic vibrations, and the hydrogen bonding becomes stronger and shorter. The ν6 vibration experiences the largest frequency shift due to the coupling to the ν1 vibration (−80 cm−1 in NH3···cis-HONO). It is worth noting that in NH3···cis-DONO the frequency shifts in question are, on average, twice as small as in NH3···cis-HONO, which is explained by the shorter OD stretch amplitude in the heavier isotopologue. On the whole, the picture of frequency shifts due to the intermode anharmonic coupling resembles that obtained for NH3···trans-HONO (DONO);16,21 however, the relative

MP2 values but does not change appreciably their ratios. In the vibrational configuration space the potential energy and dipole moment components were calculated at points related to the roots of 11th-order Hermite polynomials Hv(ξi) for each variable. In what follows the subscripts of atoms entering the complex will be omitted because this omission will not cause any confusion. Intensities of spectral transitions were calculated by the formula S=

ν1(2D) − ν1(1D)

(2)

If absorption intensity S is measured in km mol−1, transition frequency ν in cm −1 , and transition dipole moment components in D, the factor in front of ν equals 2.50643. The absolute value of intensity depends on the overlap of wave functions of initial and final states and the dipole moment function; i.e., intensity is high when integrals of products of these factors over all considered vibrational coordinates are significant. To make the multidimensional anharmonic calculations realistic, we solved first 1D anharmonic equations for seven vibrations of both complexes of interest to us. These are the Hbond stretch and all six internal modes of nitrous acid. Then we solved the 2D vibrational problems for all pairs of the modes considered. Comparison of results of the harmonic, and 1D and 2D anharmonic calculations shows effects of intramode and intermode anharmonicities on the frequencies and intensities. These data are partially summarized in Table 3 where, because of space limitations, the pairwise effects are shown only for pairs including the ν1(O−H) mode. In this table, ν1(2D) − ν1(1D) shows the difference between the 2D value of ν1(O−H) calculated for the 2D subsystem (ν1, νk) and its 1D value, and νk(2D) − νk(1D) is the difference between the value of νk perturbed by its interaction with ν1 and its 1D value. Comparison of the data of Tables 2 and 3 shows that taking into account the intramode anharmonicity decreases the frequencies of ν1 and ν7 stretching vibrations and makes stiffer the torsional ν6 vibration. The last effect was earlier observed and explained in the calculations of trans isomers and their complexes.15,21 The 1D anharmonic frequency values for the ν2−ν5 modes are very close to the harmonic values; i.e., the D


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wave functions. The parameters derived from the 4D solution are listed in Table 4. Comparison of these values with the geometrical parameters of Table 4 shows to which extent excitation of the ν1 stretching vibration strengthens the Hbond, and excitation of ν6 or ν7 weakens it. The effect of the ν3 vibration on the H-bond is more complicated. One can see in Table 4 that the 4D anharmonic frequency values are rather close to the 1D values (Table 3) for the ν1, ν3, and ν7 vibrations. This is not the case for the ν6 torsional mode, where the intramode anharmonicity is very large, and the coupling, at least, to the ν1 mode cannot be ignored. As for the transition intensities, the 4D values are very close to the 1D values in the case of the ν3 and ν6 vibrations. The ν7 H-bond stretch intensity increased on taking into account the interaction between the ν7 and other, mainly ν1, modes. The most dramatic change in the transition intensity on passing from the 1D to 4D approximation is predicted for the ν1 mode. The absolute intensity became lower by a factor of 1.82 for NH3···cis-HONO and a factor of 1.32 for NH3···cis-DONO. This effect is explained by the decrease in the overlap of vibrational wave functions of combining states on passing to the 4D system of modes, in which the ν1 mode is the main source of intensity.

values of such frequency shifts for different modes can be different, in particular, due to resonances between the excited states of the ν1 and other modes. Although the pairwise interactions of the ν1 mode with other modes can both increase and decrease the ν1 frequency, they always decrease its intensity. This effect was earlier observed in the calculations of complexes of HF with water, dimethyl ether, and acetone.24 It is noteworthy that the whole picture of interactions of different degrees of freedom in these complexes is in conformity with the properties of hydrogen bonded complexes formulated in the new IUPAC definition of the hydrogen bond.25 The performed analysis showed that the ν1, ν3, ν6, and ν7 vibrations have to be considered simultaneously by solving the 4D problem (ν1, ν3, ν6, ν 7) to obtain more reliable spectroscopic and structural parameters of NH3···cis-HONO (DONO). The 1D parameters associated with the ν4 and ν5 modes can be improved by solving the 2D problem (ν4, ν5). For NH3···cis-HONO this solution yields ν4 = 975 cm−1 with the intensity value S = 343 km mol−1 and ν5 = 690 cm−1 with S = 15 km mol−1. The analogous values for NH3···cis-DONO are ν4 = 959 cm−1 (S = 347 km mol−1) and ν5 = 654 cm−1 (S = 9 km mol−1). Taking into account the (ν4, ν5) interaction improved the agreement between the theoretical value of the ν4 frequency and the experimental22 value 947.5 cm−1. To test the accuracy of the SCF approximation for calculating the DMSs and transition intensities, we calculated the 2D DMS for the (ν1, ν7) system in the MP2/aug-cc-pVTZ approximation and found, in agreement with the earlier estimates,21 that the absolute intensities calculated with the MP2 DMS for the ν1, ν7, and ν + ν7 transitions are lower than the SCF values by 7 ± 0.5%. 2.3. Results of 3D and 4D Calculations. To better examine the effects of intermode coupling, we obtained anharmonic solutions for a number of 3D vibrational subsystems containing the ν1 mode. These calculations allowed us, in particular, to estimate the degree of additivity of the action of two vibrations on the third vibration of a subsystem. Analysis of these solutions showed that the actions of two vibrations with one common atom on a third vibration are nonadditive. The frequency shifts of a mode due to its interactions with two other modes can compensate each other; consequently, the 1D frequency value of the first mode may be quite correct. In contrast, such compensation does not take place in calculations of transition intensities. Thus, as was stated earlier,24 reliable values of transition intensities can be derived only from solutions of multidimensional vibrational problems. The geometrical and electro-optical parameters of NH3···cisHONO and NH3···cis-DONO associated with the ν1, ν3, ν6, and ν7 vibrations were obtained from solution of the 4D problem for this subsystem. Four-dimensional wave functions ψ(4) j (ξ1,ξ3,ξ6,ξ7) were sought in the form of products of anharmonic solutions of 2D problems:

3. CONCLUSIONS The hydrogen-bonded NH3···cis-HONO and NH3···cis-DONO complexes were calculated using the approach earlier tested in calculations of isolated trans- and cis-HONO (DONO) molecules,15−17 and NH3···trans-HONO (DONO) complexes.16,21 The equilibrium geometry and the harmonic vibrational frequencies and intensities were calculated in the MP2/aug-cc-pVTZ approximation with the BSSE correction taken into account. The reliability of the adopted method for calculating the transition frequencies and absolute intensities was confirmed by good agreement of the theoretical results with experimental findings in our previous calculations of related compounds. In the present calculation, anharmonic values of frequencies and, what is more important, absolute intensities were obtained for six vibrations of cis-HONO (DONO) in a complex and the H-bond stretching vibration. This information can be useful in interpretation of future experiments. The anharmonic electro-optical parameters were derived from variational solutions of vibrational Schrödinger equations in one to four dimensions using accurate ab initio PESs in the space of normal coordinates. The use of these coordinates appears to be reasonable in anharmonic calculations of different isotopologues because the isotope effects are already partially reflected in the form of normal coordinates. The geometrical parameters of these systems were evaluated by averaging over the ground and excited states with the use of vibrational wave functions. The sensitivity of electrooptical and geometrical parameters to intermode anharmonic interactions was examined by comparing the results obtained for vibrational systems of different dimensionality. The calculations performed show that the strength of interaction of the ν1(H−O) vibration with other modes decreases on H/D substitution, i.e., with decreasing amplitude of this vibration. The changes in electro-optical parameters on isotopic substitution and complexation are consistent with the analogous changes in geometrical parameters. The calculated ν4(O−N) frequency of NH3···cis-HONO is close to the experimental value,22 the only experimental datum available for this complex. The calculations predict that the ν1 and ν4

70

ψj(4)(ξ1 ,ξ3 ,ξ6 ,ξ7) =

∑ k ,n=1

Cjknψk(2)(ξ1 ,ξ7) ψn(2)(ξ3 ,ξ6)

(3)

The sets of two-dimensional solutions for each pair of degrees of freedom in (3) were chosen so that they could describe both vibrations of each subsystem with the same accuracy. 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 2D sections of 4D E


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NH3··· cis-DONO

32 68 46 564 36 27

NH3··· cis-HONO

AUTHOR INFORMATION

36 106 48 834 100 24

Corresponding Author

*K. G. Tokhadze. Phone: +7 812 4287419. E-mail: k. [email protected].

217 773 1133 2025 1504 2272

NH3··· cis-DONO

fundamental transitions are strongest in the complexes considered, and the ν5 transition is the weakest of the internal modes of nitrous acid in these complexes. The ν3 fundamental transition, which is weakest in the spectra of isolated cis isomers, increases its intensity upon complexation by a factor of 4 for cis-HONO and 2.3 for cis-DONO. In accordance with the earlier observation,24 the frequency of the strongest vibration in the group of interacting modes, the ν1 vibration in our case, can be satisfactorily predicted by an 1D anharmonic calculation. In contrast, its transition intensity can be reliably obtained only from solution of a multidimensional equation for the whole group. In our calculations the ν1 intensity decreases by a factor of 1.82 and 1.32 for NH3···cis-HONO and NH3···cis-DONO, respectively, on passing from the 1D to 4D calculation.

■

Notes

■

220 1033 1418 2656 1983 2836

ACKNOWLEDGMENTS This study was supported by the Russian Foundation for Basic Research, Grant no. 15-03-04605 and by St. Petersburg State University, Grant no. 11.38.265.2014.

■

1.029 1.028 1.026 1.031 1.070 1.024 1.041 1.037 1.035 1.032 1.038 1.084 1.030 1.047 2.799 2.834 2.836 2.808 2.770 2.865 2.823 (0,0,0,0) (0,0,0,1) (0,0,1,0) (0,1,0,0) (1,0,0,0) (0,0,2,0) (0,2,0,0)

REFERENCES

(1) McGraw, G. E.; Bernitt, D. L.; Hisatsune, I. C. Infrared Spectra of Isotopic Nitrous Acids. J. Chem. Phys. 1966, 45, 1392−1399. (2) Deeley, C. M.; Mills, I. M. The Infrared Vibrational-Rotation Spectrum of trans and cis Nitrous Acid. J. Mol. Struct. 1983, 100, 199− 213. (3) Halonen, L. O.; Deeley, C. M.; Mills, I. M.; Horneman, V.-M. Vibrational-Rotation Spectra of Deuterated Nitrous Acid, DONO. Can. J. Phys. 1984, 62, 1300−1305. (4) Maki, A. G. High-Resolution Measurements of the ν2 Band of HNO3 and the ν3 Band of trans-HONO. J. Mol. Spectrosc. 1988, 127, 104−111. (5) Dehayem-Kamadjeu, A.; Pirali, O.; Orphal, J.; Kleiner, I.; Flaudb, P.-M. The Far-Infrared Rotational Spectrum of Nitrous Acid (HONO) and Its Deuterated Species (DONO) Studied by High-Resolution Fourier-Transform Spectroscopy. J. Mol. Spectrosc. 2005, 234, 182− 189. (6) Dehayem-Kamadjeu, A.; Orphal, J.; Ibrahim, N.; Kleiner, I.; Bouba, O.; Flaud, J.-M. The ν1 Fundamental Bands of trans- and cisDONO Studied by High-Resolution Fourier-Transform Spectroscopy. J. Mol. Spectrosc. 2006, 238, 29−35. (7) Perrin, A.; Miljanic, S.; Dehayem-Kamadjeu, A.; Chélin, P.; Orphal, J.; Demaison, J. The 14−22 μm Absorption Spectrum of Nitrous Acid Studied by High-Resolution Fourier-Transform Spectroscopy: New Analysis of the ν5 and ν6 Interacting Bands transHONO and First Analysis of the ν6 Band of cis-HONO. J. Mol. Spectrosc. 2007, 245, 100−108. (8) Hall, R. T.; Pimentel, G. C. Isomerization of Nitrous Acid: An Infrared Photochemical Reaction. J. Chem. Phys. 1963, 38, 1889−1897. (9) Guillory, W. A.; Hunter, C. E. Study of H + NO2 in an Argon Matrix between 4 and 14 K. The Infrared Spectra of Matrix-Isolated cis- and trans-HONO. J. Chem. Phys. 1971, 54, 598−603. (10) Khriachtchev, L.; Lundell, J.; Isoniemi, E.; Räsänen, M. HONO in Solid Kr: Site-Selective trans↔cis Isomerization with Narrow-Band Infrared Radiation. J. Chem. Phys. 2000, 113, 4265−4273. (11) Kagann, R. H.; Maki, A. G. Infrared Absorption Intensities of Nitrous Acid (HONO) Fundamental Bands. J. Quant. Spectrosc. Radiat. Transfer 1983, 30, 37−44.

2.805 2.839 2.831 2.810 2.764 2.853 2.819

NH3··· cis-HONO

NH3··· cis-DONO

NH3··· cis-HONO

NH3··· cis-DONO

NH3··· cis-HONO

The authors declare no competing financial interest.

state

intensity, km mol−1 frequency, cm−1 r(O−H), Å r(N···O), Å

Table 4. Average Values of r(N···O) and r(O−H) (in Å) in States (ν1, ν3, ν6, ν7) of NH3···cis-HONO and NH3···cis-DONO and the Frequencies and Intensities of Transitions to the Excited States from the Ground State


F


Article

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Anharmonic Calculation of the Structure, Vibrational Frequencies, and

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