Computational Vibrational and Electronic Spectroscopy of the Water

J. Phys. Chem. A 2010, 114, 4835–4842

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Computational Vibrational and Electronic Spectroscopy of the Water Nitric Oxide Complex† Teemu Salmi,‡ Nino Runeberg,‡ Lauri Halonen,*,‡ Joseph R. Lane,§ and Henrik G. Kjaergaard*,| Laboratory of Physical Chemistry, Department of Chemistry, UniVersity of Helsinki, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 UniVersity of Helsinki, Finland, Department of Chemistry, UniVersity of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, Department of Chemistry, UniVersity of Waikato, PriVate Bag 3105, Hamilton 3240, New Zealand, and Department of Chemistry, UniVersity of Copenhagen, UniVersitetsparken 5, DK-2100 Copenhagen Ø, Denmark ReceiVed: October 1, 2009; ReVised Manuscript ReceiVed: December 12, 2009

The water nitric oxide complex has been studied computationally. We consider the four lowest energy structures of the H2O-NO complex: two from both symmetries 2A′ and 2A′′. We use the coupled cluster method with correlation consistent basis sets in all ab initio calculations. Vibrational transitions have been calculated using a model that describes the complex as two individually vibrating monomer units: H2O and NO. We use the variational method to solve the vibrational problem. The OH-stretching energy levels and transition intensities are calculated up to the second and NO-stretching to the third overtone region. We also study NO-stretching vibronic transitions (A2Σ+ r X2Π). We use an isolated local mode approach to calculate energies and oscillator strengths of the vibronic transitions. The results for the complex are compared to the corresponding monomer ones. Introduction Nitric oxide (NO) has attracted increased attention during recent years due to its role in various biological, physiological, and atmospherical processes. NO is known to be an essential part of complex biological systems that involves actions such as blood pressure control or neuronal communication.1-3 In Earth’s atmosphere, NO plays a dual role in the determination of the ozone distribution. In the upper stratosphere, NO participates in a set of catalytic reactions that transfer ozone (O3) into molecular oxygen.4 At lower altitudes, NO is active in the processes of photochemical smog where ozone is formed.5 NO also plays a role in the temperature structure of the thermosphere.6 Since water is abundant in both cellular and atmospheric environments, it is of interest to study the interaction between NO and water. Nitric oxide is a relatively stable free radical with a 2Π1/2 ground state. The unpaired electron that occupies the highest occupied molecular orbital, HOMO, has an antibonding π* character. Since the HOMO is dominated by nitrogen character, NO prefers to coordinate via nitrogen to electron acceptors (hydrogen bond donors). When the hydrogen bond is formed, electron charge is transferred from the antibonding HOMO of NO to the acceptor. This makes the complexated NO bond stronger, which is observed as a shortened N-O bond length and a blue shift of the NO-stretching transition in the infrared spectrum. The electronic absorption spectroscopy of NO is well-known and has been recorded with a variety of experimental techniques.7-9 This work has also been complemented by several theoretical investigations.10-14 Below 60 000 cm-1 (∼7.5 eV), †

Part of the special section “30th Free Radical Symposium”. * Corresponding author. E-mail: [email protected]; [email protected]. ‡ University of Helsinki. § University of Otago and University of Waikato. | University of Otago and University of Copenhagen.

the electronic absorption spectrum consists mainly of discrete vibronic transitions belonging to the γ (A2Σ+ r X2Π), β (B2Π r X2Π), δ (C2Π r X2Π), and ε (D2Σ+ r X2Π) bands. In this work, we investigate the vibrational and electronic spectroscopy of the water nitric oxide complex using coupled cluster ab initio methods and correlation consistent basis sets combined with a local mode vibrational model. We consider the four lowest energy conformers of the complex, which are all of similar energy. We calculate IR/NIR transitions from the ground to vibrationally excited NO- and OH-stretching states up to third and second overtone region, respectively. Our results confirm some assignments of experimental matrix isolation infrared spectra.15 We calculate vibronic transitions of the lowest energy γ band (A2Σ+ r X2Π) of the nitric oxide monomer and compare them to the equivalent transitions in the water nitric oxide complex. Theory and Calculations We have fully optimized the four lowest energy conformers of the water nitric oxide complex and its constituent monomers with the spin unrestricted coupled cluster singles doubles and perturbative triples [RHF-UCCSD(T)] ab initio theory using Dunning type correlation consistent basis sets.16,17 We have used the aug-cc-pVQZ basis set for the nitrogen and oxygen atoms, and the cc-pVQZ basis set for the hydrogen atoms. We refer to this composite basis set as A′VQZ. We have recently shown that restricting diffuse basis functions to heavy atoms can reduce the effects of the basis set superposition error on CCSD(T) intermolecular distances and interaction energies in hydrogen bonded complexes.18 All CCSD(T) calculations assume a frozen core (O:1s; N:1s) and were performed using the MOLPRO19,20 computer program. The optimization threshold criteria was set to: gradient ) 1 × 10-6 au, stepsize ) 1 × 10-6 au, and energy ) 1 × 10-8 au.

10.1021/jp909441u  2010 American Chemical Society Published on Web 02/03/2010

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Vibrational Modeling. We calculate the vibrational energy levels using a model that describes the H2O-NO complex as independent H2O and NO subunits with no interunit coupling. The monomer units interact only in the sense that both H2O and NO potential energy surfaces (PES) have been computed in the presence of the other monomer unit. This approach has been successfully used to calculate a number of weakly bound complexes.21-26 The vibrational Schro¨dinger equations are solved using the variational method. The one-dimensional O-H stretching potential energy grids are calculated from -0.2 to +0.4 Å around the minimum energy structure with 0.05 Å steps. We determine the H-O-H bending coordinate by keeping the position of the oxygen atom and the H-O-H angle bisecting vector fixed with respect to the position of NO and changing the H-O-H angle. We calculate the H-O-H angle bending grid from -25° to +25° with steps of 5°. The two-dimensional potential energy grids are calculated by displacing two vibrational coordinates simultaneously. To keep the required CPU time reasonable, we have reduced the displacements to (0.15 and (0.05 Å for O-H stretches and (15° and (5° for H-O-H bends in the 2D grids. NO-stretching motion cannot be determined by moving just one atom, because the N and O masses are similar. Therefore, we keep the NO center of mass fixed with respect to H2O to make the stretching motion realistic. We also fix the direction of the NO bond; i.e., the angle O1-x-O2 does not change (O1 and O2 are the two oxygen atoms in the complex and x is the NO center of mass). The potential energy grid is calculated from -0.2 to +0.2 Å around the minimum energy structure with 0.05 Å steps. Because increasing the NO bond length causes the spin contamination27 to grow rapidly, we limited the NO bond displacement to +0.2 Å. This is enough to obtain a PES that describes accurately the NO-stretching vibration up to the third overtone. An analytical potential energy function is fitted to the potential energy grid.28 For all stretches, a series expansion over the Morse variable, y, is used as a one-dimensional stretching potential. On the basis of testing and our previous work,25,26 we have used a series

V(r) )

∑

y ) 1 - exp(-a∆r)

Tnyn

(1)

n)2,3,4,6

where Tn and a are optimized parameters and ∆r the bond length displacement. The H-O-H bending motion is described using a series expansion over the angle bending displacement coordinate ∆θ

V(θ) )

fn (∆θ)n n! n)2,3,4

∑

(2)

where fn is a potential energy parameter, force constant. The same variables (y and ∆θ) are used for the two-dimensional parts of the PES. The PES is presented in the Supporting Information. We use kinetic energy operators that are exact within the Born-Oppenheimer approximation for isolated H2O and NO molecules. The operator for the water unit is described in our earlier paper.25 We solve the vibrational Schro¨dinger equations using the variational method. For OH- and NO-stretches, 10 lowest Morse oscillator eigenfunctions29 and for H-O-H bends 10 lowest harmonic oscillator eigenfunctions are used as basis functions. We obtain energies that are converged better than 1

cm-1 using this basis. We have used a similar model earlier for the water dimer and trimer with good results.25,26 We calculate the dimensionless oscillator strength30 for a transition from the ground state, 0, to an excited state, V using the expression

fV,0 ) 4.702 × 10-7 [cm D-2] ν˜ V,0 |µ bV,0 | 2

(3)

µV,0 ) 〈V|µ b|0〉, and where ν˜ V,0 is the excitation wavenumber in cm-1, b b µ is the dipole moment function. The dipole moment function is calculated at the RHF-UCCSD(T)/A′VQZ level of theory using the finite differences method with electric fields -0.0001 and +0.0001 au. We have not employed Eckart axes to minimize vibration-rotation interactions because this alternative choice makes only a small difference.31-34 The dipole moment function is expanded in a thirdorder Taylor series over the OsH bond length and HsOsH angle bending coordinates, and a fifth-order Taylor series over the NO bond displacement coordinate. It is fitted to the calculated points using the least-squares method. The dipole moment function is presented in the Supporting Information. Electronic Transitions. We calculate the NO-stretching vibronic transitions of the γ band (A2Σ+ r X2Π) of the nitric oxide monomer and the equivalent vibronic transitions of the water nitric oxide complex using an isolated local mode approach. The one-dimensional Schro¨dinger equation for the ground (2Π) and excited (2Σ+) electronic states are solved separately using the numerical finite element method to produce both the vibrational energy levels and wave functions.35 We have checked our isolated one-dimensional approach to a full normal mode approach and find that the harmonic frequency of the NO-stretching vibrational mode differs by less than 1 cm-1 between the two approaches. We calculate the NOstretching potentials of the ground 2Π and excited 2Σ+ states using the CCSD and EOM-CCSD methods, respectively. For the water nitric oxide complex, we use the CCSD(T)/A′VQZ optimized structures and displace the NO bond length about the center of mass of the nitric oxide subunit leaving all other geometric parameters fixed. This is the same approach that was used when calculating the potential energy and dipole moment surface for the NO-stretching vibrational transitions. The A2Σ+ r X2Π transition of nitric oxide can be thought of as excitation from an antibonding π* orbital to an essentially nonbonding Rydberg orbital.12 It follows that the equilibrium bond length of the ground 2Π state (1.151 Å) is appreciably longer than that of the 2Σ+ state (1.064 Å).7 For the ground state, we construct an NO-stretching potential from -0.25 to +0.3 Å in 0.01 Å steps around the ground state equilibrium bond length. For the 2Σ+ state, we nominally use a potential from -0.25 to +0.15 Å in 0.01 Å steps around the ground state equilibrium bond length. However, at NO distances of ∼1.2-1.25 Å, there is a conical intersection that causes significant state mixing in our single reference EOM-CCSD calculations. A similar discrepancy was also observed when the dipole moment surface was calculated for the vibrational transitions. As a result, the potential energy curves in this localized region are discontinuous. To alleviate convergence problems when solving the one-dimensional Schro¨dinger equation, we omit these discontinuous points from our potential energy and dipole moment curves (typically 1-2 points). The 2Σ+ excited state has significant Rydberg character12 and hence diffuse basis functions are required to properly describe this state. We have constructed a series of molecule-centered primitive basis functions, originating from the center of mass of nitric oxide according to the procedure by Kaufmann et al.36

Water Nitric Oxide Complex

Figure 1. RHF-UCCSD(T)/A′VQZ optimized structures of the H2O-NO complex. Conformers 1 and 2 have 2A′ symmetry whereas conformers 3 and 4 have 2A′′ symmetry. Key: white, H; red, O; blue, N.

For the water nitric oxide complex, these primitive basis functions originate from the center of mass of the nitric oxide subunit. We have chosen a set of 3s3p3d functions with “semiquantum numbers” from 2.0 to 3.0, in half-integral steps. The aug-cc-pVXZ (where X ) D, T, Q) correlation consistent basis sets augmented with this 3s3p3d set are denoted AVXZ+3. All CCSD and EOM-CCSD calculations were performed with the PSI3.4 computer program.37 All convergence thresholds were kept at their default values with the exception of cclambda, which was reduced to 1 × 10-5 au because of convergence difficulties. The dimensionless oscillator strength f of a vibronic transition from the vibrational ground state is calculated using eq 3. The integrals 〈V|qn|0〉 required for the electronic transition moment are evaluated by trapezoidal numeric integration. The electronic transition moment coefficients are found from a sixth-order polynomial fit to a 41 point (nominal) electronic transition moment curve calculated over the same range as the excited state potential. Results and Discussion The ground electronic state (X2Π) of the nitric oxide radical is doubly degenerate. Interaction of nitric oxide with a closed shell water molecule removes this degeneracy resulting in two low lying electronic states: 2A′ and 2A′′ within the Cs symmetry point group.38 We have optimized the two lowest energy structures of the water nitric oxide complex in both the 2A′ and 2 A′′ electronic states with the CCSD(T)/A′VQZ method. We show these four conformers graphically in Figure 1 and tabulate selected geometric parameters in Table 1. Our present CCSD(T)/ A′VQZ fully optimized structures and interaction energies are in good agreement with the partially optimized structures of Cybulski et al. at the CCSD(T) level of theory,38 where geometric parameters of the monomers were held at experimental monomeric values. The two lowest energy conformers of 2A′ symmetry (1 and 2) can be described as weak hydrogen bonded complexes where the water unit acts as the proton donor and the nitrogen atom acts as the acceptor. In contrast, the two lowest energy conformers of 2A′′ symmetry (3 and 4) are best described as

J. Phys. Chem. A, Vol. 114, No. 14, 2010 4837 electron donor-acceptor complexes with the oxygen atom of water acting as the Lewis acid and the nitrogen atom of nitric oxide acting as the Lewis base.39 The calculated interaction energies of all four conformers are similar despite the different nature of the intermolecular interactions in conformers 1 and 2 compared to conformers 3 and 4. It follows that the relative abundance of all four conformers is likely to be similar, potentially complicating experimental spectroscopic investigations of this complex. In the hydrogen bonded conformers (1 and 2), the bonded OH-bond length (ROH(b)) is slightly elongated whereas the free OH-bond length (ROH(f)) is slightly contracted when compared to that of the water monomer. These geometric changes in the water subunit upon complexation are typical of hydrogen bonded complexes where water acts as the donor.23,40 We also observe a somewhat smaller elongation of ROH(b) and contraction of ROH(f) in conformer 3, which suggests that this conformer has both electron donor-acceptor and hydrogen bonded character. We find that all four conformers exhibit as slight contraction of the nitric oxide bond length (RNO) upon complexation. However, this effect is more pronounced in the hydrogen bonded complexes than in the electron donor-acceptor complexes. Vibrational Spectroscopy. We have calculated vibrational energy levels for the H2O and NO units in the H2O-NO complex and for fully and partially deuterated isotopomers. In our model, the NO unit is unaffected by the mass of the hydrogen atom, so its vibrational energy levels are the same in all isotopomers of water. Results for H2O-NO are in Tables 2 and 3, and for the deuterated species in the Supporting Information. We use the local mode notation of symmetric C2V water for the vibrations of the H2O unit. In this notation,41,42

|mn〉( |V〉 )

1 (|mn〉 ( |nm〉)|V〉 √2

mgn

(4)

where m and n are the quantum numbers of the two OHstretching modes and V is the H-O-H angle bending quantum number. This notation is invalid for conformers 1-3 where the water unit does not possess local C2V symmetry. However, the difference in the PES and bond lengths of ROH(f) and ROH(b) is small enough for the notation to be usable. The hydrogen bonded conformers 1 and 2 are vibrationally similar. The potential energy barrier between these conformers is small. For a transition from conformer 2 to 1 through the planar transition state, it is about 40 cm-1. All OH-stretching energy levels are red-shifted from the ones of an isolated water molecule. The states |10〉+|0〉 and |10〉-|0〉 are described well using this notation. The mixing ratio is approximately 40-60% (|10〉+|0〉 ≈ 0.77 × |0〉f|1〉b|0〉 + 0.63 × |1〉f|0〉b|0〉 and |10〉-|0〉 ≈ 0.63 × |0〉f|1〉b|0〉 - 0.77 × |1〉f|0〉b|0〉; the subindices f and b refer to the free and bonded OH-stretches, respectively). In the states |20〉(|0〉 and |30〉(|0〉, the energy difference between the free and bonded OH-stretch is large enough for the mixing to be small. Hence, the symmetric states (+) consist mostly of the bonded, and the antisymmetric ones (-) mostly of the free OH-stretch. Complex formation does not have a significant effect on the water unit in conformers 3 and 4. We observe a red shift in all OH-stretching energy levels. However, the shift is small compared to that of conformers 1 and 2. In the fully deuterated isotopomer, the shifts are similar to the ones of H2O-NO. In the partially deuterated HDO unit, the OH- and ODstretches are separated from each other. The HDO unit belongs to the symmetry point group Cs in all conformers 1-4.

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TABLE 1: Calculated [RHF-UCCSD(T)/A′VQZ] Selected Geometric Parameters (Å for Distances and Degrees for Angles) for H2O-NO and the Monomers and Interaction Energies (kcal mol-1) for the Complex ROH(b) ROH(f) θHOH RNO RO · · · N ∠(N–Hb-OH2O) ∠(O–N–O) Eint

monomer

conformer 1

conformer 2

conformer 3

conformer 4

0.9589 0.9589 104.36 1.1530

0.9602 0.9588 104.51 1.1512 3.2815 169.5 125.6 –1.37

0.9601 0.9587 104.51 1.1515 3.2915 170.9 142.3 –1.27

0.9594 0.9590 104.52 1.1523 2.9126 78.5 103.3 –1.28

0.9591 0.9591 104.42 1.1527 3.0133 46.6 89.9 –1.24

TABLE 2: Calculated [RHF-UCCSD(T)/A′VQZ] Vibrational Energy Levels (cm-1) and Oscillator Strengths (in Parentheses) for the H2O Unit in H2O-NO and H2O local mode +

|00〉 |1〉 |00〉+|2〉 |10〉+|0〉 |10〉-|0〉 |10〉+|1〉 |10〉-|1〉 |20〉+|0〉 |20〉-|0〉 |11〉+|0〉 |30〉+|0〉 |30〉-|0〉 |21〉+|0〉 |21〉-|0〉

conformer 1

conformer 2 -5

1601.1 (1.0 × 10 ) 3167.8 (2.2 × 10-7) 3641.6 (7.5 × 10-6) 3746.0 (2.0 × 10-5) 5222.6 (1.7 × 10-7) 5328.2 (2.0 × 10-6) 7165.5 (4.6 × 10-8) 7232.6 (4.1 × 10-7) 7424.6 (1.6 × 10-8) 10529.4 (4.8 × 10-9) 10605.5 (1.3 × 10-8) 10832.0 (1.8 × 10-9) 11004.2 (2.7 × 10-9)

conformer 3 -5

1600.7 (1.1 × 10 ) 3166.8 (2.5 × 10-7) 3645.1 (6.9 × 10-6) 3748.2 (1.9 × 10-5) 5226.5 (8.5 × 10-8) 5330.6 (1.7 × 10-6) 7175.0 (4.1 × 10-8) 7235.2 (4.2 × 10-7) 7429.6 (2.2 × 10-8) 10547.5 (3.9 × 10-9) 10606.0 (1.3 × 10-8) 10840.7 (1.3 × 10-9) 11011.4 (2.2 × 10-9)

conformer 4 -5

1596.1 (1.6 × 10 ) 3158.1 (1.1 × 10-7) 3649.9 (6.2 × 10-7) 3754.3 (8.2 × 10-6) 5225.6 (1.9 × 10-8) 5331.3 (1.4 × 10-6) 7190.0 (9.1 × 10-8) 7242.2 (5.3 × 10-7) 7442.5 (5.3 × 10-9) 10585.2 (3.0 × 10-9) 10604.9 (1.6 × 10-8) 10857.2 (1.0 × 10-9) 11031.7 (2.5 × 10-9)

H 2O -5

1597.6 (1.4 × 10 ) 3161.2 (1.0 × 10-7) 3651.2 (7.1 × 10-7) 3755.0 (8.8 × 10-6) 5228.6 (2.6 × 10-8) 5333.7 (1.3 × 10-6) 7192.6 (1.0 × 10-7) 7243.7 (5.4 × 10-7) 7443.9 (4.8 × 10-9) 10590.7 (1.3 × 10-9) 10605.0 (1.8 × 10-8) 10859.9 (9.8 × 10-10) 11033.5 (2.4 × 10-9)

1596.4 (1.4 × 10-5) 3158.4 (8.5 × 10-8) 3652.7 (4.8 × 10-7) 3756.8 (8.0 × 10-6) 5229.0 (2.1 × 10-8) 5334.7 (1.4 × 10-6) 7195.2 (8.6 × 10-8) 7246.5 (5.5 × 10-7) 7447.3 (4.7 × 10-9) 10594.1 (1.0 × 10-9) 10608.4 (1.9 × 10-8) 10863.9 (9.3 × 10-10) 11038.0 (2.6 × 10-9)

TABLE 3: Calculated [RHF-UCCSD(T)/A′VQZ] Vibrational Energy Levels (cm-1) and Oscillator Strengths (in Parentheses) for the NO Unit in H2O-NO and Isolated NO local mode |1〉 |2〉 |3〉 |4〉

conformer 1

conformer 2 -6

1891.0 (5.5 × 10 ) 3755.5 (8.4 × 10-8) 5593.6 (2.9 × 10-9) 7405.1 (1.2 × 10-10)

conformer 3 -6

1890.0 (5.5 × 10 ) 3753.6 (8.5 × 10-8) 5590.8 (2.9 × 10-9) 7401.5 (1.3 × 10-10)

Therefore, we use the labeling |m〉H|n〉D|V〉, where m is the OHstretching, n is the OD-stretching, and V is the H-O-H angle bending quantum number. There are two possible positions for the deuterium atom in the conformers 1-3 for which we have calculated the vibrational energy levels. The vibrational spectrum of the HDO unit in conformer 4 resembles closely the one of an isolated HDO molecule. Because partial deuteration removes mixing between the free and bonded stretching motion, it reveals the true character of these two stretching motions; the bonded OH- or OD-stretch is red-shifted and therefore the free stretch remains close to the one of the isolated HDO molecule. The variationally calculated vibrational energy levels for NO are presented in Table 3. All calculated values are blue-shifted from the free NO ones. This is consistent with the shortening of NO bond length and strengthening of the NO bond upon complexation. The blue shift is largest in the hydrogen bonded conformers 1 and 2, and is approximately 10 cm-1 for the NOstretching fundamental. The intensities of the vibrational transitions for the water nitric oxide complex are presented in Tables 2 and 3, and the results for the deuterated species in the Supporting Information. The intensities of NO-stretching transitions in the complex are similar to those of free NO. The intensities of the fundamental OH-stretches increase in all conformers upon complex formation. The change is largest in the hydrogen bonded conformers 1 and 2 and minor in the 2 A′′ conformers. In the hydrogen bonded complexes 1 and 2, the intensity ratio between free (asymmetric) and bonded (symmetric) stretches is 2.7 whereas for water it is 16.7 in the

conformer 4 -6

1885.1 (5.2 × 10 ) 3743.7 (7.3 × 10-8) 5575.8 (2.2 × 10-9) 7381.2 (9.1 × 10-11)

NO -6

1881.3 (5.4 × 10 ) 3736.2 (7.4 × 10-8) 5564.4 (2.2 × 10-9) 7365.9 (9.7 × 10-11)

1880.3 (5.6 × 10-6) 3734.1 (7.5 × 10-8) 5561.2 (2.2 × 10-9) 7361.7 (8.7 × 10-11)

fundamental OH-stretching region. At the first overtone region the ratios are similar in H2O-NO and H2O, so the bonded OHstretch becomes relatively weaker. This is typical for hydrogen bonded complexes where water acts as the donor molecule.21,23,25,26,43 The effect of hydrogen bonding can be seen more clearly in the partially deuterated complex; the bonded fundamental is about 5 times as intense as the corresponding isolated HDO one, and the overtones are weaker in the complex. The free OH(D)-stretching oscillator strengths are similar to those of an isolated HDO molecule. This is true for both HfODb-NO and DfOHb-NO. The fundamental and overtone OH-stretching transitions of the H2O-N2 and H2O-O2 complexes have been previously calculated with a harmonically coupled anharmonic oscillator local mode model.23 The lowest energy structures of these two complexes are similar to the hydrogen bonded conformers of the H2O-NO complex and have comparable binding energies. Hence, it is reasonable to expect that the OH-stretching transitions of H2O-NO will be similar to the equivalent transitions of H2O-N2 and H2O-O2. The OH-stretching fundamental transitions of H2O-N2 become stronger upon complexation with the equivalent first overtone transitions becoming slightly weaker. In the second overtone, |30〉+|0〉 is more intense in the complex than in an isolated water molecule whence |30〉-|0〉 is slightly weaker in the complex. The changes in the intensities of H2O-O2 are similar, but smaller in magnitude with the exception that |10〉+ is slightly weaker in the complex than in the water molecule. Therefore, the hydrogen

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TABLE 4: Comparison of Calculated [RHF-UCCSD(T)/A′VQZ] Vibrational Shifts (ν˜ complex - ν˜ monomers, cm-1) with the Matrix Isolation Data from Ref 15 calculated

experiment conformer 4

R

–1.4 +1.2 –1.9 +1.0

–4.6 +1.5 +10.2 +1.7, +1.9

–2.0 –0.3 –1.8 +4.8

–1.1 +0.8 –1.4 +1.0

–2.9 +0.7 +8.4 +1.8, +2.0

–9.8 +1.7 –5.7 +8.3

HDOa –3.7; –0.2 –0.2; –0.4 –0.1; –5.1 +4.8

–1.2 +1.0 –1.7 +1.0

–3.2 +1.1 +9.6 +1.8, +2.0

–17.6 –1.4 +5.6 +8.3

conformer 1

conformer 2

conformer 3

ν1 ν2 ν3 νNO

–11.1 +4.7 –10.8 +10.7

–7.6 +4.3 –8.7 +9.7

–2.7 –0.3 –2.6 +4.8

ν1 ν2 ν3 νNO

–7.2 +3.4 –8.0 +10.7

–5.1 +3.1 –6.4 +9.7

ν1 ν2 ν3 νNO

–16.3; +1.3 +4.4; +3.7 +1.2; –23.5 +10.7

–12.5; +1.3 +4.0; +3.5 +1.3; –18.0 +9.7

β

β′

H2O

D 2O

+7.8 +12.2 +8.3

In conformers 1, 2, and 3 the number before a semicolon corresponds to the “deuterium bonded” HfODb-NO structure, and the second number to the DfOHb-NO structure. In the case of HDO, ν1 refers to the O-D and ν3 to O-H stretch. νNO denotes the NO-stretching fundamental. a

bonded conformers of H2O-NO remind more closely H2O-N2 than H2O-O2. Comparison to Experimental Work. Infrared matrix isolation spectra of H2O-NO, D2O-NO, and HDO-NO have been measured in the fundamental region.15 Comparison between our work and ref 15 is presented in Table 4. Three conformers, R, β, and β′, were observed, of which R is seen in all isotopomers, β in fully and partially deuterated species, and β′ in partially deuterated species. For consistency with the earlier literature, we use the notation from ref 15 instead of the local mode notation. In the R conformer, NO-stretching fundamental shifts relative to the monomer values are close to 2 cm-1. The two NO-stretching peaks are due to the matrix site effect. In the case of the OH-stretches, the symmetric stretch ν1 is shifted by -4.6 cm-1 while the antisymmetric stretch ν3 is shifted by +10.2 cm-1. Deuteration makes the OH-stretch shifts approximately 2 cm-1 smaller but has little effect on the NO-stretch. Partial deuteration does not add another R structure to the spectrum. This suggests that the water unit in R-H2O-NO possesses a local C2V symmetry or that only one orientation is energetically favorable. Our calculated results for conformer 4, where the water unit belongs to a C2V symmetry point group, are similar to those of the observed R conformer with the exception that our calculated ν3 is red-shifted. We do not compute any blue shifts in the OH(D)-stretching region for any isotopomers of water. Hence, we do not suggest an assignment for the R structure but cannot completely exclude conformer 4. The wavenumber shift in the NO-stretch is larger in both β and β′ conformers than in R. The shift is +8.3 cm-1 in both fully and partially deuterated species. Therefore, we suggest that these conformers are the ones where NO is hydrogen bonded to the water unit (conformers 1 and 2, where the blue shift is largest). The shifts of the fully deuterated conformers 1 and 2 agree with the ones of the β structure. The fact that the β′ conformer appears only in the case of partially deuterated species suggests that the two β conformers are isotopomers where the position of hydrogen and deuterium atoms is reversed. We calculate a large red shift for ν1 in HfODb-NO and for ν3 in DfOHb-NO, and correspondingly a small blue shift for the other stretching modes. Hence, we assign the β conformer to HfODb-NO and β′ to DfOHb-NO. However, the shifts related to conformers 1 and 2 are similar to each other and therefore

TABLE 5: Comparison of Calculated [RHF-UCCSD(T)/A′ VTZ] Vibrational Shifts (cm-1) in Normal Modes of the Conformer 1 ν1 ν2 ν3 νNO

H2O-NO

HfDbO-NO

DfHbO-NO

–9.2 +6.4 –10.0 +12.0

–14.5 –2.0 +1.3 +12.0

+1.1 +12.5 –20.0 +12.0

we are unable to attach the β and β′ structure to a particular conformer 1 or 2. A similar conclusion was made in ref 15. Even though the stretching degrees of freedom in the partially deuterated conformers agree with the experiment, the computed ν2 (H-O-H bend) shifts differ from the observed ones. This problem may result from the definition of the H-O-D angle bending coordinate. Let y be a point in the H-O-D angle bisecting vector. In the PES, we vary both angles H-O-y and D-O-y by an equal amount. Because of the H/D mass difference, we expect the bending motion not to appear symmetrically. We recalculated the one-dimensional bending part of the PES of conformer 1 using a bending coordinate where we vary the H-O-y angle twice as much as we vary the D-O-y angle. By doing this, we obtain shifts of -2.7 and +12.5 cm-1 instead of +4.4 and +3.7 cm-1. These numbers agree well with the matrix isolation data. We ran a normal mode calculation for conformer 1 to test the shifts in the bends (Table 5). The results agree with the results obtained with the modified bending coordinate. In our variational calculations, we are using an anharmonic model that does not contain all nine vibrational degrees of freedom. Therefore, because the choice of the coordinate definitions is not unambiguous, it does not make sense to recalculate the PES for different definitions of the bending degree of freedom. Electronic Spectroscopy. We present experimental and EOM-CCSD calculated vibronic excitation energies and oscillator strengths for the A2Σ+ r X2Π transition of the nitric oxide monomer in Table 6. We limit the present investigation to consider only excitation from the vibrational ground state as the Boltzmann population of the first excited vibrational state is just 0.01% at room temperature. We find that the calculated adiabatic excitation energy (Te) increases and converges toward the experimental value as the cardinal number of the basis set increases. This variation in the adiabatic excitation energy with

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Salmi et al.

TABLE 6: EOM-CCSD Vibronic Excitation Energies (cm-1) and Oscillator Strengths for the A2Σ+ r X2Π Transition of the NO Monomer AVDZ+3 state

E

V0,0 V1,0 V2,0 V3,0 V4,0 V5,0 V6,0 Te

42592 44981 47340 49669 51968 54236 56474 42360

AVTZ+3 f

E -4

3.6 × 10 6.6 × 10-4 5.3 × 10-4 2.4 × 10-4 7.0 × 10-5 1.3 × 10-5 1.7 × 10-6

f

E -4

3.6 × 10 6.9 × 10-4 5.7 × 10-4 2.8 × 10-4 8.5 × 10-5 1.8 × 10-5 2.6 × 10-6

43473 45887 48272 50628 52955 55251 57517 43239

expta

AVQZ+3 43749 46182 48587 50962 53308 55624 57909 43515

f -4

3.7 × 10 7.0 × 10-4 5.8 × 10-4 2.8 × 10-4 8.7 × 10-5 1.8 × 10-5 2.7 × 10-6

E

f

44207 46546 48853 51136 53297 55580 57814 43965.7

4.20 × 10-4 8.24 × 10-4 7.30 × 10-4 3.56 × 10-4

a From ref 9. Oscillator strengths for the V4,0, V5,0, and V6,0 vibronic transitions of the γ band are complicated by overlapping vibronic transitions from the β, δ, and ε bands.

TABLE 7: EOM-CCSD/AVTZ+3 Vibronic Excitation Energies (cm-1) for the A2Σ+ r X2Π Transition of H2O-NO state

NO

V0,0 V1,0 V2,0 V3,0 V4,0 V5,0 V6,0 Te

43473 45887 48272 50628 52955 55251 57517 43239

conformer 1 conformer 2 conformer 3 conformer 4 45659 48080 50472 52835 55168 57472 59746 45428

45177 47598 49989 52351 54684 56987 59269 44946

42453 44873 47264 49626 51959 54265 56541 42220

41805 44224 46613 48974 51307 53613 55886 41571

the basis set size is similar to previous vertical excitation calculations and is an indication that the 2Σ+ state of nitric oxide has significant Rydberg character.44 In general, our EOM-CCSD calculated vibronic excitation energies and oscillator strengths are in reasonably good agreement with experiment.9 The discrepancy between the calculated and measured excitation energies is primarily due to the difference between the calculated and measured adiabatic excitation energy, which is underestimated by ∼450 cm-1 even with the AVQZ+3 basis set. If we set the calculated adiabatic excitation energy equal to the measured value, then the calculated V0,0 transition is within 10 cm-1 of the experimental value with all three basis sets. The CCSD method is known to slightly underestimate calculated bond lengths and hence slightly overestimates the harmonicity of the NO-stretching potential.45 As a result, the energy spacing between consecutive vibronic transitions is also slightly overestimated as compared to experiment. Inclusion of triple or higher excitations would reduce the harmonicity of the ground and excited state NOstretching potential,45 resulting in calculated vibronic spacings in better agrement with experiment. However, these methods are not computationally practicable for calculating the excited state potentials of the water nitric oxide complex with suitably large basis sets. The EOM-CCSD calculated oscillator strengths of nitric oxide increase and appear to converge as the cardinal number of the basis set increases from AVDZ+3 to AVQZ+3. There is little variation between the AVTZ+3 and AVQZ+3 calculated

oscillator strengths, indicating that the AVTZ+3 basis set is adequate to reproduce both the vibrational wave functions and electronic transtion moment of the A2Σ+ r X2Π transition. We find that the EOM-CCSD calculated oscillator strengths are underestimated by ∼10-20% as compared to experiment. However, the calculated relative intensity of the V0,0 to V3,0 transitions is in excellent agreement (less than 1%) with the experimental relative intensity. This suggests that the variation between the calculated and experimental oscillator strengths is a result of the electronic transtion moment and not the vibrational wave function overlap. In Table 7, we present EOM-CCSD/AVTZ+3 calculated vibronic excitation energies for the A2Σ+ r X2Π transitions of the four lowest energy conformers of the water nitric oxide complex. We find that the adiabatic excitation energies of the two hydrogen bonded 2A′ conformers (1 and 2) are significantly blue-shifted (+2200 and +1700 cm-1) whereas the adiabatic excitation energies of the two electron donor-acceptor 2A′′ conformers (3 and 4) are significantly red-shifted (-1000 and -1700 cm-1). We can rationalize this difference between the adiabatic excitation energies of 2A′ and 2A′′ conformers if we consider the effect of complexation on the occupied π* orbital from which excitation occurs. In the 2A′ conformers, we find that the energy of this π* orbital becomes more negative whereas in conformer 4 (2A′′ symmetry) this orbital becomes slightly less negative. However, in conformer 3 (also 2A′′ symmetry), we find that the energy of the π* orbital becomes slightly more negative. The adiabatic excitation energy of conformer 3 is red-shifted by just 1000 cm-1 whereas in the more weakly bound conformer 4 it is red-shifted by 1700 cm-1. We suggest that competitive effects between the hydrogen bonding and electron donor-acceptor intermolecular interactions in conformer 3 somewhat cancel, resulting in the smallest change in the adiabatic excitation energy of the four conformers. We find that the energy spacing between consecutive vibronic transitions in the nitric oxide monomer and in the four conformers of the water nitric oxide complex differ by only a few wavenumbers. This indicates that the curvature of the 2Σ+ NO-stretching potential is essentially unchanged upon com-

TABLE 8: EOM-CCSD/AVTZ+3 Vibronic Oscillator Strengths for the A2Σ+ r X2Π Transition of H2O-NO state V0,0 V1,0 V2,0 V3,0 V4,0 V5,0 V6,0

NO

conformer 1 -4

3.6 × 10 6.9 × 10-4 5.7 × 10-4 2.8 × 10-4 8.5 × 10-5 1.8 × 10-5 2.6 × 10-6

-4

5.9 × 10 1.1 × 10-3 9.2 × 10-4 4.4 × 10-4 1.4 × 10-4 3.0 × 10-5 4.8 × 10-6

conformer 2 -4

5.5 × 10 1.0 × 10-3 8.4 × 10-4 4.0 × 10-4 1.2 × 10-4 2.6 × 10-5 3.8 × 10-6

conformer 3 -4

3.5 × 10 6.5 × 10-4 5.3 × 10-4 2.5 × 10-4 7.2 × 10-5 1.4 × 10-5 2.0 × 10-6

conformer 4 3.7 × 10-4 6.9 × 10-4 5.7 × 10-4 2.7 × 10-4 8.4 × 10-5 1.7 × 10-5 2.5 × 10-6

Water Nitric Oxide Complex

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