A CASSCF study on photodissociation of the N2O32- dianion

Chemical Physics Letters 431 (2006) 415–420 www.elsevier.com/locate/cplett

A CASSCF study on photodissociation of the N2O2 3 dianion Ling-Ling Lu¨ b

a,*

, Kun Yuan a, Yong-Cheng Wang b, Han-Qin Wang

c

a College of Life science and Chemistry, Tianshui Normal University, Tianshui, Gansu 741001, People’s Republic of China College of Chemistry and Chemical Engineering, Northwest Normal University, LanZhou, Gansu 730070, People’s Republic of China c Institute of Chemistry and Physics, Chinese Academy of Sciences, LanZhou, Gansu 730070, People’s Republic of China

Received 1 September 2006; in final form 29 September 2006 Available online 7 October 2006

Abstract 2 N2 O2 3 photodissociation was investigated using the CASSCF energy gradient techniques. After the N2 O3 dianion is populated in the S1 state, the system can undergo different routes. One route involves radiationless decay via an intersystem crossing T1/S1 to the T1 minimum intermediate. Then through the transition state TS (T1) and the T1/S0 to the ground state surface. The other route involves the S1/ S0 conical intersection. These results show that the main product NO of the efficient photodissociation is singlet-state rather than triplet (3R) state. Our calculated results are in close agreement with experimental observations.  2006 Elsevier B.V. All rights reserved.

1. Introduction With the development of experimental methods, especially laser techniques, the detailed processes of photochemistry have attracted growing interest. Meanwhile, recent advances in computational techniques have led to great progress in the levels and details of our understanding of photochemistry [1]. However, many photochemical reactions are nonadiabatic. The reaction starts on an excited-state potential surface and proceeds ultimately to a bonding ground-state configuration via a surface crossing (where intersystem crossing or fast internal conversion takes place). Thus, the characterization of a mechanism of photochemical reaction involves in addition to the study of ground- and excited-state reaction paths, a characterization of the region where the surface crossing occurs and the system decays nonradiatively to the ground state [2–7]. For most photoreactions, it is still largely unknown at what point along the reaction coordinate the photoexcited reactant decays [8]. Therefore, the subject of the photochemical reactions is still of considerable current interest.

*

Corresponding author. Fax: +86 0931 7971989. E-mail addresses: [email protected], [email protected] (L.-L. Lu¨). 0009-2614/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.10.004

Photochemical cleavage of the trioxodinitrate dianion (N2 O2 3 ), which can be viewed as a stable N–N adduct between NO and NO 2 , provides a convenient method to rapidly generate nitroxyl species. In strongly alkaline solutions, successive formation of several nitroxyl species has been assigned to the following reactions initiated by UV laser light [9,10]   1 1 N2 O2 3 ðþhmÞ ! NO þ NO2 1 1



ð1Þ



ð2Þ

HNO þ OH ! NO þ H2 O

ð3Þ

1

NO þ H2 O ! HNO þ OH 

3



The photochemical step is rapid, whereas the spin-forbidden reaction (3) is comparatively slow. As listed above, the ground state of NO is triplet (3R), while the product NO of the efficient photodissociation is singlet-state. Heretofore, little attention has been given to this problem. The trioxodinitrate dianion (Angeli’s salt) is a species of great interest to experimental and theoretical chemists since the first report of its synthesis in the late 1800s [11] and the suggestion several years later [12] of the production of NOH upon decomposition. To our knowledge, very recently, Dutton and co-workers [13,14] have done a series studies by experimental methods and theoretical calculations. However, the intersections between different potential surfaces and mechanistic aspects of the N2 O2 3

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photodissociation have not been studied. In the present study, we investigate the molecular structures of the trioxodinitrate dianion and its potential surfaces of lowest-lying electronic states relevant to UV photodecomposition by ab initio complete-active-space self-consistent-field (CASSCF) method. The intersection points of the S1, T1 and S0 surfaces and the transition states for dissociation both on T1 and S0 surface are determined. Then the mechanism, its implication and comparison with experiments are discussed.

2. Computational details Electronic states considered here in addition to the ground state were the first excited valence singlet and triplet states, 1np*(S1) and 3pp*(T1). Geometries were obtained by a full optimization at the complete-activespace self-consistent field (CASSCF) level for each stationary structure in each given electronic state, because the CASSCF wave function has sufficient flexibility to model the large changes in electronic structure that can take place during the chemical reactions [15]. However, the complete active space formalism contains a certain amount of ambiguity in terms of which particular electrons and orbitals are chosen for inclusion. For this reason, selection of the active space is the crucial step in CASSCF calculations, which requires some comment. The obvious choice for describing the S0, T1 and S1 states of the N2 O2 would be four electrons distributed 3 in three orbitals originating from the p and p* orbitals of the N@N double bond and n orbital of the O5 atom. It should be pointed out that this n orbital in the active space is actually delocalized into the N4–O5 backbone with remarkable antibonding character in the N4–O5 regions due to the interaction with n orbital of the N4 atom. For the dissociation channels involving breaking of the N–N bond, the corresponding r and r* orbitals are also included in the CASSCF calculations. Finally, with two additional electrons and orbitals that are automatically chosen by the program, one is a r* orbital with antibonding character in the O1–N2, O3–N2, and N4– O5 regions, the other is a p* orbital both N atomic region, it has contributions from the p* orbital of NO 2 and NO fragment. Thus, the active space is composed of eight electrons in seven orbitals, refered to as CASSCF(8,7). The cc-pVDZ basis set is mainly employed in the present calculations. Single-point CASSCF(8,7)-MP2/aug-cc-pVDZ calculations have been carried out at the CASSCF(8,7)/cc-pVDZ optimized geometries in order to improve the energies. The harmonic frequencies each structure as a minimum or transition state. The search of the singlet–triplet intersections is calculated using the state-average CASSCF/6-31G* with Slater determinant to optimize a ‘conical intersection’ [16,17]. All calculations are performed using the GAUSSIAN 98 package [18].

3. Results and discussion 3.1. Equilibrium geometries The equilibrium structure geometries and energetic data have been collected in Fig. 1 and Table 1, respectively. The labels S0, S1 and T1 are used in the table and the figure to denote the energetic ordering of the states. The S0 bond parameters and dissociation channels reported here are in close agreement with results of calculations and experiments by Dutton and co-workers [13], which give us reason to expect that our results are reasonable. It is found that N2 O2 3 (S0) has Cs symmetry. A noteworthy feature is the N2–N4 bond of N2 O2 3 . At the CASSCF(8,7) level of the˚ , which is shorter ory, the N2–N4 bond length is 1.3014 A ˚ than that typical N2–N4 single bond length of 1.41 A and longer than that of typical N@N double bond length ˚ . This result indicates that the conjugation interof 1.24 A action between the N@N double bond and lone pairs electrons of the O atoms exists in the ground state of N2 O2 3 . Further evidence for this comes from the natural bond orbital (NBO) analysis [19]. The strengths of these interactions are estimated by second-order perturbation theory b  > =er  er ). It is found that the (DEð2Þ ¼ 2 < rj Ejr important interaction occurs between the lone pairs of the O5 atom (electron donor) and the empty pN@N in the ground state of N2 O2 corresponding to DE(2), 3 , 66.22 kcal/mol. We have obtained the N2 O2 3 ðS1 Þ structures with CASSCF(8,7)/cc-pVDZ method. As shown in Fig. 1, the S1 has also a planar structure due to the keep sp2 hybridization of the N4 atom. The N2–N4 and N4–O5 ˚ in bond distances are, respectively, 1.4254 and 1.4364 A the N2 O2 ðS Þ equilibrium geometry, which are 0.1240 1 3 ˚ longer than the corresponding values in and 0.1113 A the S0 equilibrium structure. The N2–N4–O5 angle is decreased from 116.33 in the S0 to 104.51 in the S1. For the more detail information, Fig. 2 gives the schematic diagrams of the singly occupied orbitals in the S1 state, which come from the CASSCF(8,7)/cc-pVDZ calculated molecular orbitals. The first singly occupied orbital, referred to as MO1, can be approximately represented as 0.15 2py(N2) + 0.78 2px(O5) + 0.56 2py(O5) for S1 state. It is evident that it can be considered as the non-bonding orbital of O5 atom. The third singly occupied orbital (MO3), mainly composed of 0.43 2pz(O1) + 0.63 2pz(N2)  0.54 2pz(O3)  0.59 2pz(N4) + 0.39 2pz(O5) for S1 state. Obviously, it possesses p*(N@N) character. From the above analysis, it can be concluded that the S1 state originate from nO5 ! pN@N excitation. The nO5 ! pN@N excitation results in partial breaking of the N2@N4 p bond leading to the N2–N4 bond strengthened in the S1 state. As pointed out before, these results are in good agreement with that of the conjugation interaction between the N@N p electrons and lone pairs electrons of the O atoms exists in the ground state of N2 O2 3 ðS0 Þ.

L.-L. Lu¨ et al. / Chemical Physics Letters 431 (2006) 415–420

417

_

1.4254

122.95

1.3014

2 35 1.3

82 1.31

7 11 1.3

+

119.53 56

_

D(5,4,2,3) = 0.0

D(4,3,2,1) = 180.0

S0 Min

104.51

116.07 1.2864

D(4,3,2,1) = -145.26

D(5,4,2,3) = 0.0

S1 Min 731 1 .2

9 1.2 15

117.02

1.2 672

115.99

444 1.2

126.29

D(4,3,2,1) = 162.17

1.8488

118.42

2.1188

D(5,4,2,3) = -14.13

1.3014

D(4,3,2,1) = -132.12

TS (S0)

1.3 669

5 1.4729

120.46 1.3 37 3

40 5

D(5,4,2,1) = 150.84

TS(T1)

35 1.3

404 1.3

1.3121

116.87

120.49

1.3

109.18

114.08

0

1.2 62 2

D(4,3,2,1) = 163.54

D(5,4,2,1) = 98.55

115.18

D(4,3,2,1) = 147.53

S1/S0

D(5,4,2,1) = 94.03

T1/S1

678 1.2

+

2.0041

9

113.82

123.31

7 56 1.2

3 1.27

70 5

115.23

1.2

D(5,4,2,1) = 108.57

T1Min

1.32 6

D(4,3,2,1) = 180.0

1.3 1

3

116.33

1 .3

10

251

124.89

4 1.436

123.03

1.3

_

1.3436 1.4379

118.03

_

_ 116.14

D(4,3,2,1) = 180.0

D(5,4,2,3) = 0.0

NO2¯ (1A1)

T1/S0

1.2872

1.2839

3

NO¯

1

NO¯

Fig. 1. CASSCF(8,7)/cc-pVDZ structures of the reagents, the reaction products, the transition states and crossing points of the trioxodinitrate dianion (N2 O2 3 ) photodecomposition. Bond distances are given in angstroms, bond angles in degrees.

Another excited-triplet-state (T1) was optimized at the same level with the S1 state, and was confirmed to be minimum by frequency calculations. From the singly occupied orbitals MO2 [0.40 2pz(O1)  0.38 2pz(N2) + 0.36 2pz(O3)  0.30 2pz(N4) + 0.70 2pz(O5)] and MO3 in Fig. 2, one can see that the T1 state originates from an excitation from the in-plane pN@N orbital to the pN@N orbital. Thus, one electron promotion from the pN@N orbital to the pN@N orbital results in a weakening of the N@N p bond. Further evidence for this comes from the T1 state structural ˚ in T1, parameters. The N2–N4 bond length is 1.4379 A

˚ , while close to the normal N–N single bond length, 1.41 A ˚ the N2–N4 bond length is 1.3014 A, which is of between single and double bond character. Meanwhile, the dihedral angle of O5–N4–N2–O3 is remarkably decreased from 0.0 in the ground state S0 to 104.65 in T1, close to 90.0. Namely, the 3pp* state of N2 O2 3 is a state that arises from the p ! p* excitation of the N@N double bond. The excitation changes the double bond into the single bond, which makes the terminal O5 atom rotate freely and results in a rehybridization of the N4 atom from sp1.88 in S0 to sp4.03 (NBO analysis) in T1. As a consequence, the T1 state

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L.-L. Lu¨ et al. / Chemical Physics Letters 431 (2006) 415–420

Table 1 The CASSCF calculated energies (E, in hartree) and relative energies (DE, in kcal/mol) Structure

State

CASSCF(8,7)/cc-pVDZ E

DE

E

DE

S0 Min

S0 00 S1(1A ) 3 0 T1( A ) S11(n–p*) T13(pp*)

333.21104 333.01799 333.03143 333.05526 333.13430 333.08662 333.11135 333.13376 333.13433 333.13399 333.45233 333.41672

0.0 121.19 112.76 97.80 48.18 78.11 62.59 48.52 48.16 48.37 151.48 129.13

334.11373 333.96219 334.0305 333.97245 334.05473 334.00982 334.02155 334.07752 334.09517 334.05958 334.25448 334.19663

0.0 95.14 52.25 88.69 38.16 65.23 57.87 22.73 11.65 33.99 88.36 52.05

S1 Min T1 Min S1/S0(IC) T1/S1(ISC) T1/S0(ISC) TS (S0) TS (T1)  3 NO 2 þ NO  1 NO2 þ NO

CASSCF(8,7)-MP2/aug-cc-pVDZ

asymmetries electronic distribution relative to the plane of the N2 O2 3 . 3.2. Surface intersections and the mechanistic aspects

Fig. 2. Plots of singly occupied molecular orbitals come from CASSCF(8,7)/cc-pVDZ calculated molecular orbitals: MO1-nO5, MO2pN@N, MO3-pN@N .

becomes pyramidal in structure, which is quite different from the S0 state in-plane structure. However, these results can be considered due to the p ! p* excitation, which is forbidden to occur by spin–orbit coupling for in-plane structure. As a result, an out-of-plane N4O5 vibration destroys the planar symmetry and then allows mixing of the pp* state and the others. It would cause a p orbital to be transformed into an spn orbital which possesses an

The photochemical reactions are rather complicated, thus, crossing points of the S0, S1 and T1 surfaces play an important role in describing mechanistic photodissociation of the title reaction. The structures of the S1/S0, T1/S1 and T1/S0 crossing points, as shown in Fig. 1, were determined with the state-averaged CASSCF(8,7) method with 6–31G* basis set [19]. The corresponding energies of the crossing points were listed in Table 1. In Fig. 3, we briefly outline global features of the S0, S1 and T1 surfaces and indicate the decay pathways that are important in the photochemistry and photophysics. Once S0 ! S1 vertical excitation occurs, corresponding to vertical excitation energy is 95.14 kcal/mol, the system will relax from the FC point to the S1 minimum. In the course of relaxation, the

Fig. 3. Schematic representation of the optimized structures(stationary and crossing points) on the S0, S1 and T1 surfaces of the trioxodinitrate dianion (N2 O2 3 ) photodecomposition. The bond lengths are in angstroms, and the angles are in degrees. Dashed arrows indicate excited-triplet-state paths, and solid arrows indicate singlet-state paths.

L.-L. Lu¨ et al. / Chemical Physics Letters 431 (2006) 415–420

˚ in S0 to N2–N4 bond length changes from 1.3014 A ˚ 1.4254 A in S1. As far as the 0–0 energy is concerned, we find a gap of 88.69 kcal/mol for the S0 to the S1 transition. From the S1 state the system can undergo different routes. The first route involves radiative decay, via fluorescence emission, from the S1 minimum. This decay does not involve formation of new species since, after decay, the system will relax back to the starting reactant. The second route involves radiationless decay via an intersystem crossing T1/S1 to the triplet manifold, leading mainly to the production of the T1 minimum intermediate. This intermediate then decays, via the transition state TS (T1) and the second intersystem crossing T1/S0 to the ground state surface. Finally, the third route involves the singlet manifold only. In this case relaxation to S0 occurs, in a single step via decay channels corresponding to the S1/S0 conical intersection. In addition, the S1 direct dissociation is not detail discussed due to the rapid high exothermic reactions. 3.2.1. The T1/S1 and T1/S0 surface crossings The triplet radiationless decay path for S1 starts with an intersystem crossing T1/S1 to the triplet manifold. Thus, we begin with a discussion of the T1/S1 crossing. The gradient different vector x1[x1 = o(E2  E1)/oq] [20] is shown in Fig. 4a, and it is dominated by a N2–N4 bond stretch and the molecular plane twisted. The direction of the gradient difference vector is analogous to the direction of negative curvature in a transition state [8]. Therefore, the N2– N4 bond distance of the T1 minimum should be shrunken ˚ , as compared with 1.4729 A ˚ of the T1/S1 crossas 1.4379 A ing. Note the lowest energy T1/S1 crossing structure is nonplanar geometry, and located 30.82 kcal/mol at CASSCF(8,7)-MP2/aug-cc-pVDZ level below the S1 minimum. Meanwhile, the dihedral angle of O5–N4–N2–O3 is remarkably decreased from 0.0 in the excited S1 state to 104.65 in T1 state. Thus, the decay path from S1 to the triplet manifold occurs along a planar deformation coordinate, which essentially involves a bond order inversion with respect to the ground-state structure. However, the S1 ! T1 intersystem crossing (ISC) is a spin-forbidden pro-

Fig. 4. Gradient difference x1 at the minimum energy point of the T1/S1 and T1/S0 intersections for the N2 O2 3 .

419

cess [21]. On the basis of the calculated spin–orbit coupling matrix element (SOC), ÆT1jHSOjS1æ = 13.1 cm1. The results show that the ISC is the low efficient decay path. Therefore, we come to the conclusion that the S1 ! T1 intersystem crossing is not in competition with the S1 direct dissociation. All attempts to search a transition state for the N2 O2 3 direct dissociation into NO þ NO 2 on the S0 or T1 surface were unsuccessful, which shows that the N2 O2 on 3 S0 or T1 dissociate via stepwise mechanism. The structural parameters and energies of the TS (T1) and TS (S0) are shown in Fig. 1 and Table 1, respectively. The imaginary vibrational modes associated with the only negative eigenvalue of the TS (T1) and TS (S0) trends to the N2–N4 bond breaking. The barrier height is calculated to be 4.17 and 11.65 kcal/mol from the CASSCF(8,7)-MP2/aug-cc-pVDZ single point calculations, respectively. From the above discussion, we found that the path from the T1 minimum to the T1/S0 crossing or the triplet production via the TS (T1) is energetically the favorable pathway. Finally, we must discuss the intersection of T1/S0. A drawing showing the vector x1 is given in Fig. 4b. The vector x1 corresponds to the N2–N4 bond stretch. Motion from TS (T1) point to the T1/S0 crossing involves further increase in the N2–N4 bond length from 1.8488 to ˚ , respectively. Meanwhile the system must twist 2.0041 A around the N2–N4 single bond and back to the ground state surface. The T1/S0 crossing could result in a much higher ISC rate due to the angular dependence of the SOC energy ÆT1jHSOjS0æ = 91.6 cm1 [22]. Therefore, the surface crossing to the ground state surface will be clearly much more efficient at the T1/S0 crossing, not only because this is more stable species than the T1/S1 crossing, but also because of the enhanced SOC. Thus, after relaxation to the S0 surface, the system is left with sufficient internal energies to overcome the barriers on the S0 pathway. The N2–N4 single bond is further destabilized and then breaks from ˚ in TS (S0) on the ground state 2.0041 in T1/S0 and 2.1188 A surface. 3.2.2. The S1/S0 conical intersection The S0 and S1 surface conical intersection (S1/S0) was determined by the sate-averaged CASSCF(8,7)/6-31G* optimization without any symmetry constraints. The resulting S1/S0 structure is shown in Fig. 1. In comparison with the corresponding S1 or S0 minimum, the largest change is associated with the N2–N4 and N4–O5 distance. The gradient difference x1[x1 = o(E2  E1)/oq] and derivative coupling vectors x2[x2 = ÆW1joH/oqjW2æ] [20] at the S1/S0 are plotted in Fig. 5. The derivative coupling vectors mainly correspond to the N2–N4 and N4–O5 stretching, and the molecular plane bended motions, which could lead to the system in the S0 minimum. However, the gradient difference vectors correspond to a significant decrease of the N2–N4 distance and a remarkably changes of the dihedral angle of O5–N4–N2–O3, resulting in forming the S1 state. Note that the energy of the S1/S0 structure is located

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L.-L. Lu¨ et al. / Chemical Physics Letters 431 (2006) 415–420

These results show that the product NO of the efficient photodissociation is singlet-state rather than triplet (3R) state. Our calculated results are in close agreement with experimental observations. Acknowledgements The authors gratefully acknowledge the support of this work by the Natural Science Education Foundation of Gansu province (No. 021-22). Fig. 5. Gradient difference x1 (a) and nonadiabatic coupling x2 (b) vectors for the lowest energy point of the S1/S0 conical intersection for the N2 O2 3 .

23.46 kcal/mol below the S1 minimum. Thus, for the N2 O2 populated in the S1 state, the internal conversion 3 (IC) to the S0 surface through the S1/S0, is accessible in energy, include vibronic interaction. After IC to the S0 surface, the system is left with sufficient energies to overcome the barrier on the S0 pathway, leading to formation of NO þ NO 2. 4. Conclusions In summary, the reactions of photochemical cleavage of the trioxodinitrate dianion (N2 O2 3 ) have been studied using theoretical calculations. All structures of the reactions are determined and characterized at the CASSCF(8,7)/cc-pVDZ level. To accurately evaluate the energies, the single point calculations were performed at CASSCF(8,7)-MP2/aug-cc-pVDZ level. It is found that the S0 ! S1 vertical excitation occurs, the system will relax from the FC point to the S1 minimum. From the S1 state the system can undergo two main routes. One is represented as follows: 



N2 O23 ðS0 Þ þ hm ! N2 O23 ðS1 Þ 

! T1 =S1 ! N2 O23 ðT1 Þ ! TSðT1 Þ ! T1 =S0 ! 1 NO þ 1 NO 2 The other may be denoted as 



N2 O23 ðS0 Þ þ hm ! N2 O23 ðS1 Þ ! S1 =S0 ! the S0 surface

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