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Relative stabilities of (NO)2
Chemical Physics 263 (2001) 61±68
www.elsevier.nl/locate/chemphys
Relative stabilities of (NO)2 Jong Keun Park a,*, Hosung Sun b b
a Department of Chemistry, Central Laboratory, Pusan National University, Pusan 609-735, South Korea Department of Chemistry and School of Molecular Science (BK21), Sungkyunkwan University, Suwon 440-746, South Korea
Received 30 June 2000
Abstract Geometrical structures for the (NO)2 are calculated using ab initio Hartree±Fock (SCF), second-order Mùller± Plesset perturbation, and coupled cluster with the single, double, and triple substitution methods with a triple zeta plus polarization basis set including diuse Rydberg basis functions. The structure of (NO)2 can be described by two interactions (N N, N O). One is the ONNO structure with an (N N) interaction. In this structure, acyclic cisONNO with C2v -symmetry, acyclic trans-ONNO with C2h , and cyclic ONNO with trapezoidal structure (C2v ) are optimized at the MP2 level. The other structure is the ONON structure with an (N O) interaction. In the structure, acyclic cis-ONON with Cs -symmetry and cyclic ONON of the rectangular (C2h ), square (D2h ), rhombic (D2h ), and parallelogramic (D2h ) geometries are also optimized. It is found that acyclic cis-ONNO (1 A1 ) is the most stable structure. The binding energies and the relative energy gaps among the isomers are found to be relatively small. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The relative stability and geometrical structure of N2 O2 as a fundamental unit in photochemical processes of dinitrogen oxides (N2 Ox ; x 2±5) have been extensively studied with various experimental [1±15] and theoretical [16±33] methods. The dinitrogen oxides have usually a closed electronic structure. The bond strengths (N±O) of the species formed by (N N) interaction are weaker than those of nitrogen oxides (NOx ; x 1±3) and bond lengths are longer. As the result, the formation and dissociation of N2 O2 can easily take
*
Corresponding author. Tel.: +82-51-510-3404; fax: +82-51517-3760. E-mail address: [email protected] (J.K. Park).
place. N2 O2 has many geometrical isomers. It combines easily with water and becomes nitric acid. And the acid dissolves into fog or rain. Although many studies for the photochemical reactions of N2 O2 have been performed, unanimous values of the stabilities and geometrical structures have not been given. Particularly, the results calculated with the density functional theory (DFT) are dierent from those of the experiments and ab initio calculations. By the X-ray diraction experiment [1], the most stable structure of N2 O2 in solid is a trapezoidal geometry (C2v ). RNN , RNO , and \ONN of and the molecule are 2:18 0:06, 1:12 0:02 A, 101 3°, respectively. By the molecular beam spectroscopy [2], the most stable structure of N2 O2 in the gas phase is an acyclic form (C2v ). RNN , RNO , and 95°, respectively. and \ONN are 2.33, 1.15 A, Using the microwave spectroscopy [3], RNN , RNO ,
0301-0104/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 0 ) 0 0 3 5 0 - 5
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J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
and \ONN of acyclic ONNO (C2v ) are 2.237, 1.161 and 99.6°, respectively. By the result of the 15 N A, isotopic infrared spectra [4], RNN , RNO , and \ONN of acyclic ONNO with C2v -symmetry are 2.2630, and 97.17°, respectively. Particularly, the 1.1515 A, structure of gaseous N2 O2 analyzed by the infrared spectrum [5] is assigned to be acyclic ONNO (C2v ). and 90°, respectively. RNN and \ONN are 1.75 A Recently, the structures and relative stabilities of N2 O2 were investigated by Stirling et al. [16] and Duarte et al. [17] using the DFT. In the calculations of Duarte et al., the acyclic cis-ONNO conformation is more stable in all cases. The acyclic cis-ONNO with a triplet spin state is more stable than a singlet by 3.61 kcal molÿ1 . RNN , RNO , and \ONN of acyclic cis-ONNO (3 A1 ) are 2.040, 1.167 and 110.37°, respectively. According to the reA, sults of Stirling et al., the most stable structure is also acyclic cis-ONNO with a triplet spin state and the most unstable one is cyclic ONON with a singlet spin. RNN , RNO , and \ONN of acyclic cis and 109.2°, ONNO (3 A1 ) are 2.059, 1.176 A, respectively. Using the various basis sets and correlated methods, the structures of acyclic cis-N2 O2 were optimized by Lee et al. [18]. The geometrical structures are not in¯uenced by the basis sets, but by the applied methods. At a large basis set, RNN , and 91.3°, RNO , and \ONN are 2.186, 1.170 A, respectively. Con®guration interaction calculation for N2 O2 was performed by Ha [19]. The structure of the ground state is acyclic cis-ONNO (C2v ) with a singlet spin state. RNN , RNO , and \ONN of the and 90°, respecground state are 2.39, 1.19 A, tively. The energy gap between the ground (1 A1 ) and the ®rst excited (3 B2 ) states is 0.43 eV. Although the structure and stability of N2 O2 have already been studied by many groups, further investigations seem to be worth carrying out on the base of following points. (i) The structure of N2 O2 is grouped as two possible geometrical isomers. One is a dimeric structure (ONNO) formed by an interaction between N and N. The other is a dimerization (ONON) by two interactions between O and N. Which structure is the more stable form? (ii) According to the spin state in the same structure, the relative stability is dierent from each other. Which spin state is more stable? (iii) Although the binding energy of (NO)2 is known to be
relatively small, there are many geometrical isomers which should be all investigated. Is the binding energy between two monomers (NO NO) as low as 2±5 kcal molÿ1 ?
2. Computational methods The basis set chosen is the triple zeta basis on N 421=31 and O 421=31. Two extra d type polarization functions are added to nitrogen (ad 0:4, 1.6) and oxygen (ad 0:35, 1.5) [33]. The diuse basis functions are additionally augmented on nitrogen (as 0:028, 0.0066; ap 0:025; ad 0:015) [34] and oxygen (as 0:028,0.0066; ap 0:025; ad 0:015) [35] to describe the Rydberg states of N2 O2 . The total number of contracted basis functions used is 106. The geometrical structures of the ground states of N2 O2 , NO, and O2 are optimized with the Hartree±Fock (SCF) and second-order Mùller± Plesset (MP2) levels using G A U S S I A N 9 4 . To examine the appropriateness of the procedure, the geometrical structure of the species has been also optimized with the coupled cluster with the single, double, and triple substitution [CCSD(T)] method. In addition, the harmonic vibrational frequencies of the species have been analyzed to con®rm the existence of the stable structure at the SCF and MP2 levels. To ®nd the geometrical conformers and isomers, the optimized geometrical structures from acyclic trans-ONNO to trianglic NNOO are drawn using the MP2 results. To investigate the relative stability of the optimized geometries, a schematic energy diagram is made using the results of the MP2 calculations. In the diagram, the potential energy of acyclic cis-ONNO is set to be zero. To investigate the binding energies and potential barriers from acyclic trans-ONNO and cyclic ONNO to the (NO NO) asymptotes, the potential energy curves are drawn using the MP2 results. The internuclear distances (RNN ) consid To connect the poered are from 1.1 to 2.4 A. tential curves between the equilibrium geometry of N2 O2 and the (NO NO) asymptotes, the singly and doubly excited con®guration interaction
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
(SDCI) for NO are performed using the package.
GAMESS
3. Results and discussion The structure of N2 O2 is divided as two groups by (N N) and (N O) interactions. One is ONNO with an (N N) interaction. Acyclic transONNO (1 A1 ), acyclic cis-ONNO (1 A1 , 3 A1 ), and cyclic ONNO (1 A1 , 3 A1 ) are optimized at the MP2 level. The other group is ONON with the (N O) interaction. Acyclic cis-ONON with Cs -symmetry and ®ve cyclic ONON of the rectangular (1 A1 ), square (1 A1 , 3 A1 ), rhombic (1 A1 ), and parallelogramic (1 A1 ) geometries are also optimized. Although acyclic trans-ONNO (3 A1 ), acyclic transONON (1 A1 ), acyclic cis-ONON (3 A1 ), and bicyclic ONON (1 A1 ) cannot be optimized at the MP2 level, the molecules are optimized at the SCF level and the harmonic vibrational frequencies are the positive values. But cyclic and acyclic NOON with an (O O) interaction, acyclic trans-ONON (3 A1 ), and cyclic ONON (3 A1 ; rectangle, square, rhombus, and parallelogram) with two (N O) interactions cannot be optimized at both levels. Acyclic cis- and trans-NOON and cyclic ONON (3 A1 ; rectangle) are optimized to become acyclic cis- and trans-ONNO and acyclic cis-ONON (3 A1 ) without a potential barrier, respectively. Acyclic transONON (3 A1 ) are found to be the transition state having a negative imaginary vibrational frequency. Additionally, two isomers of NNOO made from the (O N) interaction between O2 and N2 are also optimized at the MP2 level. Using the DFT, the eight structures of N2 O2 were optimized by Stirling et al. [16]. Acyclic cisand trans-ONNO (1 A1 , 3 A1 ) and acyclic cis- and trans-ONON (1 A1 , 3 A1 ) are found as stable species. The most stable one is acyclic cis-ONNO (3 A1 ) and the most unstable one is acyclic trans-ONON (1 A1 ). The geometrical structures of ONNO lie lower in potential energy than the ONON species. And the conformers with the triplet spin state are more stable than the corresponding one with the singlet state. In particular, acyclic cis-ONNO with the triplet state is more stable than that of the singlet state. Very recently, Duarte et al. [17] op-
63
timized four isomers of N2 O2 using the various DFT. At all the DFT calculations, the optimized geometrical structures of acyclic cis-ONNO (1 A1 , 3 A1 ) are more stable than acyclic trans-ONON (1 A1 , 3 A1 ). Acyclic cis-ONNO with the triplet spin state is more stable than acyclic cis-ONNO with the singlet state. Although acyclic trans-ONNO (3 A1 ), acyclic cis-ONON (3 A1 ), and trans-ONON (3 A1 , 1 A1 ) are optimized at the DFT levels, the isomers cannot be optimized at our MP2 calculation. With a relatively large basis set and the various applied methods including the DFT method, acyclic cis- and trans-ONNO were investigated by Nguyen et al. [20,21]. At the SCF level, transONNO is more stable than the cis-isomer by 2.65 kcal molÿ1 . While, at the MP2 and DFT levels, cisONNO is more stable. Two isomers [bicyclic ONON (C2v ) and trianglic NNOO (C2v ) with two (O N) interaction] of N2 O2 with relatively high energy with respect to 2NO were also optimized by Nguyen et al. [20±23]. At the SCF level, the isomers are found at local minima of energy hypersurface having all positive frequencies. While, at the MP2 and MCSCF levels, bicyclic NONO and trianglic NNOO have one imaginary frequency. In our MP2 result, bicyclic ONON (1 A1 ) is found to be a transition state, while the trianglic NNOO is found as a local minimum species. The eight low-lying states of N2 O2 (four singlets and four triplets) were investigated by East [24]. The cis-ONNO is more stable than the cis-ONON and trans-ONNO by 0.19 and 0.21 eV, respectively. Although the ground state of cis-ONNO could not be de®nitely determined due to the narrow energy span, the ordering of the lowest four states are X~ 1 A1 , 3 B1 , 1 B1 , and 1 A1 . They concluded that the only potential minimum lying below the lowest (NO NO) asymptote is the cisONNO conformer in a ground X~ 1 A1 state. Following the con®guration interaction calculation for N2 O2 performed by Ha [19], the structure of the ground state is also acyclic cis-ONNO (C2v ) with a singlet spin state. The energy gap between the ground (1 A1 ) and the ®rst excited (3 B2 ) states is 0.43 eV. Experimentally the stable structure of N2 O2 is acyclic cis-ONNO with C2v -symmetry. But in the
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J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
Raman and infrared spectra for four dierent isotopes of nitric oxide investigated by Ohlsen and Laane [6], the peaks of asymmetric ONON were observed. Simultaneously the harmonic frequencies of four isomers were also analyzed with the force constant calculation. The calculated frequencies are compared with their experimental values. From the comparison, they concluded that the most stable molecule is acyclic cis-ONON, that is, it exists as a polymer form rather than a simple dimer. In the electron spin resonance spectrum of NO adsorbed in Na±A zeolite [7], the spectrum of the NO monomer is observed to be well-de®ned form. According to the results, an unpaired electron of the nitrogen atom combines with a sodium cation. And the ONON species with the triplet state in zeolite are weakly dimerized like a van der Waals complex. The internuclear distance between But, in the absorption two monomers is 4.6 A. spectrum of (NO)2 studied by Holland and Maier [8], the infrared spectra of the red-colored ONON species were not observed. Our values for the species calculated with the Hartree±Fock (SCF) and MP2 methods are in reasonable agreement with experimental [1±15] or other theoretical [16±32] values. In addition, to ®nd a more stable structure between the singlet and triplet spin states and between the cis- and trans-conformers, the geometrical structures of acyclic cis- and trans-ONNO have been also optimized using the [CCSD(T)] method. But, transONNO cannot be optimized at the CCSD(T) calculation. NO and O2 are open shell molecules. These molecules have unpaired electrons in the antibonding orbital. Our results of NO and O2 are in good agreement with other theoretical [25±28] or experimental [9±11] values. In the present work, ®ve isomers made from an (N N) interaction between two NO molecules are optimized at the MP2 level. The most stable structure is acyclic cis-ONNO (1 A1 ) with C2v symmetry. The geometrical parameters of RNO , RNN , and \NNO are in good agreement with experimental [2,4,5] or other theoretical [15± 19,24,30] values (see Table 1). Particularly, the parameters of acyclic cis-ONNO (1 A1 ) optimized by CCSD(T) are similar to the experimental results of Kukolich [3]. Salahub group [16,17] optimized
the structure of acyclic cis-ONNO (1 A1 , 3 A1 ) at the DFT level. The most stable isomer is acyclic cis-ONNO (3 A1 ) and the second stable one is acyclic cis-ONNO (1 A1 ). The geometrical parameters of acyclic cis-ONNO optimized with the DFT method are in good agreement with our CCSD(T) results. Using several basis sets and theoretical methods, the structures of acyclic cis-ONNO were calculated by Lee et al. [18]. The optimized parameters are greatly in¯uenced from the applied computational methods (CCSD, CISD, CPF). At the CPF level, RNN , RNO , and \ONN are 2.160, and 98.1°, respectively. The previous 1.154 A, theoretical values of RNO of acyclic cis-ONNO (1 A1 ) are longer than the experiments, while the theoretical values of RNN are shorter. The geometries of the lowest singlet and triplet states of (NO)2 are provided in Table 1 along with the equilibrium geometries of NO and O2 . And Table 2 shows the harmonic vibrational frequencies of the lowest two states. At the CCSD(T) level, the geometrical structure of acyclic trans-ONNO (1 A1 , 3 A1 ) cannot be optimized. While, at the SCF and MP2 levels, the structure of acyclic trans-ONNO (1 A1 ) is optimized. Our MP2 results of acyclic trans-ONNO (1 A1 ) are similar to the DFT results. Although acyclic trans-ONNO with the triplet spin state was optimized by Salahub group [16,17], we could not optimize the molecule at the MP2 and CCSD(T) levels. Six isomers with (N O) interaction [acyclic cis-ONON (1 A1 ; Cs ), cyclic ONON (1 A1 ; rectangle), cyclic ONON (1 A1 , 3 A1 ; square), cyclic ONON (1 A1 ; rhombus), and cyclic ONON (1 A1 ; parallelogram)] are optimized at the MP2 level, while acyclic cis-NONO (3 A1 ), acyclic transONON, and bicyclic ONON (C2v ) are not optimized. But, RNN of cyclic ONON with the rhombic geometry is quite dierent from that of Nguyen et al. [20±23]. Although the structure of bicyclic NONO (1 A1 , C2v ) was optimized by Nguyen et al., we could not optimize the structure at the MP2 level. Four isomers of cis- and trans-ONON with the singlet and triplet states were optimized by Stirling et al. [16]. In their results, cis-ONON (3 A1 ) is more stable than trans-ONNO (1 A1 ). Cyclic ONON with the trapezoidal geometry (C2h ) was
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
65
Table 1 and angles (\ in deg) of the lowest singlet and triplet states of N2 O2 Optimized internuclear distances (R in A) SCF
MP2
CCSD(T)
DFT [25]
CI [26]
CI [27]
1.115 1.163
1.137 1.235
1.156 1.221
1.167 1.223
1.164 1.210 [28]
1.162 1.215
Acyclic cis-ONNO (1 A1 ; C2v ) RNO 1.135 1.173
1.161
1.167 [17] 1.174 [16] 1.175 [15]
1.170 [18]
1.19 [19]
1.149
1.169 1.180 [29]
R(NO) R(O2 )
ACPF [30]
CCSD(T) [24]
1.151 [9] 1.208 [10] 1.216 [11]
RNN
1.613
2.218
2.203
2.089 [17] 2.119 [16] 2.121 [15]
2.186 [18]
2.39 [19]
2.284
2.227 2.354 [29]
\ONN
109.9
91.0
96.5
99.43 [17] 97.6 [16] 100.5 [15]
91.3 [18]
90 [19]
96.1
96.2 95.3 [29]
1.159
1.168 [17] 1.176 [16] 2.085 [17] 2.059 [16] 109.85 [17] 109.2 [16]
Acyclic cis-ONNO (3 A1 ; C2v ) 1.126 1.171 RNO RNN
1.725
2.310
2.128
\ONN
113.7
93.8
105.3
optimized by Skaarup et al. [31]. And the geometrical parameters are quite dierent from our SCF results. Optimized parameters of acyclic NNOO (1 A1 ; Cs ) and trianglic NNOO (1 A1 , C2v ) are similar to the results of Nguyen et al. A schematic energy diagram of the structural change from acyclic trans-ONNO to trianglic NNOO at the MP2 level is drawn in Fig. 1. In the diagram, the potential energy of acyclic cis-ONNO (1 A1 ) is set equal to zero. All energies are adiabatic values and are in units of eV. Acyclic cis-ONNO (1 A1 ) is the most stable, while cyclic ONNO (3 A1 ) with the trapezoidal geometry is the most unstable. The second stable one is the parallelogramic form of cyclic ONON (1 A1 ) and the third one is acyclic cis-ONNO (3 A1 ) with the rectangular structure. Our results for the relative stabilities of (NO)2 are dierent from the result of Stirling et al. [16]. In the results of Stirling et al., the most stable isomer is acyclic cis-ONNO with a triplet spin state and the
Experimental [3]
1.161 1.12 [1] 1.15 [2] 1.1515 [4] 2.237 2.18 [1] 2.33 [2] 2.263 [4] 1.75 [5] 99.6 101 [1] 95 [2] 97.17 [4] 90 [5] 1.161 2.237 99.6
most unstable one is cyclic ONON with a singlet state. The structures with the triplet spin state are more stable than those with the singlet state. Particularly, acyclic trans-ONNO and acyclic cisand trans-ONON with a triplet spin state have not been optimized by us. In the triplet and singlet, their dissociation energies are 14.9 and 10.7 kcal molÿ1 , respectively. Some conformers (cis-, gauche-, and trans-N2 O2 ) are optimized at the SCF level. The results are dierent from each other. Although the energy dierence is small, the cisconformer calculated with small basis set is more stable than the trans. With increasing size of basis sets, the trans-conformer is more stable than the cis. By the molecular beam techniques, the binding energy of the gaseous acyclic cis-ONNO (1 A1 ) observed by Kukolich [3] is about 4 kcal molÿ1 (about 700 cmÿ1 ). And the energy (D0 ) of the dimer reported by Hetzler et al. [12] is 710 40 cmÿ1
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J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
Table 2 Calculated harmonic vibrational frequencies (cmÿ1 ) of the lowest singlet and triplet states of N2 O2 at the SCF and MP2 levels 1
A2
1
A1
2
A1
1
B2
2
B2
3
A1
1
Acyclic cis-ONNO ( A1 ) SCF MP2 CCSD(T) [36] LSD [16] BPW91 [15] GGA-PP [17] SCF [31] Experimental [6] Experimental [36] Experimental [4]
158 285 191 243 226 230 190 161 117 119.2
432 326 201 310 257 264 439 262 239.361 258.9
578 353 279 375 386 381 635 202 134.503 127.2
Acyclic cis-ONNO (3 A1 ) SCF MP2 LSD [16] GGA-PP [17] Experimental [6] Experimental [36] Experimental [4]
298 225 182 253 161 117 119.2
393 277 248 157 202 134.503 127.2
553 435 252 333 262 239.361 258.9
(2:03 0:12 kcal molÿ1 ). The dissociation energies (D0 ) of ONNO in the gas phase using the Fourier transform infrared spectrometer are 639 35 cmÿ1 (1:83 0:1 kcal molÿ1 ) and 764 18 cmÿ1 (2:18 0:05 kcal molÿ1 ) [13]. Using the electron impact method, the binding energy estimated is 800 150 cmÿ1 (2:29 0:43 kcal molÿ1 ). Fischer et al. [14]
978 627 536 644 659 652 768
1963 1721
2051 1846
1684 1693 1680 1707
429.140 430.0
1788 [5] 1789.1
1845 1837 1839 1858 1858 1860 [5] 1868.3
650 524 467 461
1930 1808 1650 1651
429.140 430.0
1788 [5] 1789.1
2064 1855 1820 1825 1858 1860 [5] 1868.3
measured the binding energy of 787 cmÿ1 (0.098 eV) using the high resolution photoelectron spectra. The heats of formation of ONNO from 2NO analyzed by the infrared spectrum [5] and the far ultraviolet spectrum are 2.45 and 2.24 kcal molÿ1 , respectively. By the above experimental results, the binding energies of acyclic cis-ONNO with a
Fig. 1. Schematic energy diagram of the structural change from the acyclic conformer to the cyclic. All energies are adiabatic values and are in units of eV.
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
very weak N±N bond are in the range of 2±4 kcal molÿ1 . Recently, at the various DFT levels, the dimerization energies (De ) of acyclic cis-ONNO with the triplet and singlet spin states were calculated by some groups [16,17,30]. In the result of Duarte et al. [17], the energies are in the range from 6.12 to 14.62 kcal molÿ1 . Canty et al. [27] calculated the dimerization energies of 9.75 and 10.2 kcal molÿ1 with the BLYP and B3LYP methods, respectively. Jursic et al. [32] calculated the energies of 7.63 kcal molÿ1 with the BLYP method, while 2.3 kcal molÿ1 with the ab initio MP2 method. The dissociation energies of N2 O2 with the triplet and singlet states determined by Stirling et al. [16] are 14.9 and 10.7 kcal molÿ1 , respectively. Meanwhile, using ab initio MRCI method, the binding energy of acyclic cis-ONNO obtained by Roos group [30] is 3.3 kcal molÿ1 . The previous calculated values are higher than those (the range from 2.0 to 4 kcal molÿ1 ) of the experimental results. Our binding energies calculated by the ab initio method are relatively closer to the experimental values. 4. Conclusions Geometrical structures for the dimeric form of (NO)2 from (NO NO) have been calculated using ab initio Hartree±Fock (SCF), MP2, and coupled cluster with single, double, and triple excitations [CCSD(T)] methods with a triple zeta plus polarization basis set including diuse Rydberg basis functions. In addition, the harmonic vibrational frequencies of the species have been analyzed to con®rm the potential energy minima of the structures. The geometrical structure of N2 O2 is divided by the two categories. One is N2 O2 with an (N N) interaction. In this category, acyclic cis-ONNO (C2v ), acyclic trans-ONNO (C2h ), and cyclic ONNO with trapezoidal form are optimized at the MP2 level. But, at the CCSD(T) level, acyclic transONNO (C2h ) cannot be optimized. The other is N2 O2 with two (N O) interactions. Acyclic cisONON (Cs ) and cyclic ONON of the rectangular (C2h ), square (D2h ), rhombic (D2h ), and parallelogramic (D2h ) geometries are also optimized. Acyclic trans-ONNO (3 A1 ), acyclic trans-ONON,
67
bicyclic ONON (C2v ), and acyclic cis- and transNOON with an (O O) interaction cannot be optimized at the MP2 level. While two structures of NNOO formed by the (O N) interaction between O2 and N2 are also optimized. Acyclic cis-ONNO (1 A1 ) is the most stable and cyclic ONNO with trapezoidal form is the most unstable. The second stable one is the parallelogramic form of cyclic ONON (1 A1 ) and the third one is acyclic cis-ONNO (3 A1 ) with the rectangular structure. At the MP2 level, the structures of ONNO and ONON with the singlet state are more stable than those of ONNO and ONON with the triplet. Our results for the relative stabilities of (NO)2 are dierent from those of Stirling et al. and Duarte et al. That is, the energetically most stable isomer is acyclic cis-ONNO with a triplet spin state. The binding energies and the relative energy gaps between the isomers are found to be relatively small. NO has an unpaired electron in the nitrogen atom. A monomer combines with the other and makes an electron pair in the dimeric form of (NO)2 . But, this interaction is very weak like a van der Waals complex. Due to the small binding energy, the formation and dissociation of N2 O2 from (NO NO) occur easily. As the result, N2 O2 has many geometrical isomers. Our binding energy of acyclic cis-ONNO (1 A1 ) is 0.2 eV at the MP2 level, while 0.08 eV (645 cmÿ1 ) at the CCSD(T) level. This value is similar to the experimental value. In the formation of (NO)2 from the (NO NO) asymptotes, the energy barrier is found to be very low. A full report will be published elsewhere. Acknowledgements The authors wish to acknowledge the ®nancial support of Korea Research Foundation made in the program year of 1997. References [1] W.N. Lipscomb, F.E. Wang, W.R. May, E.L. Lippert, Acta Cryst. 14 (1961) 1100. [2] C.M. Western, P.R.R. Langridge-Smith, B.J. Howard, S.E. Novick, Mol. Phys. 44 (1981) 145.
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J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
[3] S.G. Kukolich, J. Mol. Spectrosc. 98 (1983) 80. [4] A.R.W. McKellar, J.K.G. Watson, B.J. Howard, Mol. Phys. 86 (1995) 273. [5] C.E. Dinerman, G.E. Ewing, J. Chem. Phys. 53 (1970) 626. [6] J.R. Ohlsen, J. Laane, J. Am. Chem. Soc. 100 (1978) 6948. [7] P.H. Kasal, R.M. Gaura, J. Phys. Chem. 86 (1982) 4257. [8] R.F. Holland, W.B. Maier II, J. Chem. Phys. 78 (1983) 2928. [9] G. Herzberg, Molecular Spectra and Structure I, Spectra of Diatomic Molecules, second ed., Van Nostrand, New York, 1950. [10] T.G. Slanger, P.C. Cosby, J. Chem. Phys. 92 (1988) 267. [11] J.J.P. Stewart, J. Comput. Aided Mol. Design 4 (1990) 1. [12] J.R. Hetzler, M.P. Casassa, D.S. King, J. Phys. Chem. 95 (1991) 8086. [13] A. Dkhissi, P. Soulard, A. Perrin, N. Lacome, J. Mol. Spectrosc. 183 (1997) 12. [14] I. Fischer, A. Strobel, J. Staecker, G. Niedner-Schatteburg, K. M uller-Dethlefs, V.E. Bodybey, J. Chem. Phys. 96 (1992) 7171. [15] J.F. Canty, E.G. Stone, S.B.H. Bach, D.W. Ball, Chem. Phys. 216 (1997) 81. [16] A. Stirling, I. Papai, J. Mink, D.R. Salahub, J. Chem. Phys. 100 (1994) 2910. [17] H.A. Duarte, E. Proynov, D.R. Salahub, J. Chem. Phys. 109 (1998) 26. [18] T.J. Lee, J.E. Rice, G.E. Scuseria, H.F. Schaefer III, Theoret. Chim. Acta 75 (1989) 81. [19] T.-K. Ha, Theoret. Chim. Acta 58 (1981) 125. [20] K.A. Nguyen, M.S. Gordon, J.A. Boatz, J. Am. Chem. Soc. 116 (1994) 9241.
[21] K.A. Nguyen, M.S. Gordon, J.A. Montgomery Jr., H.H. Michels, J. Phys. Chem. 98 (1994) 10072. [22] K.A. Nguyen, M.S. Gordon, J.A. Montgomery Jr., H.H. Michels, D.R. Yarkony, J. Chem. Phys. 98 (1993) 3845. [23] G. Chaban, M.S. Gordon, K.A. Nguyen, J. Phys. Chem. 101 (1997) 4283. [24] A.L. East, J. Chem. Phys. 109 (1998) 2185. [25] J. Andzelm, E. Wimmer, J. Chem. Phys. 96 (1992) 1280. [26] L.A. Eriksson, J. Wang, R.J. Boyd, S. Lunell, J. Phys. Chem. 98 (1994) 792. [27] B.G. Johnson, P.M. Gill, J.A. Pople, J. Phys. Chem. 98 (1993) 5612. [28] H. Partridge, C.W. Bauschlicher Jr., S.R. Langho, J. Chem. Phys. 95 (1991) 8292. [29] T.J. Lee, A.P. Rendell, P.R. Taylor, J. Phys. Chem. 94 (1990) 5463. [30] R. Gonz alez-Luque, M. Merch an, B.O. Roos, Theoret. Chim. Acta 88 (1994) 425. [31] S. Skaarup, P.N. Skancke, J.E. Boggs, J. Am. Chem. Soc. 98 (1976) 6106. [32] B.S. Jursic, Z. Zdravkovski, Int. J. Quant. Chem. 54 (1995) 161. [33] K. Hasimoto, Y. Osamura, J. Chem. Phys. 95 (1991) 1121. [34] S. Huzinaga, J. Andzelm, J.M. Klobukowski, E. RadzioAndzelm, Y. Sakai, H. Tatewaki, Physical Science Data, Gaussian Basis Sets for Molecular Calculations, vol. 16, Elsevier, Amsterdam, 1984. [35] R. Poirier, R. Kari, I.G. Csizmadia, Physical Science Data, Handbook of Gaussian Basis Sets, vol. 24, Elsevier, Amsterdam, 1984. [36] A.L.L. East, A.R.W. McKeller, J.K.G. Watson, J. Chem. Phys. 109 (1998) 4378.
www.elsevier.nl/locate/chemphys
Relative stabilities of (NO)2 Jong Keun Park a,*, Hosung Sun b b
a Department of Chemistry, Central Laboratory, Pusan National University, Pusan 609-735, South Korea Department of Chemistry and School of Molecular Science (BK21), Sungkyunkwan University, Suwon 440-746, South Korea
Received 30 June 2000
Abstract Geometrical structures for the (NO)2 are calculated using ab initio Hartree±Fock (SCF), second-order Mùller± Plesset perturbation, and coupled cluster with the single, double, and triple substitution methods with a triple zeta plus polarization basis set including diuse Rydberg basis functions. The structure of (NO)2 can be described by two interactions (N N, N O). One is the ONNO structure with an (N N) interaction. In this structure, acyclic cisONNO with C2v -symmetry, acyclic trans-ONNO with C2h , and cyclic ONNO with trapezoidal structure (C2v ) are optimized at the MP2 level. The other structure is the ONON structure with an (N O) interaction. In the structure, acyclic cis-ONON with Cs -symmetry and cyclic ONON of the rectangular (C2h ), square (D2h ), rhombic (D2h ), and parallelogramic (D2h ) geometries are also optimized. It is found that acyclic cis-ONNO (1 A1 ) is the most stable structure. The binding energies and the relative energy gaps among the isomers are found to be relatively small. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The relative stability and geometrical structure of N2 O2 as a fundamental unit in photochemical processes of dinitrogen oxides (N2 Ox ; x 2±5) have been extensively studied with various experimental [1±15] and theoretical [16±33] methods. The dinitrogen oxides have usually a closed electronic structure. The bond strengths (N±O) of the species formed by (N N) interaction are weaker than those of nitrogen oxides (NOx ; x 1±3) and bond lengths are longer. As the result, the formation and dissociation of N2 O2 can easily take
*
Corresponding author. Tel.: +82-51-510-3404; fax: +82-51517-3760. E-mail address: [email protected] (J.K. Park).
place. N2 O2 has many geometrical isomers. It combines easily with water and becomes nitric acid. And the acid dissolves into fog or rain. Although many studies for the photochemical reactions of N2 O2 have been performed, unanimous values of the stabilities and geometrical structures have not been given. Particularly, the results calculated with the density functional theory (DFT) are dierent from those of the experiments and ab initio calculations. By the X-ray diraction experiment [1], the most stable structure of N2 O2 in solid is a trapezoidal geometry (C2v ). RNN , RNO , and \ONN of and the molecule are 2:18 0:06, 1:12 0:02 A, 101 3°, respectively. By the molecular beam spectroscopy [2], the most stable structure of N2 O2 in the gas phase is an acyclic form (C2v ). RNN , RNO , and 95°, respectively. and \ONN are 2.33, 1.15 A, Using the microwave spectroscopy [3], RNN , RNO ,
0301-0104/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 0 ) 0 0 3 5 0 - 5
62
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
and \ONN of acyclic ONNO (C2v ) are 2.237, 1.161 and 99.6°, respectively. By the result of the 15 N A, isotopic infrared spectra [4], RNN , RNO , and \ONN of acyclic ONNO with C2v -symmetry are 2.2630, and 97.17°, respectively. Particularly, the 1.1515 A, structure of gaseous N2 O2 analyzed by the infrared spectrum [5] is assigned to be acyclic ONNO (C2v ). and 90°, respectively. RNN and \ONN are 1.75 A Recently, the structures and relative stabilities of N2 O2 were investigated by Stirling et al. [16] and Duarte et al. [17] using the DFT. In the calculations of Duarte et al., the acyclic cis-ONNO conformation is more stable in all cases. The acyclic cis-ONNO with a triplet spin state is more stable than a singlet by 3.61 kcal molÿ1 . RNN , RNO , and \ONN of acyclic cis-ONNO (3 A1 ) are 2.040, 1.167 and 110.37°, respectively. According to the reA, sults of Stirling et al., the most stable structure is also acyclic cis-ONNO with a triplet spin state and the most unstable one is cyclic ONON with a singlet spin. RNN , RNO , and \ONN of acyclic cis and 109.2°, ONNO (3 A1 ) are 2.059, 1.176 A, respectively. Using the various basis sets and correlated methods, the structures of acyclic cis-N2 O2 were optimized by Lee et al. [18]. The geometrical structures are not in¯uenced by the basis sets, but by the applied methods. At a large basis set, RNN , and 91.3°, RNO , and \ONN are 2.186, 1.170 A, respectively. Con®guration interaction calculation for N2 O2 was performed by Ha [19]. The structure of the ground state is acyclic cis-ONNO (C2v ) with a singlet spin state. RNN , RNO , and \ONN of the and 90°, respecground state are 2.39, 1.19 A, tively. The energy gap between the ground (1 A1 ) and the ®rst excited (3 B2 ) states is 0.43 eV. Although the structure and stability of N2 O2 have already been studied by many groups, further investigations seem to be worth carrying out on the base of following points. (i) The structure of N2 O2 is grouped as two possible geometrical isomers. One is a dimeric structure (ONNO) formed by an interaction between N and N. The other is a dimerization (ONON) by two interactions between O and N. Which structure is the more stable form? (ii) According to the spin state in the same structure, the relative stability is dierent from each other. Which spin state is more stable? (iii) Although the binding energy of (NO)2 is known to be
relatively small, there are many geometrical isomers which should be all investigated. Is the binding energy between two monomers (NO NO) as low as 2±5 kcal molÿ1 ?
2. Computational methods The basis set chosen is the triple zeta basis on N 421=31 and O 421=31. Two extra d type polarization functions are added to nitrogen (ad 0:4, 1.6) and oxygen (ad 0:35, 1.5) [33]. The diuse basis functions are additionally augmented on nitrogen (as 0:028, 0.0066; ap 0:025; ad 0:015) [34] and oxygen (as 0:028,0.0066; ap 0:025; ad 0:015) [35] to describe the Rydberg states of N2 O2 . The total number of contracted basis functions used is 106. The geometrical structures of the ground states of N2 O2 , NO, and O2 are optimized with the Hartree±Fock (SCF) and second-order Mùller± Plesset (MP2) levels using G A U S S I A N 9 4 . To examine the appropriateness of the procedure, the geometrical structure of the species has been also optimized with the coupled cluster with the single, double, and triple substitution [CCSD(T)] method. In addition, the harmonic vibrational frequencies of the species have been analyzed to con®rm the existence of the stable structure at the SCF and MP2 levels. To ®nd the geometrical conformers and isomers, the optimized geometrical structures from acyclic trans-ONNO to trianglic NNOO are drawn using the MP2 results. To investigate the relative stability of the optimized geometries, a schematic energy diagram is made using the results of the MP2 calculations. In the diagram, the potential energy of acyclic cis-ONNO is set to be zero. To investigate the binding energies and potential barriers from acyclic trans-ONNO and cyclic ONNO to the (NO NO) asymptotes, the potential energy curves are drawn using the MP2 results. The internuclear distances (RNN ) consid To connect the poered are from 1.1 to 2.4 A. tential curves between the equilibrium geometry of N2 O2 and the (NO NO) asymptotes, the singly and doubly excited con®guration interaction
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
(SDCI) for NO are performed using the package.
GAMESS
3. Results and discussion The structure of N2 O2 is divided as two groups by (N N) and (N O) interactions. One is ONNO with an (N N) interaction. Acyclic transONNO (1 A1 ), acyclic cis-ONNO (1 A1 , 3 A1 ), and cyclic ONNO (1 A1 , 3 A1 ) are optimized at the MP2 level. The other group is ONON with the (N O) interaction. Acyclic cis-ONON with Cs -symmetry and ®ve cyclic ONON of the rectangular (1 A1 ), square (1 A1 , 3 A1 ), rhombic (1 A1 ), and parallelogramic (1 A1 ) geometries are also optimized. Although acyclic trans-ONNO (3 A1 ), acyclic transONON (1 A1 ), acyclic cis-ONON (3 A1 ), and bicyclic ONON (1 A1 ) cannot be optimized at the MP2 level, the molecules are optimized at the SCF level and the harmonic vibrational frequencies are the positive values. But cyclic and acyclic NOON with an (O O) interaction, acyclic trans-ONON (3 A1 ), and cyclic ONON (3 A1 ; rectangle, square, rhombus, and parallelogram) with two (N O) interactions cannot be optimized at both levels. Acyclic cis- and trans-NOON and cyclic ONON (3 A1 ; rectangle) are optimized to become acyclic cis- and trans-ONNO and acyclic cis-ONON (3 A1 ) without a potential barrier, respectively. Acyclic transONON (3 A1 ) are found to be the transition state having a negative imaginary vibrational frequency. Additionally, two isomers of NNOO made from the (O N) interaction between O2 and N2 are also optimized at the MP2 level. Using the DFT, the eight structures of N2 O2 were optimized by Stirling et al. [16]. Acyclic cisand trans-ONNO (1 A1 , 3 A1 ) and acyclic cis- and trans-ONON (1 A1 , 3 A1 ) are found as stable species. The most stable one is acyclic cis-ONNO (3 A1 ) and the most unstable one is acyclic trans-ONON (1 A1 ). The geometrical structures of ONNO lie lower in potential energy than the ONON species. And the conformers with the triplet spin state are more stable than the corresponding one with the singlet state. In particular, acyclic cis-ONNO with the triplet state is more stable than that of the singlet state. Very recently, Duarte et al. [17] op-
63
timized four isomers of N2 O2 using the various DFT. At all the DFT calculations, the optimized geometrical structures of acyclic cis-ONNO (1 A1 , 3 A1 ) are more stable than acyclic trans-ONON (1 A1 , 3 A1 ). Acyclic cis-ONNO with the triplet spin state is more stable than acyclic cis-ONNO with the singlet state. Although acyclic trans-ONNO (3 A1 ), acyclic cis-ONON (3 A1 ), and trans-ONON (3 A1 , 1 A1 ) are optimized at the DFT levels, the isomers cannot be optimized at our MP2 calculation. With a relatively large basis set and the various applied methods including the DFT method, acyclic cis- and trans-ONNO were investigated by Nguyen et al. [20,21]. At the SCF level, transONNO is more stable than the cis-isomer by 2.65 kcal molÿ1 . While, at the MP2 and DFT levels, cisONNO is more stable. Two isomers [bicyclic ONON (C2v ) and trianglic NNOO (C2v ) with two (O N) interaction] of N2 O2 with relatively high energy with respect to 2NO were also optimized by Nguyen et al. [20±23]. At the SCF level, the isomers are found at local minima of energy hypersurface having all positive frequencies. While, at the MP2 and MCSCF levels, bicyclic NONO and trianglic NNOO have one imaginary frequency. In our MP2 result, bicyclic ONON (1 A1 ) is found to be a transition state, while the trianglic NNOO is found as a local minimum species. The eight low-lying states of N2 O2 (four singlets and four triplets) were investigated by East [24]. The cis-ONNO is more stable than the cis-ONON and trans-ONNO by 0.19 and 0.21 eV, respectively. Although the ground state of cis-ONNO could not be de®nitely determined due to the narrow energy span, the ordering of the lowest four states are X~ 1 A1 , 3 B1 , 1 B1 , and 1 A1 . They concluded that the only potential minimum lying below the lowest (NO NO) asymptote is the cisONNO conformer in a ground X~ 1 A1 state. Following the con®guration interaction calculation for N2 O2 performed by Ha [19], the structure of the ground state is also acyclic cis-ONNO (C2v ) with a singlet spin state. The energy gap between the ground (1 A1 ) and the ®rst excited (3 B2 ) states is 0.43 eV. Experimentally the stable structure of N2 O2 is acyclic cis-ONNO with C2v -symmetry. But in the
64
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
Raman and infrared spectra for four dierent isotopes of nitric oxide investigated by Ohlsen and Laane [6], the peaks of asymmetric ONON were observed. Simultaneously the harmonic frequencies of four isomers were also analyzed with the force constant calculation. The calculated frequencies are compared with their experimental values. From the comparison, they concluded that the most stable molecule is acyclic cis-ONON, that is, it exists as a polymer form rather than a simple dimer. In the electron spin resonance spectrum of NO adsorbed in Na±A zeolite [7], the spectrum of the NO monomer is observed to be well-de®ned form. According to the results, an unpaired electron of the nitrogen atom combines with a sodium cation. And the ONON species with the triplet state in zeolite are weakly dimerized like a van der Waals complex. The internuclear distance between But, in the absorption two monomers is 4.6 A. spectrum of (NO)2 studied by Holland and Maier [8], the infrared spectra of the red-colored ONON species were not observed. Our values for the species calculated with the Hartree±Fock (SCF) and MP2 methods are in reasonable agreement with experimental [1±15] or other theoretical [16±32] values. In addition, to ®nd a more stable structure between the singlet and triplet spin states and between the cis- and trans-conformers, the geometrical structures of acyclic cis- and trans-ONNO have been also optimized using the [CCSD(T)] method. But, transONNO cannot be optimized at the CCSD(T) calculation. NO and O2 are open shell molecules. These molecules have unpaired electrons in the antibonding orbital. Our results of NO and O2 are in good agreement with other theoretical [25±28] or experimental [9±11] values. In the present work, ®ve isomers made from an (N N) interaction between two NO molecules are optimized at the MP2 level. The most stable structure is acyclic cis-ONNO (1 A1 ) with C2v symmetry. The geometrical parameters of RNO , RNN , and \NNO are in good agreement with experimental [2,4,5] or other theoretical [15± 19,24,30] values (see Table 1). Particularly, the parameters of acyclic cis-ONNO (1 A1 ) optimized by CCSD(T) are similar to the experimental results of Kukolich [3]. Salahub group [16,17] optimized
the structure of acyclic cis-ONNO (1 A1 , 3 A1 ) at the DFT level. The most stable isomer is acyclic cis-ONNO (3 A1 ) and the second stable one is acyclic cis-ONNO (1 A1 ). The geometrical parameters of acyclic cis-ONNO optimized with the DFT method are in good agreement with our CCSD(T) results. Using several basis sets and theoretical methods, the structures of acyclic cis-ONNO were calculated by Lee et al. [18]. The optimized parameters are greatly in¯uenced from the applied computational methods (CCSD, CISD, CPF). At the CPF level, RNN , RNO , and \ONN are 2.160, and 98.1°, respectively. The previous 1.154 A, theoretical values of RNO of acyclic cis-ONNO (1 A1 ) are longer than the experiments, while the theoretical values of RNN are shorter. The geometries of the lowest singlet and triplet states of (NO)2 are provided in Table 1 along with the equilibrium geometries of NO and O2 . And Table 2 shows the harmonic vibrational frequencies of the lowest two states. At the CCSD(T) level, the geometrical structure of acyclic trans-ONNO (1 A1 , 3 A1 ) cannot be optimized. While, at the SCF and MP2 levels, the structure of acyclic trans-ONNO (1 A1 ) is optimized. Our MP2 results of acyclic trans-ONNO (1 A1 ) are similar to the DFT results. Although acyclic trans-ONNO with the triplet spin state was optimized by Salahub group [16,17], we could not optimize the molecule at the MP2 and CCSD(T) levels. Six isomers with (N O) interaction [acyclic cis-ONON (1 A1 ; Cs ), cyclic ONON (1 A1 ; rectangle), cyclic ONON (1 A1 , 3 A1 ; square), cyclic ONON (1 A1 ; rhombus), and cyclic ONON (1 A1 ; parallelogram)] are optimized at the MP2 level, while acyclic cis-NONO (3 A1 ), acyclic transONON, and bicyclic ONON (C2v ) are not optimized. But, RNN of cyclic ONON with the rhombic geometry is quite dierent from that of Nguyen et al. [20±23]. Although the structure of bicyclic NONO (1 A1 , C2v ) was optimized by Nguyen et al., we could not optimize the structure at the MP2 level. Four isomers of cis- and trans-ONON with the singlet and triplet states were optimized by Stirling et al. [16]. In their results, cis-ONON (3 A1 ) is more stable than trans-ONNO (1 A1 ). Cyclic ONON with the trapezoidal geometry (C2h ) was
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
65
Table 1 and angles (\ in deg) of the lowest singlet and triplet states of N2 O2 Optimized internuclear distances (R in A) SCF
MP2
CCSD(T)
DFT [25]
CI [26]
CI [27]
1.115 1.163
1.137 1.235
1.156 1.221
1.167 1.223
1.164 1.210 [28]
1.162 1.215
Acyclic cis-ONNO (1 A1 ; C2v ) RNO 1.135 1.173
1.161
1.167 [17] 1.174 [16] 1.175 [15]
1.170 [18]
1.19 [19]
1.149
1.169 1.180 [29]
R(NO) R(O2 )
ACPF [30]
CCSD(T) [24]
1.151 [9] 1.208 [10] 1.216 [11]
RNN
1.613
2.218
2.203
2.089 [17] 2.119 [16] 2.121 [15]
2.186 [18]
2.39 [19]
2.284
2.227 2.354 [29]
\ONN
109.9
91.0
96.5
99.43 [17] 97.6 [16] 100.5 [15]
91.3 [18]
90 [19]
96.1
96.2 95.3 [29]
1.159
1.168 [17] 1.176 [16] 2.085 [17] 2.059 [16] 109.85 [17] 109.2 [16]
Acyclic cis-ONNO (3 A1 ; C2v ) 1.126 1.171 RNO RNN
1.725
2.310
2.128
\ONN
113.7
93.8
105.3
optimized by Skaarup et al. [31]. And the geometrical parameters are quite dierent from our SCF results. Optimized parameters of acyclic NNOO (1 A1 ; Cs ) and trianglic NNOO (1 A1 , C2v ) are similar to the results of Nguyen et al. A schematic energy diagram of the structural change from acyclic trans-ONNO to trianglic NNOO at the MP2 level is drawn in Fig. 1. In the diagram, the potential energy of acyclic cis-ONNO (1 A1 ) is set equal to zero. All energies are adiabatic values and are in units of eV. Acyclic cis-ONNO (1 A1 ) is the most stable, while cyclic ONNO (3 A1 ) with the trapezoidal geometry is the most unstable. The second stable one is the parallelogramic form of cyclic ONON (1 A1 ) and the third one is acyclic cis-ONNO (3 A1 ) with the rectangular structure. Our results for the relative stabilities of (NO)2 are dierent from the result of Stirling et al. [16]. In the results of Stirling et al., the most stable isomer is acyclic cis-ONNO with a triplet spin state and the
Experimental [3]
1.161 1.12 [1] 1.15 [2] 1.1515 [4] 2.237 2.18 [1] 2.33 [2] 2.263 [4] 1.75 [5] 99.6 101 [1] 95 [2] 97.17 [4] 90 [5] 1.161 2.237 99.6
most unstable one is cyclic ONON with a singlet state. The structures with the triplet spin state are more stable than those with the singlet state. Particularly, acyclic trans-ONNO and acyclic cisand trans-ONON with a triplet spin state have not been optimized by us. In the triplet and singlet, their dissociation energies are 14.9 and 10.7 kcal molÿ1 , respectively. Some conformers (cis-, gauche-, and trans-N2 O2 ) are optimized at the SCF level. The results are dierent from each other. Although the energy dierence is small, the cisconformer calculated with small basis set is more stable than the trans. With increasing size of basis sets, the trans-conformer is more stable than the cis. By the molecular beam techniques, the binding energy of the gaseous acyclic cis-ONNO (1 A1 ) observed by Kukolich [3] is about 4 kcal molÿ1 (about 700 cmÿ1 ). And the energy (D0 ) of the dimer reported by Hetzler et al. [12] is 710 40 cmÿ1
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J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
Table 2 Calculated harmonic vibrational frequencies (cmÿ1 ) of the lowest singlet and triplet states of N2 O2 at the SCF and MP2 levels 1
A2
1
A1
2
A1
1
B2
2
B2
3
A1
1
Acyclic cis-ONNO ( A1 ) SCF MP2 CCSD(T) [36] LSD [16] BPW91 [15] GGA-PP [17] SCF [31] Experimental [6] Experimental [36] Experimental [4]
158 285 191 243 226 230 190 161 117 119.2
432 326 201 310 257 264 439 262 239.361 258.9
578 353 279 375 386 381 635 202 134.503 127.2
Acyclic cis-ONNO (3 A1 ) SCF MP2 LSD [16] GGA-PP [17] Experimental [6] Experimental [36] Experimental [4]
298 225 182 253 161 117 119.2
393 277 248 157 202 134.503 127.2
553 435 252 333 262 239.361 258.9
(2:03 0:12 kcal molÿ1 ). The dissociation energies (D0 ) of ONNO in the gas phase using the Fourier transform infrared spectrometer are 639 35 cmÿ1 (1:83 0:1 kcal molÿ1 ) and 764 18 cmÿ1 (2:18 0:05 kcal molÿ1 ) [13]. Using the electron impact method, the binding energy estimated is 800 150 cmÿ1 (2:29 0:43 kcal molÿ1 ). Fischer et al. [14]
978 627 536 644 659 652 768
1963 1721
2051 1846
1684 1693 1680 1707
429.140 430.0
1788 [5] 1789.1
1845 1837 1839 1858 1858 1860 [5] 1868.3
650 524 467 461
1930 1808 1650 1651
429.140 430.0
1788 [5] 1789.1
2064 1855 1820 1825 1858 1860 [5] 1868.3
measured the binding energy of 787 cmÿ1 (0.098 eV) using the high resolution photoelectron spectra. The heats of formation of ONNO from 2NO analyzed by the infrared spectrum [5] and the far ultraviolet spectrum are 2.45 and 2.24 kcal molÿ1 , respectively. By the above experimental results, the binding energies of acyclic cis-ONNO with a
Fig. 1. Schematic energy diagram of the structural change from the acyclic conformer to the cyclic. All energies are adiabatic values and are in units of eV.
J.K. Park, H. Sun / Chemical Physics 263 (2001) 61±68
very weak N±N bond are in the range of 2±4 kcal molÿ1 . Recently, at the various DFT levels, the dimerization energies (De ) of acyclic cis-ONNO with the triplet and singlet spin states were calculated by some groups [16,17,30]. In the result of Duarte et al. [17], the energies are in the range from 6.12 to 14.62 kcal molÿ1 . Canty et al. [27] calculated the dimerization energies of 9.75 and 10.2 kcal molÿ1 with the BLYP and B3LYP methods, respectively. Jursic et al. [32] calculated the energies of 7.63 kcal molÿ1 with the BLYP method, while 2.3 kcal molÿ1 with the ab initio MP2 method. The dissociation energies of N2 O2 with the triplet and singlet states determined by Stirling et al. [16] are 14.9 and 10.7 kcal molÿ1 , respectively. Meanwhile, using ab initio MRCI method, the binding energy of acyclic cis-ONNO obtained by Roos group [30] is 3.3 kcal molÿ1 . The previous calculated values are higher than those (the range from 2.0 to 4 kcal molÿ1 ) of the experimental results. Our binding energies calculated by the ab initio method are relatively closer to the experimental values. 4. Conclusions Geometrical structures for the dimeric form of (NO)2 from (NO NO) have been calculated using ab initio Hartree±Fock (SCF), MP2, and coupled cluster with single, double, and triple excitations [CCSD(T)] methods with a triple zeta plus polarization basis set including diuse Rydberg basis functions. In addition, the harmonic vibrational frequencies of the species have been analyzed to con®rm the potential energy minima of the structures. The geometrical structure of N2 O2 is divided by the two categories. One is N2 O2 with an (N N) interaction. In this category, acyclic cis-ONNO (C2v ), acyclic trans-ONNO (C2h ), and cyclic ONNO with trapezoidal form are optimized at the MP2 level. But, at the CCSD(T) level, acyclic transONNO (C2h ) cannot be optimized. The other is N2 O2 with two (N O) interactions. Acyclic cisONON (Cs ) and cyclic ONON of the rectangular (C2h ), square (D2h ), rhombic (D2h ), and parallelogramic (D2h ) geometries are also optimized. Acyclic trans-ONNO (3 A1 ), acyclic trans-ONON,
67
bicyclic ONON (C2v ), and acyclic cis- and transNOON with an (O O) interaction cannot be optimized at the MP2 level. While two structures of NNOO formed by the (O N) interaction between O2 and N2 are also optimized. Acyclic cis-ONNO (1 A1 ) is the most stable and cyclic ONNO with trapezoidal form is the most unstable. The second stable one is the parallelogramic form of cyclic ONON (1 A1 ) and the third one is acyclic cis-ONNO (3 A1 ) with the rectangular structure. At the MP2 level, the structures of ONNO and ONON with the singlet state are more stable than those of ONNO and ONON with the triplet. Our results for the relative stabilities of (NO)2 are dierent from those of Stirling et al. and Duarte et al. That is, the energetically most stable isomer is acyclic cis-ONNO with a triplet spin state. The binding energies and the relative energy gaps between the isomers are found to be relatively small. NO has an unpaired electron in the nitrogen atom. A monomer combines with the other and makes an electron pair in the dimeric form of (NO)2 . But, this interaction is very weak like a van der Waals complex. Due to the small binding energy, the formation and dissociation of N2 O2 from (NO NO) occur easily. As the result, N2 O2 has many geometrical isomers. Our binding energy of acyclic cis-ONNO (1 A1 ) is 0.2 eV at the MP2 level, while 0.08 eV (645 cmÿ1 ) at the CCSD(T) level. This value is similar to the experimental value. In the formation of (NO)2 from the (NO NO) asymptotes, the energy barrier is found to be very low. A full report will be published elsewhere. Acknowledgements The authors wish to acknowledge the ®nancial support of Korea Research Foundation made in the program year of 1997. References [1] W.N. Lipscomb, F.E. Wang, W.R. May, E.L. Lippert, Acta Cryst. 14 (1961) 1100. [2] C.M. Western, P.R.R. Langridge-Smith, B.J. Howard, S.E. Novick, Mol. Phys. 44 (1981) 145.
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