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Theoretical study of the HCN–CH3 and HNC–CH3 radicals: Hydrogen and covalent bonding
Chemical Physics Letters 406 (2005) 351–354 www.elsevier.com/locate/cplett
Theoretical study of the HCN–CH3 and HNC–CH3 radicals: Hydrogen and covalent bonding M. Solimannejad
a,1
, M.E. Alikhani
b,*
a
b
Quantum Chemistry Group, Department of Chemistry, Arak University, Arak 38156-879, Iran Laboratoire de Dynamique, Interactions et Re´activite´, UMR 7075, Universite´ P. et M. Curie, Boıˆte 49, baˆtiment F74, 4 Place Jussieu 75252 Paris Cedex 05, France Received 6 December 2004; in final form 17 February 2005 Available online 25 March 2005
Abstract The interaction between the methyl radical with hydrogen cyanide and hydrogen iso-cyanide is reported at several ab initio levels of theory. Four structures are studied: two hydrogen-bonded (H3C HCN and H3C HNC) and two covalent-bonded (H3C–NCH and H3C–CNH) structures. It is shown that hydrogen cyanide forms a weak hydrogen bond with the methyl radical ðDCP e ¼ 1:3 kcal=molÞ, while its covalent-bonded isomer is mostly unbound with respect to the fragments ground state ðDCP e ¼ þ0:5 kcal=molÞ. The ground state of the hydrogen isocyanide complexed with the methyl radical is found to be a covaCP lent-bonded complex ðDCP e ¼ 25:5 kcal=molÞ, whereas its hydrogen-bonded isomer is only a weak complex ðDe ¼ 2:2 kcal=molÞ. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Interest in hydrogen bonds has increased since the beginning of 20th century due to their widely recognized importance in chemistry, physics, and biology [1–3]. A hydrogen bond is an intermolecular attraction between a hydrogen atom with a partial positive charge and an electronegative region in an acceptor molecule. Previous theoretical works [4] have reported the existence of a mono-electron dihydrogen bond H e H in the dicoordinated solvated electron system (FH)2{e}(HF)2. In (FH)2{e}(HF)2, the loosely bound (excess) electron can form a bridge to connect two separated hydrogen fluoride dimers acting as a proton acceptor for two hydrogen atoms. The methyl radical is a proper model for a proton acceptor with an unpaired electron. According to a recent paper on the H3C HF and H3C HCCH *
Corresponding author. E-mail addresses: [email protected] (M. Solimannejad), [email protected] (M.E. Alikhani). 1 Fax: +98 861 2774031. 0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.03.025
complexes [5], the unpaired electron of methyl radical may attract the hydrogen atom of proton donor forming some kind of Ôunconventional hydrogen bondÕ. Alkorta et al. [6], have analysed the ability of carbon radicals as hydrogen bond acceptors basing on energetic and geometrical considerations. The authors have concluded that the carbon radicals are poor hydrogen bond acceptors. Moreover, as the result of topological studies (Atoms In Molecules [7,8]), they have suggested that hydrogen-bonded complexes involving radicals behave differently than hydrogen bonds formed between neutral molecules. Nevertheless, it is worth noting that hydrogen bonds formed from radicals exhibit the same spectroscopic properties as the classical hydrogen-bonded compounds (A H–B): a lengthening of the H–B distance [6], and a red-shift of the H–B vibrational frequency [5] in going from free H–B to the hydrogen bond complex. Since the methyl radical is a simple prototype for a wide class of organic radicals which play an important role as intermediates in biochemistry [9], we present in this letter, a theoretical study of the CH3–HCN and
352
M. Solimannejad, M.E. Alikhani / Chemical Physics Letters 406 (2005) 351–354
CH3–HNC compounds. Two important aspects are treated here. In the first part, we examine a radical species (CH3 + HCN) at both, restricted and unrestricted levels of theory, in order to emphasize the particular aspect of open-shell systems for a theoretical study. In the second part, hydrogen-bonded as well as covalentbonded interactions between methyl radical and hydrogen isocyanide are discussed.
2. Computational details All calculations have been performed with the GAUSSIAN 03 quantum chemical package [10] using unrestricted second Perturbation Theory (labeled as UMP2), restricted open-shell MP2 (labeled as ROMP2), and unrestricted Coupled Cluster method including single and double substitutions and triple excitations no-iteratively (labeled as UCCSD(T)) within the frozen core approximation. We have used two types of basis sets (as included in GAUSSIAN 03): the 6-311++G(2d,2p) extended basis set and the triple-zeta DunningÕs correlation consistent basis set (labeled as AUG-cc-pVTZ). The counterpoise (CP) method (using Ôcounterpoise = 2Õ keyword in GAUSSIAN package) has been used to take into account the basis set superposition error (BSSE) in the calculation of the binding energies.
3. Results and discussion It is well known that hydrogen bond properties can be well described only if the electron correlation effects together with basis sets supplemented with diffuse functions are taken into account in the quantum chemical model [11–13]. Previous theoretical works have established that in the case of closed-shell systems, a good compromise can be obtained by using the second order Møller–Plesset Perturbation theory and 6-311++G(d,p) (or AUG-cc-pVDZ) basis set. In particular, the red-shift of the H–C and N–C frequencies in the H2O HCN [14,15] and the NH3 HCN [16,17] complexes have been succesfully described by that methodology. Despite the fact that some researchers have suggested that this Ôpractical ruleÕ could well describe also some open-shell hydrogen-bonded complexes [5,6], in the next section it will be shown that this Ôpractical ruleÕ fails when applying UMP2 approach to the frequency predictions of the H3C HNC complex.
concluded that this new kind of hydrogen bond has similar characteristics to the conventional hydrogen bond, namely, the lengthening of the X–H (X = F and C) bonds of the proton donor and the red-shiftings of the H–F and H–C stretching vibration modes in the hydrogen bond complexes. Accordingly, we intuitively expect that the hydrogen bond in H3C HCN will exhibit the same spectroscopic properties as the traditional hydrogen bond complexes: the lengthening of the H–C distance and the lowering of the C–H frequency upon complexation. Two structures have been studied for the interaction between CH3 and HCN: H3C HCN and H3C-NCH. The geometrical parameters displayed in Fig. 1 have been obtained at the UCCSD(T), ROMP2, and UMP2 levels of theory using the 6-311++G(2d,2p) basis sets. It has been shown that the H3C–NCH complex is mostly unbound ðDCP with the e ¼ þ0:5 kcal=molÞ UCCSD(T) method, while the H3C HCN forms a weakly hydrogen-bonded complex, with respect to the fragments ground state. In Table 1 are gathered the optimized geometrical, energetic, and vibrational properties of the H3C HCN complex at the MP2 and CCSD(T) levels of theory. The complex has mostly a C3v symmetry. The spin contamination is slightly larger than the expected value by about 1.6% for all unrestricted wave function. The calculated binding energy (corrected by basis set superposition error) with UMP2 and ROMP2 methods is similar to that obtained at the UCCSD(T) level (5 kJ/mol), with the similar ˚ ). The formaintermolecular distance (r(H C) 2.6 A tion of the complex is characterized by a lengthening ˚ ) of the proton donor of the H–C bond ( 0.003 A and by a concomitant red-shift in the H–C stretching frequency. Compared with the calculated UCCSD(T) H–C frequency-shift (48 cm1), the ROMP2 method
N
Sun and coworkers [5] have recently presented theoretical results on the ability of methyl radical to act as hydrogen bond acceptor when it is complexed with hydrogen fluoride and ethyne. These authors have
C
1.0693 1.0664 1.0659
H
2.5864 2.5854 2.6276
H 1.0786 1.0741 1.0739
H
1.1755 1.1763 1.1763
N
1.0033 1.0034 1.0033
H
2.3009 2.2762 2.2820
1.2353 1.2300 1.2068 111.7 C 125.5 111.3 128.8 110.5 124.6 133.1 124.1 N C 123.1 1.4651 1.4563 1.4504
H
C H
C 3v symmetry ( 2A1 )
C
3.1. Hydrogen-bonded H3C HCN complex
1.1603 1.1668 1.1658
1.0925 1.0909 1.0954
symmetry (2 A')
Cs
H
C
1.0793 1.0747 1.0747
H H
1.0176 1.0158 1.0132
H
H 1.0908 1.0866 1.0867
H H
1.2451 1.2411 1.2220 H 110.5 N 128.6 110.9 129.0 111.1 1.0924 116.5 129.3 1.0890 117.6 C 1.0885 C 119.9 1.4987 1.4903 H 1.4907 H
Fig. 1. Optimized structures of the four studied complexes. Distances ˚ , and angles in degrees. The UCCSD(T) values are reported in are in A the first row, the ROMP2 values in the second row, and the UMP2 values in the third row.
M. Solimannejad, M.E. Alikhani / Chemical Physics Letters 406 (2005) 351–354
353
Table 1 Relevant properties of the free HCN and H3C HCN complex Free HCN (closed-shell) Experiment b MP2/aug-cc-pVTZ With 6-311++G(2d,2p) basis MP2 CCSD(T)
r(HC)
r(CN)
1.065 1.0645 set 1.0633 1.0661
r(H C)
x(HC)
x(NC)
1.153 1.1670
3311.5 3467
2096.9 2022
1.1666 1.1601
3463 3425
2015 2096
H3C HCN complex (open-shell) UMP2/aug-cc-pVTZ 1.0675[0.003] 1.1660[0.001] 2.5509 3429[+38] With 6-311++G(2d,2p) basis set UMP2 1.0659[0.003] 1.1657[0.0009] 2.6276 3426[+38] UCCSD(T) 1.0693[0.003] 1.1603[+0.0002] 2.5864 3377[+48] ROMP2 1.0664[0.003] 1.1668[+0.0002] 2.5854 3414[+50] ˚ , frequencies in cm1, and DCP (CP corrected binding energy) in kJ/mol.a Distances are in A e compl a Bond length differences and frequency-shifts ðpropertyfree HCN propertyHCN Þ are reported in square brackets. b Ref. [18].
gives a better result (50 cm1) than the UMP2 approach (38 cm1). As shown in Table 1, the C–N bond length increases at the UMP2 level (with both basis sets), whereas it decreases when using the ROMP2 and UCCSD(T) levels of theory. Consequently, the N–C frequency has been calculated to be largely blueshifted with UMP2 (147 and 171 cm1 with the 6-311++G(2d,2p) and aug-cc-pVTZ basis sets, respectively), while it is slightly red-shifted with UCCSD(T) and ROMP2 (1 and 3 cm1). Therefore, the UMP2 method fails to give the correct frequency-shift for the N–C stretch mode upon complexation. This example clearly shows that the use of ROMP2 could be considered as a safe route to evaluate the spectroscopic properties of the open-shell hydrogen-bonded systems, if the energetic and structural parameters remain close to those obtained at UCCSD(T) (and UMP2) level. It is interesting to note that the frequency calculations with UCCSD(T) are very time consuming, whereas ROMP2 method could be considered as a quite good approach to do the vibrational analysis with a much lower computational effort. 3.2. Covalent-bonded H3C-CNH complex For the interaction between CH3 and HNC, two structures have been studied: the hydrogen-bonded H3C HNC and the covalent-bonded H3C–CNH complexes. In Fig. 1 are displayed the geometrical parameters of these two complexes. The BSSE corrected binding energy of the H3C–CNH complex is calculated to be 25.5, 24.1, and 24.8 kcal/mol at UCCSD(T), ROMP2, and UMP2 levels of theory, respectively. Its hydrogen-bonded counterpart is found to be a weakly bound complex (2.2, 2.4, and 2.2 kcal/mol with UCCSD(T), ROMP2, and UMP2, respectively). The calculated binding energies with the restricted and unre-
DCP e
2193[171]
5.5
2162[147] 2095[+1] 2012[+3]
5.3 5.3 5.5
stricted MP2 methods are quite close to the UCCSD(T) results. Therefore, the covalent-bonded complex corresponds to the ground state of the isocyanide complexed with the methyl radical. Inspection of the geometrical parameters (Fig. 1) shows that the ROMP2 method gives once again even better results than the UMP2 approach with respect to the UCCSD(T) values. In the H3C–CNH complex, the unpaired electron is almost located on the carbon atom of HNC and the C–C distance belongs to the single C–C bond range. The C–C stretching vibrational frequency is found to be 1180 cm1, in a strong coupling with the H–N–C bending mode. Upon complexation, the HNC unit has a distorted geometry, in which the H–N and C–N frequencies are largely red-shifted by 334 and 224 cm1, respectively (see Table 2).
Table 2 Vibrational frequencies (in cm1) of the H3C–NH complex at UCCSD(T), ROMP2, and UMP2 levels with the 6-311++G(2d,2p) basis seta
m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 a
UCCSD(T) ROMP2
UMP2
Mode descriptions
93 440 677 900 976 1050 1180 1399 1478 1487 1806(2030) 3026 3113 3127 3475(3809)
156 447 673 882 980 1058 1168 1406 1495 1496 2232(2011) 3078 3176 3188 3560(3825)
Torsion CCN bend HN libration HNC bend + CC stretch HN libration HCH bend CC stretch + HNC bend H3C breath HCH bend HCH bend NC stretch HC stretch HC stretch HC stretch HN stretch
137 442 672 901 962 1056 1160 1407 1493 1498 1792(2013) 3074 3169 3183 3520(3830)
In parentheses are reported the frequencies of free HNC.
354
M. Solimannejad, M.E. Alikhani / Chemical Physics Letters 406 (2005) 351–354
4. Conclusions A comparative theoretical study of the interaction between a methyl radical and HCN/HNC molecules has been performed with the coupled-cluster and Møller– Plesset Perturbation theories. It has been shown that the product of the CH3 + HCN reaction is a weakly hydrogen-bonded complex, while we obtain a covalent-bonded compound in the case of CH3 + HNC. Even though the UMP2 and ROMP2 methods give spectroscopic parameters mostly close to those obtained at a highly correlated method (coupled-cluster), the UMP2 method fails to predict correctly the N–C frequency-shift in the H3C HCN open-shell hydrogenbond. In such case, the use of a restricted wave function at the second order Møller–Plesset Perturbation Theory gives the best agreement with the UCCSD(T) results.
References [1] G.C. Pimentel, A.L. MacClellan, The Hydrogen Bond, van Nostrand Reinhold, San Francisco, 1960. [2] P. Schuster, G. Zundel, C. Sandorfy, The Hydrogen Bond, Elsevier, North-Holland, Amsterdam, 1976.
[3] S. Scheiner, Hydrogen Bonding, Oxford University Press, New York, 1997. [4] X. Hao, Z. Li, D. Wu, Y. Wang, Z. Li, C. Sun, J. Chem. Phys. 118 (2003) 83. [5] B. Wang, Z. Li, D. Wu, X. Hao, R. Li, C. Sun, Chem. Phys. Lett. 375 (2003) 91. [6] I. Alkorta, I. Rozas, J. Elguero, Ber. Bunsen. Phys. Chem. 102 (1998) 429. [7] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, 1994. [8] U. Koch, P.L.A. Popelier, J. Phys. Chem. 99 (1995) 9747. [9] A. Romieu, S. Bellon, D. Gasparutto, J. Cadet, Org. Lett. 2 (2000) 1085. [10] M.J. Frisch et al., GAUSSIAN 2003. Revision B.02, Gaussian, Inc., Pittsburgh, PA, 2003. [11] Z. Latajka, Y. Bouteiller, J. Chem. Phys. 101 (1994) 9793. [12] J.E. Del Bene, W.B. Person, K. Szczepaniak, J. Phys. Chem. 99 (1995) 10705. [13] B. Silvi, R. Wieczorek, Z. Latajka, M.E. Alikhani, A. Dkhissi, Y. Bouteiller, J. Chem. Phys. 111 (1999) 6671. [14] R. Rivelino, S. Canuto, J. Phys. Chem. A 105 (2001) 11260. [15] R. Rivelino, S. Canuto, Chem. Phys. Lett. 322 (2000) 207. [16] G.T. Fraser, K.R. Leopold, D.D. Nelson Jr., A. Tung, W. Klemperer, J. Chem. Phys. 80 (1984) 3073. [17] R.S. Ruoff, T. Emilsson, C. Chuang, T.D. Klots, H.S. Gutowsky, J. Chem. Phys. 93 (1990) 6363. [18] D.C. Harris, M.D. Bertolucci, Symmetry and Spectroscopy. An Introduction to Vibrational and Electronic Spectroscopy, Dover, New York, 1989.
Theoretical study of the HCN–CH3 and HNC–CH3 radicals: Hydrogen and covalent bonding M. Solimannejad
a,1
, M.E. Alikhani
b,*
a
b
Quantum Chemistry Group, Department of Chemistry, Arak University, Arak 38156-879, Iran Laboratoire de Dynamique, Interactions et Re´activite´, UMR 7075, Universite´ P. et M. Curie, Boıˆte 49, baˆtiment F74, 4 Place Jussieu 75252 Paris Cedex 05, France Received 6 December 2004; in final form 17 February 2005 Available online 25 March 2005
Abstract The interaction between the methyl radical with hydrogen cyanide and hydrogen iso-cyanide is reported at several ab initio levels of theory. Four structures are studied: two hydrogen-bonded (H3C HCN and H3C HNC) and two covalent-bonded (H3C–NCH and H3C–CNH) structures. It is shown that hydrogen cyanide forms a weak hydrogen bond with the methyl radical ðDCP e ¼ 1:3 kcal=molÞ, while its covalent-bonded isomer is mostly unbound with respect to the fragments ground state ðDCP e ¼ þ0:5 kcal=molÞ. The ground state of the hydrogen isocyanide complexed with the methyl radical is found to be a covaCP lent-bonded complex ðDCP e ¼ 25:5 kcal=molÞ, whereas its hydrogen-bonded isomer is only a weak complex ðDe ¼ 2:2 kcal=molÞ. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Interest in hydrogen bonds has increased since the beginning of 20th century due to their widely recognized importance in chemistry, physics, and biology [1–3]. A hydrogen bond is an intermolecular attraction between a hydrogen atom with a partial positive charge and an electronegative region in an acceptor molecule. Previous theoretical works [4] have reported the existence of a mono-electron dihydrogen bond H e H in the dicoordinated solvated electron system (FH)2{e}(HF)2. In (FH)2{e}(HF)2, the loosely bound (excess) electron can form a bridge to connect two separated hydrogen fluoride dimers acting as a proton acceptor for two hydrogen atoms. The methyl radical is a proper model for a proton acceptor with an unpaired electron. According to a recent paper on the H3C HF and H3C HCCH *
Corresponding author. E-mail addresses: [email protected] (M. Solimannejad), [email protected] (M.E. Alikhani). 1 Fax: +98 861 2774031. 0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.03.025
complexes [5], the unpaired electron of methyl radical may attract the hydrogen atom of proton donor forming some kind of Ôunconventional hydrogen bondÕ. Alkorta et al. [6], have analysed the ability of carbon radicals as hydrogen bond acceptors basing on energetic and geometrical considerations. The authors have concluded that the carbon radicals are poor hydrogen bond acceptors. Moreover, as the result of topological studies (Atoms In Molecules [7,8]), they have suggested that hydrogen-bonded complexes involving radicals behave differently than hydrogen bonds formed between neutral molecules. Nevertheless, it is worth noting that hydrogen bonds formed from radicals exhibit the same spectroscopic properties as the classical hydrogen-bonded compounds (A H–B): a lengthening of the H–B distance [6], and a red-shift of the H–B vibrational frequency [5] in going from free H–B to the hydrogen bond complex. Since the methyl radical is a simple prototype for a wide class of organic radicals which play an important role as intermediates in biochemistry [9], we present in this letter, a theoretical study of the CH3–HCN and
352
M. Solimannejad, M.E. Alikhani / Chemical Physics Letters 406 (2005) 351–354
CH3–HNC compounds. Two important aspects are treated here. In the first part, we examine a radical species (CH3 + HCN) at both, restricted and unrestricted levels of theory, in order to emphasize the particular aspect of open-shell systems for a theoretical study. In the second part, hydrogen-bonded as well as covalentbonded interactions between methyl radical and hydrogen isocyanide are discussed.
2. Computational details All calculations have been performed with the GAUSSIAN 03 quantum chemical package [10] using unrestricted second Perturbation Theory (labeled as UMP2), restricted open-shell MP2 (labeled as ROMP2), and unrestricted Coupled Cluster method including single and double substitutions and triple excitations no-iteratively (labeled as UCCSD(T)) within the frozen core approximation. We have used two types of basis sets (as included in GAUSSIAN 03): the 6-311++G(2d,2p) extended basis set and the triple-zeta DunningÕs correlation consistent basis set (labeled as AUG-cc-pVTZ). The counterpoise (CP) method (using Ôcounterpoise = 2Õ keyword in GAUSSIAN package) has been used to take into account the basis set superposition error (BSSE) in the calculation of the binding energies.
3. Results and discussion It is well known that hydrogen bond properties can be well described only if the electron correlation effects together with basis sets supplemented with diffuse functions are taken into account in the quantum chemical model [11–13]. Previous theoretical works have established that in the case of closed-shell systems, a good compromise can be obtained by using the second order Møller–Plesset Perturbation theory and 6-311++G(d,p) (or AUG-cc-pVDZ) basis set. In particular, the red-shift of the H–C and N–C frequencies in the H2O HCN [14,15] and the NH3 HCN [16,17] complexes have been succesfully described by that methodology. Despite the fact that some researchers have suggested that this Ôpractical ruleÕ could well describe also some open-shell hydrogen-bonded complexes [5,6], in the next section it will be shown that this Ôpractical ruleÕ fails when applying UMP2 approach to the frequency predictions of the H3C HNC complex.
concluded that this new kind of hydrogen bond has similar characteristics to the conventional hydrogen bond, namely, the lengthening of the X–H (X = F and C) bonds of the proton donor and the red-shiftings of the H–F and H–C stretching vibration modes in the hydrogen bond complexes. Accordingly, we intuitively expect that the hydrogen bond in H3C HCN will exhibit the same spectroscopic properties as the traditional hydrogen bond complexes: the lengthening of the H–C distance and the lowering of the C–H frequency upon complexation. Two structures have been studied for the interaction between CH3 and HCN: H3C HCN and H3C-NCH. The geometrical parameters displayed in Fig. 1 have been obtained at the UCCSD(T), ROMP2, and UMP2 levels of theory using the 6-311++G(2d,2p) basis sets. It has been shown that the H3C–NCH complex is mostly unbound ðDCP with the e ¼ þ0:5 kcal=molÞ UCCSD(T) method, while the H3C HCN forms a weakly hydrogen-bonded complex, with respect to the fragments ground state. In Table 1 are gathered the optimized geometrical, energetic, and vibrational properties of the H3C HCN complex at the MP2 and CCSD(T) levels of theory. The complex has mostly a C3v symmetry. The spin contamination is slightly larger than the expected value by about 1.6% for all unrestricted wave function. The calculated binding energy (corrected by basis set superposition error) with UMP2 and ROMP2 methods is similar to that obtained at the UCCSD(T) level (5 kJ/mol), with the similar ˚ ). The formaintermolecular distance (r(H C) 2.6 A tion of the complex is characterized by a lengthening ˚ ) of the proton donor of the H–C bond ( 0.003 A and by a concomitant red-shift in the H–C stretching frequency. Compared with the calculated UCCSD(T) H–C frequency-shift (48 cm1), the ROMP2 method
N
Sun and coworkers [5] have recently presented theoretical results on the ability of methyl radical to act as hydrogen bond acceptor when it is complexed with hydrogen fluoride and ethyne. These authors have
C
1.0693 1.0664 1.0659
H
2.5864 2.5854 2.6276
H 1.0786 1.0741 1.0739
H
1.1755 1.1763 1.1763
N
1.0033 1.0034 1.0033
H
2.3009 2.2762 2.2820
1.2353 1.2300 1.2068 111.7 C 125.5 111.3 128.8 110.5 124.6 133.1 124.1 N C 123.1 1.4651 1.4563 1.4504
H
C H
C 3v symmetry ( 2A1 )
C
3.1. Hydrogen-bonded H3C HCN complex
1.1603 1.1668 1.1658
1.0925 1.0909 1.0954
symmetry (2 A')
Cs
H
C
1.0793 1.0747 1.0747
H H
1.0176 1.0158 1.0132
H
H 1.0908 1.0866 1.0867
H H
1.2451 1.2411 1.2220 H 110.5 N 128.6 110.9 129.0 111.1 1.0924 116.5 129.3 1.0890 117.6 C 1.0885 C 119.9 1.4987 1.4903 H 1.4907 H
Fig. 1. Optimized structures of the four studied complexes. Distances ˚ , and angles in degrees. The UCCSD(T) values are reported in are in A the first row, the ROMP2 values in the second row, and the UMP2 values in the third row.
M. Solimannejad, M.E. Alikhani / Chemical Physics Letters 406 (2005) 351–354
353
Table 1 Relevant properties of the free HCN and H3C HCN complex Free HCN (closed-shell) Experiment b MP2/aug-cc-pVTZ With 6-311++G(2d,2p) basis MP2 CCSD(T)
r(HC)
r(CN)
1.065 1.0645 set 1.0633 1.0661
r(H C)
x(HC)
x(NC)
1.153 1.1670
3311.5 3467
2096.9 2022
1.1666 1.1601
3463 3425
2015 2096
H3C HCN complex (open-shell) UMP2/aug-cc-pVTZ 1.0675[0.003] 1.1660[0.001] 2.5509 3429[+38] With 6-311++G(2d,2p) basis set UMP2 1.0659[0.003] 1.1657[0.0009] 2.6276 3426[+38] UCCSD(T) 1.0693[0.003] 1.1603[+0.0002] 2.5864 3377[+48] ROMP2 1.0664[0.003] 1.1668[+0.0002] 2.5854 3414[+50] ˚ , frequencies in cm1, and DCP (CP corrected binding energy) in kJ/mol.a Distances are in A e compl a Bond length differences and frequency-shifts ðpropertyfree HCN propertyHCN Þ are reported in square brackets. b Ref. [18].
gives a better result (50 cm1) than the UMP2 approach (38 cm1). As shown in Table 1, the C–N bond length increases at the UMP2 level (with both basis sets), whereas it decreases when using the ROMP2 and UCCSD(T) levels of theory. Consequently, the N–C frequency has been calculated to be largely blueshifted with UMP2 (147 and 171 cm1 with the 6-311++G(2d,2p) and aug-cc-pVTZ basis sets, respectively), while it is slightly red-shifted with UCCSD(T) and ROMP2 (1 and 3 cm1). Therefore, the UMP2 method fails to give the correct frequency-shift for the N–C stretch mode upon complexation. This example clearly shows that the use of ROMP2 could be considered as a safe route to evaluate the spectroscopic properties of the open-shell hydrogen-bonded systems, if the energetic and structural parameters remain close to those obtained at UCCSD(T) (and UMP2) level. It is interesting to note that the frequency calculations with UCCSD(T) are very time consuming, whereas ROMP2 method could be considered as a quite good approach to do the vibrational analysis with a much lower computational effort. 3.2. Covalent-bonded H3C-CNH complex For the interaction between CH3 and HNC, two structures have been studied: the hydrogen-bonded H3C HNC and the covalent-bonded H3C–CNH complexes. In Fig. 1 are displayed the geometrical parameters of these two complexes. The BSSE corrected binding energy of the H3C–CNH complex is calculated to be 25.5, 24.1, and 24.8 kcal/mol at UCCSD(T), ROMP2, and UMP2 levels of theory, respectively. Its hydrogen-bonded counterpart is found to be a weakly bound complex (2.2, 2.4, and 2.2 kcal/mol with UCCSD(T), ROMP2, and UMP2, respectively). The calculated binding energies with the restricted and unre-
DCP e
2193[171]
5.5
2162[147] 2095[+1] 2012[+3]
5.3 5.3 5.5
stricted MP2 methods are quite close to the UCCSD(T) results. Therefore, the covalent-bonded complex corresponds to the ground state of the isocyanide complexed with the methyl radical. Inspection of the geometrical parameters (Fig. 1) shows that the ROMP2 method gives once again even better results than the UMP2 approach with respect to the UCCSD(T) values. In the H3C–CNH complex, the unpaired electron is almost located on the carbon atom of HNC and the C–C distance belongs to the single C–C bond range. The C–C stretching vibrational frequency is found to be 1180 cm1, in a strong coupling with the H–N–C bending mode. Upon complexation, the HNC unit has a distorted geometry, in which the H–N and C–N frequencies are largely red-shifted by 334 and 224 cm1, respectively (see Table 2).
Table 2 Vibrational frequencies (in cm1) of the H3C–NH complex at UCCSD(T), ROMP2, and UMP2 levels with the 6-311++G(2d,2p) basis seta
m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 a
UCCSD(T) ROMP2
UMP2
Mode descriptions
93 440 677 900 976 1050 1180 1399 1478 1487 1806(2030) 3026 3113 3127 3475(3809)
156 447 673 882 980 1058 1168 1406 1495 1496 2232(2011) 3078 3176 3188 3560(3825)
Torsion CCN bend HN libration HNC bend + CC stretch HN libration HCH bend CC stretch + HNC bend H3C breath HCH bend HCH bend NC stretch HC stretch HC stretch HC stretch HN stretch
137 442 672 901 962 1056 1160 1407 1493 1498 1792(2013) 3074 3169 3183 3520(3830)
In parentheses are reported the frequencies of free HNC.
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4. Conclusions A comparative theoretical study of the interaction between a methyl radical and HCN/HNC molecules has been performed with the coupled-cluster and Møller– Plesset Perturbation theories. It has been shown that the product of the CH3 + HCN reaction is a weakly hydrogen-bonded complex, while we obtain a covalent-bonded compound in the case of CH3 + HNC. Even though the UMP2 and ROMP2 methods give spectroscopic parameters mostly close to those obtained at a highly correlated method (coupled-cluster), the UMP2 method fails to predict correctly the N–C frequency-shift in the H3C HCN open-shell hydrogenbond. In such case, the use of a restricted wave function at the second order Møller–Plesset Perturbation Theory gives the best agreement with the UCCSD(T) results.
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