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The effect of a neon matrix on the hyperfine structure of CH+4. A model study
Volume 2 I 1,number 1
CHEMICAL PHYSICS LETTERS
6 August
1993
The effect of a neon matrix on the hyperfine structure of CH: . A model study Leif A. E&son, Department
Jian Wang and Russell J. Boyd
of Chemiswy? Dalhourie University, Ha&q
Received 28 April
Nova Scotia, Canada B3H 4J3
1993;in final form 24 May 1993
The influence of up to six Ne atoms on the isotropic hypertine (hf) coupling constants of the hydrogen atoms in CH$ is investigated using density functional theory. It is found that at very short Ne-H distances (R= 1.8 A), the hf structure is strongly affected, whereas at the more realistic van der Waals distance (R1: 2.5 A), the methane radical experiences a very weak field from the surrounding Ne atoms. At larger distances, the effects of the Ne matrix are negligible. It is furthermore found that at small R, the changes in a,,(H) are strongly dependent on the relative positions of the Ne atoms.
1. Introduction In the study of small, short-lived (organic) radical cations, low-temperature matrix isolation electronspin resonance (ESR) techniques have proven to be very valuable experimental tools (see, e.g., refs. [ 1,2] ), One problem with the ESR measurements is, however, that it is frequently found that different matrix compounds (such as Ne, SF6, CF,CC&, etc.) influence the solute molecules through steric and electronic interactions, thus generating slightly different spectra depending on the choice of matrix substance [ 3-71. In some cases, the radical cations have also been shown to react or decompose within the matrix, forming new radical compounds [5,812 1. For, e.g., the propane radical cation, different matrices are even found to stabilize different electronic states. Using SF6, the symmetric CZvgeometry is obtained [ 5 1, whereas using CXFB,an asymmetric structure of C, symmetry is observed [ 121. Noble-gas matrices (Ne and Ar ) have been claimed to be chemically inert [ 1,2 1, although this hypothesis naturally is very difficult to prove experimentally. By performing the ESR experiments at very low temperatures (4 K), the matrix-solute interactions are assumed to decrease even more. At low temperatures, the internal vibrational/rotational motion of the test molecules is significantly reduced, which also contributes to better resolved spectra. This has been 88
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addressed in great detail in earlier work [ 13-l 71. Very few previous theoretical studies have, however, been made to elucidate the question of matrix-solute interactions, although it has been shown in molecular dynamics calculations, that an Ar matrix stabilizes the planar cis form of butadiene over the trans conformation [ 18 1. As a complement to, and aid for, the experimental ESR studies, the hyperfine structures of radical systems can also be computed with high accuracy (typically, within 5%- 10% error), using ab initio configuration-interaction (CI) techniques and first principles density functional theory (DFT) [ 19-22 1, In the theoretical treatments, the radical cation is, however, always assumed to be in vacuum, i.e. all interactions with the surrounding matrix compounds are being neglected. The methane cation has turned out to be a particularly difficult compound for ESR measurements, due to its high ionization potential. In, e.g., SF6 matrices, the cation readily deprotonates, and reacts with the matrix molecules through complex formation as well as by (partially) replacing the remaining hydrogen atoms with fluorines [ 23 1. It is the objective of the present Letter to investigate a similar, but less reactive case, namely whether a neon matrix influences the isotropic hf couplings of the methane radical cation or not.
06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 2 11, number I
6 August 1993
CHEMICAL PHYSICS LETTERS
2. Theory We use, in the present study, the linear combination of Gaussian type orbitals-density functional theory (LCGTO-DFT) program deMon [ 241, and the hf calculation routine by Malkin and co-workers [ 2 11. All calculations are performed within the local density approximation (LDA), using the formalism by Vosko, Wilk and Nusair [ 251. DFT has previously been shown to yield highly accurate geometries and hyperline structures of a number of hydrocarbon radical cations [21,26] and nitrogen oxides [ 221. It also has the advantage over, e.g., configuration-interaction techniques, that we are able to accurately treat much larger systems without exhausting available computational time or memory requirements. Weusethecontracted(5111111/211111/11)and 3111/ 11) orbital basis sets (“IGLO-III”) for the carbon and hydrogen atoms [ 27,28 1, and the “DZP” basis (621/41/l*) for the neon atoms [29]. The auxiliary basis sets, for the fitting of the charge density and the exchange and correlation potentials, are (5,2; 5, 2) for carbon, (5, 1; 5, 1) for the hydrogens, and (4, 3; 4, 3) for the neon atoms, respectively [ 29,301. The IGLO-III bases are those by Kutzelnigg et al. [ 271 (IGLO: individual gauge of localized orbitals), used with great success for ab initio NMR calculations. We use the same contraction schemes and exponents, but retain the s-type linear combination of d,, d, and d,,. This basis has previously been shown to yield highly accurate NMR and ESR parameters in conjunction with density functional theory [21,22,28]. In each SCF calculation we set the energy convergence criterion to 1.0 X low6 au, and use the DIIS (direct inversion of the iterative subspace) routine by Pulay [ 311. Convergence is generally reached within 30 iterations.
Jahn-Teller distort from the symmetric Td structure of the neutral parent molecule, to a structure of Czv symmetry with two elongated and two shorter C-H bonds [ 34,35 1. At the non-local DFT level, the two elongated bonds (C-H 1 of fig. 1) are 1.208 8, ( L H 1-C-H 1 = 58.6” ), and the two shorter bonds (C-H2) are 1.104 A (LH~-C-H2~124.5”) [26]. This geometry was held fixed throughout the present study. Four different
arrangements of neon atoms, and combinations of these, were used to investigate the changes in hf structures of the methane cation hydrogens. The basic structures are shown in fig. 1. In all cases, the distance “R” between Ne and the nearest hydrogen atom(s) is varied symmetrically between 1.8 and 3.0 A. In t1 and III, the Ne atoms are placed equidistant from H 1, H 1, H2 and H 1, H2, H2, respectively, whereas in I, each neon interacts
13 NC
Hl @
Hl ,;-@
. . . . __\I ;;C( HZ
HZ
II
I @
@ : Hl
Hl
Hl
Hl
96
pd
/Y ,’
3. Computational model and results
A2
, H2
Ne ci
The geometry of the methane radical cation used is that of ref. [ 261, in which we used DFT with the inclusion of non-local corrections to the exchange and correlation potentials [ 32,331 for the geometry optimizations. The methane radical cation is known to
III
IV
-.
*. 0
Ne
Fig. 1. The four unique Ne,-CH: models, used in the present investigation. Combinations of the three first (I, II and III ) are also used. The distances between the Ne atoms and the nearest atom(s) in CH: are varied between 1.8 and 3.0 A.
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pairwise with the two “Hl” or the two “H2” hydrogens. In III, where the Ne atoms are located above/ below the plane of the paper, the C-Ne distances are the shortest ones, and are used as “R” in the following discussions. For the fourth arrangement, the Ne atoms are positioned a distance “R” from the nearest hydrogen, along the extension of the corresponding C-H bond. We also used the combinations I + II, ISIII, II-t111 and I+11 +I11 in the study. In the ESR experiments, the solute/solvent gas mixture is sprayed onto a cold finger, leading to an instantaneous freezing of the sample. There is thus not suffkient time for the solvent atoms/molecules (Ne) to form a perfect crystal lattice with the solute molecules ( CHI) located in hollow sites or as crystal defects; instead the generated matrix can be regarded as fully amorphous. The choice of “pairwise random” positions of the Ne atoms in the present model calculations may thus be justified on these grounds. The experimental hf couplings, determined inaNematrixat4Kare 121.7Gand (-)14.6G, respectively [ 341. Previous CI calculations including single and double excitations (SDCI) have given 2x137 G and 2x-17 G [34], whereas the DFT computed couplings of the free radical have been reported as 2x121.1 G and 2x-16.3 G [21]. The present model is chosen such as to retain this pairwise symmetry of the hydrogen hf coupling constants. In figs. 2a and 2b we plot the relative energies of the systems with CH$ interacting with (a) two and (b) four or six Ne atoms, respectively, at distances R = 1.8-3-O A. As seen, all cases except arrangement IV of fig_ 1, yield local energy minima at R = 2.5 _+0.1 A, in excellent agreement with the known Ne-H van der Waals distance 2.5 8, [ 361. Assuming the matrix to consist of a set of quasi-randomly ordered van der Waals particles thus yields a realistic picture from an energetic point of view. Also when combining the three models I, II and III, this energy minimum is observed. Shortening the distance leads for all cases involving arrangements I, II and III to a dramatic increase in energy. For the “end-on” arrangement IV, minima are, however, found at distances below R = 1.8 A. In this case, it is clear that the Ne atoms interact strongly with the hydrogens, as is also reflected in the slightly increased spin density at the Ne nuclei at short distances. On the other hand, a model assuming four 90
6 August 1993
simultaneous “end-on” bonds formed between the Ne atoms and the hydrogens may be argued to have limited probability. In figs. 3a and 3b, the hf coupling constants of the corresponding pairwise equivalent hydrogens (“Hl” and “H2”) are shown as functions of the Ne distance. As seen from figs. 3a and 3b, it is only at very small R that the hf couplings are influenced at any larger extent, irrespective of the number of Ne atoms or their arrangement. For the “sideways” interacting system II (and combinations containing this), Qiw(H 1) 2 150 G at 1.8 A. This value decreases rapidly, and at R ~2.4 A the computed free molecule value 121.1 G is virtually obtained. For the “end-on” arrangement IV, we instead note a minor decrease in aim at short distances. The two negative couplings corresponding to “H2”, only deviate from the free value - 16.3 G [ 2 1] for those Ne arrangements containing positions III. At short distances Uim(H2) z - 14.5 G in these cases. This arrangement also shows as non-negligible induced spin density at the Ne nuclei for short distances. This declines, however, rapidly with increasing R. For all systems, the matrix-cation interactions are negligible above R=2.4 A.
4. Summary The interactions between a methane radical cation and up to six Ne atoms have been investigated at the first-principles DFT level. An all-electron, extended basis set model is used, and all calculations are performed assuming the local density approximation to be valid. The distance between the Ne atoms and the nearest atom(s) in the CH: moiety is varied between 1.8 and 3.0 A; all geometrical parameters of the methane cation are, however, assumed unchanged in the process. Three different Ne,-CH,+, four Ne,-CH: , and one Ne,-CH: supermolecules are considered. For all arrangements, the relative energies of each system as well as the computed isotropic hf structures of the CH: hydrogens are reported. It is found that for all arrangements investigated, matrix-solute interactions are negligible at distances above 2.5 A. This also corresponds to the Ne-H van der Waals distance [36], which is a local energy
Volume 2 1I, number I
6 August 1993
CHEMICAL PHYSKS LETTERS
50
(4 2 2 -E ;;i : B 5
40
30
20
: ji ._ z TJ s
10
0
-10
1.8
2.0
2.2 Distance
-10
’ 1.8
I
2.0
1
2.4
2.6
2.8
3.0
(Angstrcm)
I
I
2.2 2.4 2.6 Distance (Angstri,m)
4
2.8
Fig. 2. Relative energies of CH: inttracting with (a) two, (b) four or six Ne atoms, as functions of distance.
3.0
The fourmodelsI-IV are
depictedin fig. I. minimum for cases I, II and III, and combinations of these. At shorter distances, the energy rises rapidly by up to 80 kcal/mol (fig. 2b). For the “endon” arrangement IV, however, strong Ne-H interactions are observed, leading to a decrease in total energy at shorter distances. The hf structures are strongly influenced by the “above/below” arrangements III and the “end-on” model IV at short distances. As the Ne-H distances
increase to above 2.4 A, the free cation hf couplings are, however, rapidly obtained. It is thus concluded that in the amorphous Ne matrices used in ESR experiments, the matrix substance has very little, if any, effect on the hf structure of the solute, in this case the methane radical cation. This is in agreement with the general assumptions 11321.
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Volume2 11, number 1
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CHEMICALPHYSICSLETTERS
150 z
,
140-
‘\
.’ g ii VI
130120 .-...-
z 8
110 -
u
\
(a)
\
4\
-\
N-w_
---____
-!
I ‘“:,p
F ._ z. 2
-5 -
u 0 ;;” b
---_ ----__ -15 ~_.................__.~~~~~----------
X,”
-20 -
-10 -
I
-25
1.8
2.2
2.0
Distance
I
I
I
2.4
2.6
2.8
J
3.0
(Angstribm)
(b)
u x i;: ki
-10 :, -----a,_ -15 : ._.-. -l.--.--1-_-----.--.
-25 ’ 1.8
f.
I
I
I
2.0
2.2
2.4
Distance
2.6
(.&ngstrBm)
Fig. 3. The isotropic hypertine coupling constants of the two pairs of hydrogens in the methane radical cation. The same models and legend are used as in fig. 2. The experimental values are Ui,(2XHI)=l21.7 G and ai,(2xH2)=(-)14.6 G [34], and the DFT computed free-molecule values are 12I, 1 and - 16.3 G, respectively [ 2 11.
Acknowledgement
References
This work was financed by the Swedish Natural Science Research Council (NFR), the Killam Trust,
[ 1 ] A. Lund and M. Shiotani, eds., Radical ionic systems. Properties in condensed phases (Kluwer, Dordrecht, I99 I )
and the Natural
[2] L.B. Knight Jr., AccountsChem. Res. 19 (1986) 313.
Sciences
Council of Canada
and Engineering
(NSERC).
Research
[31 T. Sbida, Y. Egawa,H. Kubodera and T.J. Kato, J. Chem. - Phys. 73 (1980) 5963. [4] J. Fujisawa, S. Shato, K. Shimokoshi and T. Shida, 1. Phys. Chem. 89 ( 1985) 548 1.
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[ 51 K. Toriyama, K. Nunome and M. Iwasaki, J. Chem. Phys. 77 (1982) 5891; S. Lunell, M.-B. Huang and A. Lund, Faraday Discussions Chem. Sot. 78 (1984) 35. [6] M. Shiotani, L. Sjiiqvist, A. Lund, S. Lunell, L.A. Eriksson and M.-B. Huang, J. Phys. Chem. 94 ( 1990) 8081. [7] M. Shiotani, Y. Nagata and J. Sohma, J. Phys. Chem. 88 (1984) 4078. [S] J.R. Morton, K.F. Preston and S.J. Strach, J. Phys. Chem. 83(1979)533. [ 91 L.A. Eriksson, L. SjBqvist, S. Lunell, M. Shiotani, M. Usui and A. Lund, J. Am. Chem. Sot., in press. [ IO] J. Fnjisawa, S. Sato and K. Shimokoshi, Chem. Phys. Letters 124 (1986) 391. [I I] R. Alvarez-Idaboy, T. Fgngstrom, L.A. Eriksson and S. Lnnell, J. Phys. Chem., submitted for publication. [ 121K. Toriyama, Chem. Phys. Letters 177 (1991) 39. [ 131S. Lunell and L.A. Eriksson, Intern. J. Quantum Chem. Symp. 26 (1992) 575. [ 141 K. Matsnura, K. Nunome, M. Okazaki, K. Toriyama and M. Iwasaki, J. Phys. Chem. 93 (1989) 6642. [IS] M. Lindgren, A. Lund and G. Dolivo, Chem. Phys. 99 (1985) 103. [ 161M. Lindgren and A. Lund, J. Chem. Sot. Faraday Trans. 83 (1987) 1815. [ 171L. Sjiiqvist, Ph.D. Thesis, Linkiiping University, Sweden (1991). [ 181 M. Kofranek, A. Karpfen and H. Lischka, Chem. Phys. Letters 189 (1992) 281. [ 191S. Lunell, L.A. Eriksson and M.-B. Huang, J. Mol. Strut. THEOCHEM 230 ( 1991) 263. [ 201 D. Feller and E.R. Davison, J. Chem. Phys. 80 ( 1984) 1006. [ 2 I] L.A. Eriksson, V.G. Malkin, O.L. Malkina and D.R. Salahub, J. Chem. Phys., submitted for publication. [ 221 L.A. Eriksson, J. Wang, R.J. Boyd and S. Lunell, J. Chem. Phys., submitted for publication.
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[ 231 K.Toriyama, K. Nunome and M. Iwasaki, J. Phys. Chem. 92 ( 1988) 5097. [24] A. St-Amant and D.R. Salahub, Chem. Phys. Letters 169 ( 1990) 387; A. St-Amant, Ph.D. Thesis, Universitt de Montreal, 1991; D.R. Salahub, R. Foumier, P. Mlynarksi, I. Papai, A. StAmant and J. Ushio, in: Density functional methods in chemistry, J. Labanowski and J. Andzelm, eds. (Springer, Berlin, I99 I) [25 ] S.H. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58 ( 1980) 1200. [26] L.A. Eriksson, S. Lunell and R.J. Boyd, J. Am. Chem. Sot., accepted for publication. [27] W. Kutzelnigg, U. Fleischer and M. Schindler, in: NMRbasic principles and progress, Vol. 23 (Springer, Berlin, 1990) p. 165. [28] V.G. Malkin, O.L. Malkina and D.R. Salahub, Chem. Phys. Letters 204 ( 1993) 8887. [29] N. Godbont, D.R. Salahub, J. Andzclm and E. Wimmer, Can. J. Chem. 70 (1992) 560. [30] F. Sim, D.R. Salahub, S. Chin and M. Dupuis, J. Chem. Phys.95 (1991)4317. [ 3 1]P. Pulay, Chem. Phys. Letters 73 ( 1980) 393; J. Comput. Chem.3(1982)556. [32] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [33] J.P. Perdew, Phys. Rev. B 33 (1986) 8822; 34 ( 1986) 7406. [ 341 L.B. Knight Jr., J. Steadman, D. Feller and E.R. Davidson, J. Am. Chem. Sot. 106 (1984) 3700. (351 W.J. Bouma, D. Poppinger and L. Radom, Isr. J. Chem. 23 (1983) 21; M.N. Paddon-Row, D.J. Fox, J.A. Pople, K.N. Honk and D.W. Pratt, J. Am. Chem. Sot. 107 (1985) 7696; R.J. Boyd, K.V. Darvesh and P.D. Fricker, J. Chem. Phys. 94 ( 1991) 8083. [36] L. Pauling, The nature of the chemical bond, 3rd Ed. (Cornell Univ. Press., Ithaca, 1960).
93
CHEMICAL PHYSICS LETTERS
6 August
1993
The effect of a neon matrix on the hyperfine structure of CH: . A model study Leif A. E&son, Department
Jian Wang and Russell J. Boyd
of Chemiswy? Dalhourie University, Ha&q
Received 28 April
Nova Scotia, Canada B3H 4J3
1993;in final form 24 May 1993
The influence of up to six Ne atoms on the isotropic hypertine (hf) coupling constants of the hydrogen atoms in CH$ is investigated using density functional theory. It is found that at very short Ne-H distances (R= 1.8 A), the hf structure is strongly affected, whereas at the more realistic van der Waals distance (R1: 2.5 A), the methane radical experiences a very weak field from the surrounding Ne atoms. At larger distances, the effects of the Ne matrix are negligible. It is furthermore found that at small R, the changes in a,,(H) are strongly dependent on the relative positions of the Ne atoms.
1. Introduction In the study of small, short-lived (organic) radical cations, low-temperature matrix isolation electronspin resonance (ESR) techniques have proven to be very valuable experimental tools (see, e.g., refs. [ 1,2] ), One problem with the ESR measurements is, however, that it is frequently found that different matrix compounds (such as Ne, SF6, CF,CC&, etc.) influence the solute molecules through steric and electronic interactions, thus generating slightly different spectra depending on the choice of matrix substance [ 3-71. In some cases, the radical cations have also been shown to react or decompose within the matrix, forming new radical compounds [5,812 1. For, e.g., the propane radical cation, different matrices are even found to stabilize different electronic states. Using SF6, the symmetric CZvgeometry is obtained [ 5 1, whereas using CXFB,an asymmetric structure of C, symmetry is observed [ 121. Noble-gas matrices (Ne and Ar ) have been claimed to be chemically inert [ 1,2 1, although this hypothesis naturally is very difficult to prove experimentally. By performing the ESR experiments at very low temperatures (4 K), the matrix-solute interactions are assumed to decrease even more. At low temperatures, the internal vibrational/rotational motion of the test molecules is significantly reduced, which also contributes to better resolved spectra. This has been 88
0009-2614/93/$
addressed in great detail in earlier work [ 13-l 71. Very few previous theoretical studies have, however, been made to elucidate the question of matrix-solute interactions, although it has been shown in molecular dynamics calculations, that an Ar matrix stabilizes the planar cis form of butadiene over the trans conformation [ 18 1. As a complement to, and aid for, the experimental ESR studies, the hyperfine structures of radical systems can also be computed with high accuracy (typically, within 5%- 10% error), using ab initio configuration-interaction (CI) techniques and first principles density functional theory (DFT) [ 19-22 1, In the theoretical treatments, the radical cation is, however, always assumed to be in vacuum, i.e. all interactions with the surrounding matrix compounds are being neglected. The methane cation has turned out to be a particularly difficult compound for ESR measurements, due to its high ionization potential. In, e.g., SF6 matrices, the cation readily deprotonates, and reacts with the matrix molecules through complex formation as well as by (partially) replacing the remaining hydrogen atoms with fluorines [ 23 1. It is the objective of the present Letter to investigate a similar, but less reactive case, namely whether a neon matrix influences the isotropic hf couplings of the methane radical cation or not.
06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 2 11, number I
6 August 1993
CHEMICAL PHYSICS LETTERS
2. Theory We use, in the present study, the linear combination of Gaussian type orbitals-density functional theory (LCGTO-DFT) program deMon [ 241, and the hf calculation routine by Malkin and co-workers [ 2 11. All calculations are performed within the local density approximation (LDA), using the formalism by Vosko, Wilk and Nusair [ 251. DFT has previously been shown to yield highly accurate geometries and hyperline structures of a number of hydrocarbon radical cations [21,26] and nitrogen oxides [ 221. It also has the advantage over, e.g., configuration-interaction techniques, that we are able to accurately treat much larger systems without exhausting available computational time or memory requirements. Weusethecontracted(5111111/211111/11)and 3111/ 11) orbital basis sets (“IGLO-III”) for the carbon and hydrogen atoms [ 27,28 1, and the “DZP” basis (621/41/l*) for the neon atoms [29]. The auxiliary basis sets, for the fitting of the charge density and the exchange and correlation potentials, are (5,2; 5, 2) for carbon, (5, 1; 5, 1) for the hydrogens, and (4, 3; 4, 3) for the neon atoms, respectively [ 29,301. The IGLO-III bases are those by Kutzelnigg et al. [ 271 (IGLO: individual gauge of localized orbitals), used with great success for ab initio NMR calculations. We use the same contraction schemes and exponents, but retain the s-type linear combination of d,, d, and d,,. This basis has previously been shown to yield highly accurate NMR and ESR parameters in conjunction with density functional theory [21,22,28]. In each SCF calculation we set the energy convergence criterion to 1.0 X low6 au, and use the DIIS (direct inversion of the iterative subspace) routine by Pulay [ 311. Convergence is generally reached within 30 iterations.
Jahn-Teller distort from the symmetric Td structure of the neutral parent molecule, to a structure of Czv symmetry with two elongated and two shorter C-H bonds [ 34,35 1. At the non-local DFT level, the two elongated bonds (C-H 1 of fig. 1) are 1.208 8, ( L H 1-C-H 1 = 58.6” ), and the two shorter bonds (C-H2) are 1.104 A (LH~-C-H2~124.5”) [26]. This geometry was held fixed throughout the present study. Four different
arrangements of neon atoms, and combinations of these, were used to investigate the changes in hf structures of the methane cation hydrogens. The basic structures are shown in fig. 1. In all cases, the distance “R” between Ne and the nearest hydrogen atom(s) is varied symmetrically between 1.8 and 3.0 A. In t1 and III, the Ne atoms are placed equidistant from H 1, H 1, H2 and H 1, H2, H2, respectively, whereas in I, each neon interacts
13 NC
Hl @
Hl ,;-@
. . . . __\I ;;C( HZ
HZ
II
I @
@ : Hl
Hl
Hl
Hl
96
pd
/Y ,’
3. Computational model and results
A2
, H2
Ne ci
The geometry of the methane radical cation used is that of ref. [ 261, in which we used DFT with the inclusion of non-local corrections to the exchange and correlation potentials [ 32,331 for the geometry optimizations. The methane radical cation is known to
III
IV
-.
*. 0
Ne
Fig. 1. The four unique Ne,-CH: models, used in the present investigation. Combinations of the three first (I, II and III ) are also used. The distances between the Ne atoms and the nearest atom(s) in CH: are varied between 1.8 and 3.0 A.
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pairwise with the two “Hl” or the two “H2” hydrogens. In III, where the Ne atoms are located above/ below the plane of the paper, the C-Ne distances are the shortest ones, and are used as “R” in the following discussions. For the fourth arrangement, the Ne atoms are positioned a distance “R” from the nearest hydrogen, along the extension of the corresponding C-H bond. We also used the combinations I + II, ISIII, II-t111 and I+11 +I11 in the study. In the ESR experiments, the solute/solvent gas mixture is sprayed onto a cold finger, leading to an instantaneous freezing of the sample. There is thus not suffkient time for the solvent atoms/molecules (Ne) to form a perfect crystal lattice with the solute molecules ( CHI) located in hollow sites or as crystal defects; instead the generated matrix can be regarded as fully amorphous. The choice of “pairwise random” positions of the Ne atoms in the present model calculations may thus be justified on these grounds. The experimental hf couplings, determined inaNematrixat4Kare 121.7Gand (-)14.6G, respectively [ 341. Previous CI calculations including single and double excitations (SDCI) have given 2x137 G and 2x-17 G [34], whereas the DFT computed couplings of the free radical have been reported as 2x121.1 G and 2x-16.3 G [21]. The present model is chosen such as to retain this pairwise symmetry of the hydrogen hf coupling constants. In figs. 2a and 2b we plot the relative energies of the systems with CH$ interacting with (a) two and (b) four or six Ne atoms, respectively, at distances R = 1.8-3-O A. As seen, all cases except arrangement IV of fig_ 1, yield local energy minima at R = 2.5 _+0.1 A, in excellent agreement with the known Ne-H van der Waals distance 2.5 8, [ 361. Assuming the matrix to consist of a set of quasi-randomly ordered van der Waals particles thus yields a realistic picture from an energetic point of view. Also when combining the three models I, II and III, this energy minimum is observed. Shortening the distance leads for all cases involving arrangements I, II and III to a dramatic increase in energy. For the “end-on” arrangement IV, minima are, however, found at distances below R = 1.8 A. In this case, it is clear that the Ne atoms interact strongly with the hydrogens, as is also reflected in the slightly increased spin density at the Ne nuclei at short distances. On the other hand, a model assuming four 90
6 August 1993
simultaneous “end-on” bonds formed between the Ne atoms and the hydrogens may be argued to have limited probability. In figs. 3a and 3b, the hf coupling constants of the corresponding pairwise equivalent hydrogens (“Hl” and “H2”) are shown as functions of the Ne distance. As seen from figs. 3a and 3b, it is only at very small R that the hf couplings are influenced at any larger extent, irrespective of the number of Ne atoms or their arrangement. For the “sideways” interacting system II (and combinations containing this), Qiw(H 1) 2 150 G at 1.8 A. This value decreases rapidly, and at R ~2.4 A the computed free molecule value 121.1 G is virtually obtained. For the “end-on” arrangement IV, we instead note a minor decrease in aim at short distances. The two negative couplings corresponding to “H2”, only deviate from the free value - 16.3 G [ 2 1] for those Ne arrangements containing positions III. At short distances Uim(H2) z - 14.5 G in these cases. This arrangement also shows as non-negligible induced spin density at the Ne nuclei for short distances. This declines, however, rapidly with increasing R. For all systems, the matrix-cation interactions are negligible above R=2.4 A.
4. Summary The interactions between a methane radical cation and up to six Ne atoms have been investigated at the first-principles DFT level. An all-electron, extended basis set model is used, and all calculations are performed assuming the local density approximation to be valid. The distance between the Ne atoms and the nearest atom(s) in the CH: moiety is varied between 1.8 and 3.0 A; all geometrical parameters of the methane cation are, however, assumed unchanged in the process. Three different Ne,-CH,+, four Ne,-CH: , and one Ne,-CH: supermolecules are considered. For all arrangements, the relative energies of each system as well as the computed isotropic hf structures of the CH: hydrogens are reported. It is found that for all arrangements investigated, matrix-solute interactions are negligible at distances above 2.5 A. This also corresponds to the Ne-H van der Waals distance [36], which is a local energy
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CHEMICAL PHYSKS LETTERS
50
(4 2 2 -E ;;i : B 5
40
30
20
: ji ._ z TJ s
10
0
-10
1.8
2.0
2.2 Distance
-10
’ 1.8
I
2.0
1
2.4
2.6
2.8
3.0
(Angstrcm)
I
I
2.2 2.4 2.6 Distance (Angstri,m)
4
2.8
Fig. 2. Relative energies of CH: inttracting with (a) two, (b) four or six Ne atoms, as functions of distance.
3.0
The fourmodelsI-IV are
depictedin fig. I. minimum for cases I, II and III, and combinations of these. At shorter distances, the energy rises rapidly by up to 80 kcal/mol (fig. 2b). For the “endon” arrangement IV, however, strong Ne-H interactions are observed, leading to a decrease in total energy at shorter distances. The hf structures are strongly influenced by the “above/below” arrangements III and the “end-on” model IV at short distances. As the Ne-H distances
increase to above 2.4 A, the free cation hf couplings are, however, rapidly obtained. It is thus concluded that in the amorphous Ne matrices used in ESR experiments, the matrix substance has very little, if any, effect on the hf structure of the solute, in this case the methane radical cation. This is in agreement with the general assumptions 11321.
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CHEMICALPHYSICSLETTERS
150 z
,
140-
‘\
.’ g ii VI
130120 .-...-
z 8
110 -
u
\
(a)
\
4\
-\
N-w_
---____
-!
I ‘“:,p
F ._ z. 2
-5 -
u 0 ;;” b
---_ ----__ -15 ~_.................__.~~~~~----------
X,”
-20 -
-10 -
I
-25
1.8
2.2
2.0
Distance
I
I
I
2.4
2.6
2.8
J
3.0
(Angstribm)
(b)
u x i;: ki
-10 :, -----a,_ -15 : ._.-. -l.--.--1-_-----.--.
-25 ’ 1.8
f.
I
I
I
2.0
2.2
2.4
Distance
2.6
(.&ngstrBm)
Fig. 3. The isotropic hypertine coupling constants of the two pairs of hydrogens in the methane radical cation. The same models and legend are used as in fig. 2. The experimental values are Ui,(2XHI)=l21.7 G and ai,(2xH2)=(-)14.6 G [34], and the DFT computed free-molecule values are 12I, 1 and - 16.3 G, respectively [ 2 11.
Acknowledgement
References
This work was financed by the Swedish Natural Science Research Council (NFR), the Killam Trust,
[ 1 ] A. Lund and M. Shiotani, eds., Radical ionic systems. Properties in condensed phases (Kluwer, Dordrecht, I99 I )
and the Natural
[2] L.B. Knight Jr., AccountsChem. Res. 19 (1986) 313.
Sciences
Council of Canada
and Engineering
(NSERC).
Research
[31 T. Sbida, Y. Egawa,H. Kubodera and T.J. Kato, J. Chem. - Phys. 73 (1980) 5963. [4] J. Fujisawa, S. Shato, K. Shimokoshi and T. Shida, 1. Phys. Chem. 89 ( 1985) 548 1.
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[ 51 K. Toriyama, K. Nunome and M. Iwasaki, J. Chem. Phys. 77 (1982) 5891; S. Lunell, M.-B. Huang and A. Lund, Faraday Discussions Chem. Sot. 78 (1984) 35. [6] M. Shiotani, L. Sjiiqvist, A. Lund, S. Lunell, L.A. Eriksson and M.-B. Huang, J. Phys. Chem. 94 ( 1990) 8081. [7] M. Shiotani, Y. Nagata and J. Sohma, J. Phys. Chem. 88 (1984) 4078. [S] J.R. Morton, K.F. Preston and S.J. Strach, J. Phys. Chem. 83(1979)533. [ 91 L.A. Eriksson, L. SjBqvist, S. Lunell, M. Shiotani, M. Usui and A. Lund, J. Am. Chem. Sot., in press. [ IO] J. Fnjisawa, S. Sato and K. Shimokoshi, Chem. Phys. Letters 124 (1986) 391. [I I] R. Alvarez-Idaboy, T. Fgngstrom, L.A. Eriksson and S. Lnnell, J. Phys. Chem., submitted for publication. [ 121K. Toriyama, Chem. Phys. Letters 177 (1991) 39. [ 131S. Lunell and L.A. Eriksson, Intern. J. Quantum Chem. Symp. 26 (1992) 575. [ 141 K. Matsnura, K. Nunome, M. Okazaki, K. Toriyama and M. Iwasaki, J. Phys. Chem. 93 (1989) 6642. [IS] M. Lindgren, A. Lund and G. Dolivo, Chem. Phys. 99 (1985) 103. [ 161M. Lindgren and A. Lund, J. Chem. Sot. Faraday Trans. 83 (1987) 1815. [ 171L. Sjiiqvist, Ph.D. Thesis, Linkiiping University, Sweden (1991). [ 181 M. Kofranek, A. Karpfen and H. Lischka, Chem. Phys. Letters 189 (1992) 281. [ 191S. Lunell, L.A. Eriksson and M.-B. Huang, J. Mol. Strut. THEOCHEM 230 ( 1991) 263. [ 201 D. Feller and E.R. Davison, J. Chem. Phys. 80 ( 1984) 1006. [ 2 I] L.A. Eriksson, V.G. Malkin, O.L. Malkina and D.R. Salahub, J. Chem. Phys., submitted for publication. [ 221 L.A. Eriksson, J. Wang, R.J. Boyd and S. Lunell, J. Chem. Phys., submitted for publication.
6 August 1993
[ 231 K.Toriyama, K. Nunome and M. Iwasaki, J. Phys. Chem. 92 ( 1988) 5097. [24] A. St-Amant and D.R. Salahub, Chem. Phys. Letters 169 ( 1990) 387; A. St-Amant, Ph.D. Thesis, Universitt de Montreal, 1991; D.R. Salahub, R. Foumier, P. Mlynarksi, I. Papai, A. StAmant and J. Ushio, in: Density functional methods in chemistry, J. Labanowski and J. Andzelm, eds. (Springer, Berlin, I99 I) [25 ] S.H. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58 ( 1980) 1200. [26] L.A. Eriksson, S. Lunell and R.J. Boyd, J. Am. Chem. Sot., accepted for publication. [27] W. Kutzelnigg, U. Fleischer and M. Schindler, in: NMRbasic principles and progress, Vol. 23 (Springer, Berlin, 1990) p. 165. [28] V.G. Malkin, O.L. Malkina and D.R. Salahub, Chem. Phys. Letters 204 ( 1993) 8887. [29] N. Godbont, D.R. Salahub, J. Andzclm and E. Wimmer, Can. J. Chem. 70 (1992) 560. [30] F. Sim, D.R. Salahub, S. Chin and M. Dupuis, J. Chem. Phys.95 (1991)4317. [ 3 1]P. Pulay, Chem. Phys. Letters 73 ( 1980) 393; J. Comput. Chem.3(1982)556. [32] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [33] J.P. Perdew, Phys. Rev. B 33 (1986) 8822; 34 ( 1986) 7406. [ 341 L.B. Knight Jr., J. Steadman, D. Feller and E.R. Davidson, J. Am. Chem. Sot. 106 (1984) 3700. (351 W.J. Bouma, D. Poppinger and L. Radom, Isr. J. Chem. 23 (1983) 21; M.N. Paddon-Row, D.J. Fox, J.A. Pople, K.N. Honk and D.W. Pratt, J. Am. Chem. Sot. 107 (1985) 7696; R.J. Boyd, K.V. Darvesh and P.D. Fricker, J. Chem. Phys. 94 ( 1991) 8083. [36] L. Pauling, The nature of the chemical bond, 3rd Ed. (Cornell Univ. Press., Ithaca, 1960).
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