J. Phys. Chem. 1996, 100, 19771-19782
19771
Magnetizabilities and Nuclear Shielding Constants of the Fluoromethanes in the Gas Phase and Solution Per-Olof A° strand,*,†,‡ Kurt V. Mikkelsen,†,‡ Kenneth Ruud,§ and Trygve Helgaker§ Department of Chemistry, Aarhus UniVersity, DK-8000 A° rhus C, Denmark, and Department of Chemistry, UniVersity of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway ReceiVed: June 11, 1996; In Final Form: September 17, 1996X
The effects of a dielectric medium on the magnetizabilities and nuclear shielding constants of the fluoromethanes are calculated in a gauge-origin independent approach. It is shown that in order to model the effects of a dielectric medium properly, we have to go beyond the dipole approximation and the geometry has to be optimized for each value of the dielectric constant. Geometrical distortions play an important role, as is clearly demonstrated for the magnetizability of the CH3F molecule where the geometrical distortions alter the sign of the dielectric contribution to the solvent shift. The effects on the nuclear shielding constants from a dielectric medium are interpreted in terms of the polarization of the charge distribution and the change in geometry. Other medium effects on nuclear shielding constants are discussed, and it is demonstrated that they must be included in order to reproduce the experimental gas-to-liquid chemical shift of the CH3F and CHF3 molecules. Basis set convergence and electron correlation effects of the magnetizabilities and the nuclear shielding constants in the gas phase are also investigated.
I. Introduction
II. Theoretical Background
Quantum chemistry can today provide accurate magnetic properties of molecules in the gas phase.1 However, even though some experimental gas phase data are available in the literature,2 nuclear magnetic resonance (NMR) spectroscopy usually takes place in solution or in the solid state. In this work we investigate the effects of a dielectric medium on the fluoromethanes, motivated by the fact that the solvent shifts (σsolvent - σgas) of the fluorine shielding of both CH3F and CHF3 in neat samples are negative,3 whereas the only theoretical work estimates these shifts to be positive.4 Furthermore, despite large differences between theory and experiment for the fluorine shielding in the gas phase, electron correlation is not believed to be important.5 We would like to explore this in greater detail and therefore also present some investigations of the basis set convergence and electron correlation dependence of these properties. The effects of a surrounding medium on shielding constants are normally partitioned as6
The theory for calculating gauge-origin independent magnetizabilities and nuclear shieldings of a molecule embedded in a dielectric continuum has been presented previously,7 and only some key features of the theory are given here. The solvent is described as a homogeneous, isotropic, and linear dielectric medium. The solvated molecule and optional solvation shells are placed in a spherical cavity within the dielectric medium. The polarization energy arising from the interaction between the molecule and the dielectric medium is calculated by using a multipole expansion of the charge distribution of the molecule. The dielectric medium is thus characterized by three parameters: the dielectric constant of the solvent , the radius of the cavity Rcav, and the order of the multipole expansion lmax. This approach is discussed in more detail elsewhere.9-13 Nuclear shieldings and magnetizabilities are conveniently calculated by adopting quantum mechanical response theory14,15 and London atomic orbitals to ensure gaugeorigin independent results and fast basis set convergence.16,17 The magnetizability ξ is given as
σsolvent ) σb + σa + σw + σE
(1)
where σb is proportional to the magnetic susceptibility, σa arises from the anisotropy of the magnetizability of the solvent molecules close to the molecule of interest, σw is due to van der Waals interactions, and σE is caused by electrostatic interactions that polarize the charge distribution. Note that a geometry distortion term is included implicitly in the van der Waals and electrostatic terms. The pure electrostatic part may be described by a dielectric continuum,7 but if strong specific interactions such as hydrogen bonding are present, the dielectric approximation may give a poor description for the atoms involved in the hydrogen bond.8
|
B) ∂2E(B ξ)2 ∂B B
(2) B B)0
where E is the electronic energy functional and B B the magnetic field induction. The shielding constant of the Kth nucleus, σK, is calculated as18
σ )1+ K
|
B,m b) ∂2E(B ∂B B∂m bK
(3) B B)m b )0
where m b K is the magnetic moment of the Kth nucleus and m b denote collectively all nuclear moments. The energy functional may be partitioned as
†
Aarhus University. Present address: Department of Chemistry, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 København Ø, Denmark. § University of Oslo. X Abstract published in AdVance ACS Abstracts, December 1, 1996. ‡
S0022-3654(96)01701-7 CCC: $12.00
E(B B,m b ) ) Evac(B B,m b ) + Esolvent(B B)
(4)
The terms arising from the gas phase (vacuum) and solvent parts of the energy functional are discussed elsewhere.7,19-21 © 1996 American Chemical Society
A° strand et al.
19772 J. Phys. Chem., Vol. 100, No. 51, 1996 TABLE 1: Gas Phase Magnetizabilities (in cgs) methoda
CH4
GIAO/6-311+G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3[2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
-19.01 -19.03 -19.05 -18.94 -18.93 -18.94 -18.93
IGLO/HII[5s4p1d/3s1p]b IGLO/HIII[7s6p2d/4s2p]c IGAIM/6-311++G(2d,2p)d
-19.4
experimental experimental
-18.7e -17.4 ( 0.8f
-18.2
CH2F2
CHF3
-19.13 -19.22 -19.22 -19.18 -19.14 -19.15 -19.14
CH3F
-22.85 -22.84 -22.82 -22.81 -22.75 -22.75 -22.73
-28.56 -28.49 -28.47 -28.51 -28.40 -28.36 -28.36
-34.26 -34.11 -34.10 -33.95 -33.97 -33.94
CF4
-19.4 -18.8
-23.1 -22.3
-28.9 -27.8
-34.6 -33.1
-17.7 ( 0.8f
-24g
-30 ( 4g
-36 ( 5g -31.00h
a Hartree-Fock calculations. b See ref 52. c See ref 5. d See ref 53. e See ref 51. f See ref 43. There is a reason to believe that this number should be scaled by a factor of 1.07 due to a calibration error in the experiment.54 The corrected values are -18.6 cgs for the CH4 molecule and -18.9 cgs for the CH3F molecule. g See ref 50. h Quoted in ref 46.
III. Computational Details and Notation The magnetizabilities and shielding constants have been calculated using the DALTON program.22 The 6-311++G(2d,2p) basis set23 has been used in most of the calculations, but an atomic natural orbital (ANO) basis set24 has also been employed. The contraction of the ANO basis sets is denoted as in the following example: ANO[4s3p2d/3s2p], where 4s3p2d indicates the contraction of the carbon and fluorine basis sets and 3s2p denotes the contraction of the hydrogen basis set. The complete active space SCF (CASSCF)25 and restricted active space SCF (RASSCF)26,27 methods are used to calculate effects from electron correlation. The CAS and RAS orbital spaces are denoted according to the number of orbitals belonging to each irreducible representation (irrep) of the largest possible subgroup of the D2h point symmetry group. As an example, for the methane molecule 1000CAS4220 indicates a CASSCF calculation where the inactive space (always doubly occupied) consists of one orbital in the totally symmetric irrep and no orbitals in the other irreps. The active space (all possible distributions) consists of four orbitals in the totally symmetric irrep, two orbitals in each of the irreps that are antisymmetric with respect to one coordinate axes, and no orbitals in the irrep that is antisymmetric with respect to two coordinate axes. An RASSCF calculation is denoted in the same fashion as inactive RAS2 RAS1 RASRAS3 where the inactiVe space is always doubly occupied and the RAS2 space corresponds to the active space in a CASSCF calculation. Single and double excitations are allowed out of the RAS1 space and into the RAS3 space. A calculation of magnetic properties is denoted by the kind of orbitals adopted, the amount of electron correlation included, and the basis set employed (e.g. GIAO/HF/ANO[4s3p2d/3s2p], where GIAO (gauge independent atomic orbital) is the acronym introduced by Ditchfield17 for London atomic orbitals16). IV. Basis Set and Electron Correlation Effects The dependence of magnetic properties on basis set,14,28-30 electron correlation,20,21,31-34 and geometry35 has been studied extensively. The choice of molecular geometry is crucial in order to obtain good agreement with experimental data, which may be realized from the substantial rovibrational contributions to shielding constants. The rovibrational contributions to 13C and 19F shielding constants of the fluoromethanes are in the range 2-8 ppm.36-39 It may therefore be tempting to use experimental geometries to calculate magnetic properties instead of ab initio optimized geometries because large basis sets and a large part of the electron correlation are required for an accurate geometry. Furthermore, part of the zero-point vibra-
tional effects are included implicitly if the calculation is carried out at an averaged geometry, r0.40 This means, however, that it will be difficult to compare magnetic properties calculated at experimental geometries, r0, with experimental data including rovibrational averaging (σ0) or with experimental quantities that are corrected for rovibrational contributions in order to obtain equilibrium properties (σe). Furthermore, optimized geometries have to be used if solvent effects are included since the change in the geometry due to the surrounding medium will affect the solvent contributions to magnetic properties. The ANO basis sets24 are a set of general purpose basis sets that give a good description of the charge distribution and that are successful in reproducing for example electronic spectra.41 It would be interesting to see how the ANO basis sets perform for the magnetic properties of the fluoromethanes since it has been noticed in a previous work that fluorine shieldings are sensitive to the basis set.5 In these studies of the performance of the ANO basis sets we have used experimental geometries (see ref 42 and references therein) and calculated magnetizability and nuclear shielding tensors for a set of balanced contractions of the ANO basis set. A. Magnetizabilities. Both the isotropic magnetizability and its anisotropy (see Tables 1 and 2) are remarkably constant with respect to the basis set and close to experiment43-51 as well as to other theoretical calculations.5,52,53 Even the smallest basis set gives results in good agreement with experiment, and deviations are probably due to the choice of equilibrium geometry, rovibrational effects, and electron correlation. We note that f-functions on carbon and fluorine and d-functions on hydrogen, respectively, are unimportant. These results thus confirm previous findings that results within 2% of the HF limit can be obtained with basis sets of DZP quality30 and that these results are within the error bars of the experiment.54 B. Carbon Shielding Constants. In agreement with experiment,36,55-57 the carbon shielding (Table 3) decreases significantly with the number of fluorine atoms in the molecule. The carbon shieldings are rather insensitive to the basis, although basis set effects increase markedly with an increasing number of fluorine atoms. It is also noticed that the deviation from experiment increases with the number of fluorine atoms also for the largest basis set. Since the basis sets should be close to the basis set limit, this discrepancy must be due to effects such as electron correlation, rovibrational averaging, and the choice of geometry. The corresponding anisotropies are given in Table 4. The basis set effects are smaller than for the isotropic shielding, and the results are close to other calculations.5,14,58 Comparison with experiment59-62 is difficult since the experiments either have
Magnetic Properties of Fluoromethanes
J. Phys. Chem., Vol. 100, No. 51, 1996 19773
TABLE 2: Anisotropya of the Magnetizability in the Gas Phase (in cgs) CH2F2
CH3F ∆ξ
methodb
∆ξ1
CHF3 ∆ξ
∆ξ2
GIAO/6-311++G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2f] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
-7.84 -7.87 -7.86 -7.76 -7.78 -7.77 -7.77
-4.64 -4.53 -4.48 -4.44 -4.40 -4.48 -4.44
IGLO/HIII[7s6p2d/4s2p]c
-7.61
-4.43
0.73
1.46
experimental
-8.2 ( 0.8d -8.5 ( 0.6g
-4.16 ( 0.02e -3.9 ( 0.5h
0.58 ( 0.01e 0.8 ( 0.4h
1.2 ( 0.6f 1.727i
0.58 0.70 0.71 0.52 0.65 0.66 0.70
1.56 1.46 1.44 1.69 1.48 1.49 1.45
a ∆ξ ) ξ - ξ for molecules with axial symmetry. Otherwise ∆ξ ) 2ξ | ⊥ 1 aa - ξbb - ξcc and ∆ξ2 ) 2ξbb - ξaa - ξcc, where ξaa < ξbb < ξcc. Hartree-Fock calculations. c See ref 5. d R. L. Shoemaker, S. G. Kukolich and W. H. Flygare (unpublished results), quoted in ref 45. e See ref 47. f See ref 50. g See ref 48. h See ref 44. i See ref 49, quoted in ref 5. b
TABLE 3:
13C
Nuclear Shielding Constants (in ppm)
methoda
a
CH4
CH3F
GIAO/6-311G++(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
195.1 191.0 191.4 194.2 193.5 193.5 193.6
125.1 124.0 123.5 123.0 122.3 122.0 122.0
GIAO/6-311G+(2d,2p)b IGLO/HIII[7s6p2d/4s2p]c LORG/6-311G(d,p)d IGAIM/6-311++G(2d,2p)e
196
126.2 122.1 132 130.2
experimental, σ0(300 K) experimental, σe
194.8 ( 198.1 ( 0.9i
197 197.4 0.9f
116.4 (
CH2F2
CHF3
CF4
93.5 93.0 92.6 90.9 90.5 89.5 89.6
86.7 87.7 88.1 84.4 84.5 82.6 82.6
82.8 86.1 86.4 81.9 81.8 79.1
89.1
81.2
76.5 86.0
77.2 (
0.9g
68.1 (
0.9h
0.9i
64.1 ( 0.9i
Hartree-Fock calculations. b See ref 14. c See ref 5. d See ref 58. e See ref 53. f See ref 57. g See ref 56, 57. h See refs 55, 57. i See refs 36, 57.
TABLE 4: Anisotropya of the 13C Shielding Constant (in ppm) methodb
CH3F ∆σ
GIAO/6-311+G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
90.9 92.9 92.0 92.9 92.3 92.2 92.1
GIAO/6-311G+(2d,2p)c IGLO/HIII[7s6p2d/4s2p]d LORG/4-31Ge LORG/6-311G(d,p)e
91 92.4 77 85
experimentalf experimental, argon matrixg experimental, liquid crystalh experimental, liquid crystali
68 ( 30 90 ( 20 87.4 ( 3.5 113.5 ( 0.7
CH2F2
CHF3 ∆σ
∆σ1
∆σ2
-32.08 -31.78 -28.43 -32.15 -31.26 -31.83 -33.04
-19.24 -22.78 -23.09 -19.89 -20.77 -21.67 -20.93
-11.20 -10.94 -10.94 -10.21 -11.68 -11.39 -11.97
-36.4
-18.4
-13.0 -10
-60.4 ( 0.7
∆σ ) σ| - σ⊥ if there is an axial symmetry. Otherwise, ∆σ1 ) 2σaa - σbb - σcc and ∆σ2 ) 2σbb - σaa - σcc, where σaa < σbb < σcc and a, b, and c denote principal axis. b Hartree-Fock calculations. c See ref 14. d See ref 5. e See ref 58. f See ref 59. g See ref 60. h See ref 61. i See ref 62. a
large error bars or have been carried out within a liquid crystal, whichsas seen from the different results obtained for different liquid crystalssare expected to give large solvent effects. C. Fluorine Shielding Constants. As for the carbon shielding, the fluorine shielding decreases with the number of fluorine atoms. The basis set effects are stronger than for the carbon shielding, and it is difficult to see any trends in the fluorine shielding constants (Table 5). Thus the changes in the fluorine shielding when increasing the basis set are significant also for the largest basis set, and even larger basis sets may be required to reach the basis set limit. Our calculated values compare well with other calculations,5,14,58 but they are all 1020 ppm higher than experiment.3,38,39,63,64
The anisotropy of the fluorine shielding is presented in Table 6. As for the isotropic shielding, the basis set effects are larger than for ∆σC and it is difficult to see any trends with respect to increasing size of the basis set. As for the anisotropy of the carbon shielding, comparison with experiment47,59,61,65-67 is difficult since they differ from each other and have rather large error bars. Especially the second anisotropy of the CH2F2 molecule differs substantially from experiment.47 D. Hydrogen Shielding Constants. The proton shieldings are relatively insensitive to the size of the basis set (Table 7). The deviations from experiment68,69 are probably due to other effects such as rovibrational effects and the choice of the geometries. The anisotropies of the proton shielding constants
A° strand et al.
19774 J. Phys. Chem., Vol. 100, No. 51, 1996 TABLE 5:
19F
Shielding Constant in the Gas Phase (in ppm) methoda
j
CH3F
CH2F2
CHF3
CF4
GIAO/6-311++G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
480.6 477.6 480.0 486.8 485.6 482.2 482.0
363.2 359.5 362.5 369.2 365.6 363.3 363.7
301.4 297.9 301.3 304.5 303.2 300.8 302.0
278.1 273.6 277.8 282.1 281.0 278.0
GIAO/6-311G+(2d,2p)b IGLO/HIII[7s6p2d/4s2p]c LORG/6-311G(d,p)d
483 474 454
356
295
271
experimental, σ0(300 K) experimental, σe
471.0 ( 6e 473.1 ( 6h
339.1 ( 6f 343.9 ( 6i
274.1 ( 6g 282.4 ( 6j
259.0 ( 6g 266.2 ( 6k
a Hartree-Fock calculations. b See ref 14. c See ref 5. d See ref 58. e See ref 3. f See ref 64. g See refs 3, 63. h See refs 3, 38. i See refs 38, 64. See refs 3, 38, 63. k See refs 3, 39, 63.
TABLE 6: Anisotropya of the 19F Shielding Constant (in ppm) CH2F2
CH3F ∆σ
methodb
∆σ1
GIAO/6-311++G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
-67.8 -72.8 -78.0 -60.2 -59.8 -68.5 -69.6
-350.8 -348.2 -343.0 -360.5 -362.7 -357.1 -354.0
GIAO/6-311G+(2d,2p)c IGLO/HIII[7s6p2d/4s2p]d LORG/4-31Ge
-67 -66 30
-376
-90 ( 4f -159.3 ( 0.7 -66 ( 8h
experimental, liquid crystal experimental, liquid crystalg experimental, clathrate experimentalj experimentalk experimentalk experimentalk
CHF3 ∆σ2
∆σ1
98.5 101.3 105.8 97.9 97.6 99.7 101.1
-258.1 -262.1 -256.4 -264.0 -265.0 -263.0 -259.3
78
-267.0
∆σ2 67.9 68.9 62.8 66.9 69.7 69.9 67.7
CF4 ∆σ 158.3 163.3 156.9 158.5 159.9 161.0
165
-35 ( 20i -335 ( 35
9 ( 13
-80 ( 3i -83.2 -80.2 ( 2.0 -94.9 ( 2.9
∆σ ) σ| - σ⊥ if there is an axial symmetry. Otherwise, ∆σ1 ) 2σcc - σaa - σbb and ∆σ2 ) σaa - σbb, where σaa > σbb > σcc and a, b, and c denote principal axis. b Hartree-Fock calculations. c See ref 14. d See ref 5. e See ref 58. f See ref 61. g See ref 66. h See ref 65. i See ref 50, defined as σ| - σ⊥. j See ref 50. k See ref 67, defined as σ| - σ⊥. a
TABLE 7:
1H
Shielding Constants (in ppm)
methoda
CH4
CH3F CH2F2 CHF3
GIAO/6-311++G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d]
31.71 31.51 31.47 31.47 31.40 31.47 31.41
experimental, σ(0)
30.611 ( 0.024b 26.6c
a
27.79 27.61 27.54 27.53 27.51 27.57 27.52
26.89 26.70 26.59 26.57 26.56 26.62 26.58
26.19 26.01 25.81 25.80 25.76 25.86 25.80
Hartree-Fock calculations. b See ref 69. c See refs 68, 69.
in Table 8 are also rather insensitive to variations in the basis set, except for the second anisotropy of the CH3F molecule. As for the anisotropy of the other nuclei, comparison with experiment61,66,67 is difficult. E. Correlation Effects. Correlation effects on the fluorine shieldings have been regarded as unimportant since the values calculated at the Hartree-Fock level with an experimental geometry are slightly higher than experiment and electron correlation is expected to increase the shielding constant.5 Nonetheless, in this work we use the GIAO-MCSCF approach20 for calculations of shielding constants in methane and the fluoromethanes. Here, we have also used experimental geometries. Nuclear shielding constants for methane have previously been calculated at the MCSCF level,20,70 at the MP2 level,32 and recently at the CCSD(T) level.71 The results presented in Table
9 are in agreement with previous calculations and also with experiment.36,57,69 Note that the correlation effect on the carbon shielding of methane is about 4 ppm, and our final value is within the experimental error bars.36,57 The correlation effects on the proton shielding constants are, on the other hand, negligible. It is noted from Table 10 that a RAS calculation on the CH3F molecule including all valence electrons give similar results as the Hartree-Fock calculation. The inclusion of the fluorine 2s electrons in the correlation treatment is essential for an adequate description of the fluorine shielding. It is also noted that an MP2 calculation32 gives a similar result for the carbon shielding of the CH3F molecule. Further investigations are required to determine whether the difference from experiment (Table 10) is due to correlation, geometry, or rovibrational effects. Calculations on the CH2F2 molecule (Table 11) also indicate that correlation effects cannot account for the difference between calculated values and experimental data for the fluorine shieldings. The discrepancies between our calculated values and the experiments38,55,57,64 are about 14 ppm for the carbon shielding and about 17 ppm for the rovibrationally corrected fluorine shielding. From this work it is hard to believe that the differences are due to basis set or electron correlation effects. The discrepancies therefore arise either because the rovibrational effects are larger than obtained in the experiment or because of the choice of geometry.
Magnetic Properties of Fluoromethanes
J. Phys. Chem., Vol. 100, No. 51, 1996 19775
TABLE 8: Anisotropya of 1H Shielding Constants (in ppm) CH4 ∆σ
methodb GIAO/6-311++G(2d,2p) GIAO/ANO[4s3p2d/3s2p] GIAO/ANO[4s3p2d1f/3s2p1d] GIAO/ANO[5s4p3d/4s3p] GIAO/ANO[5s4p3d2f/4s3p2d] GIAO/ANO[6s5p4d/5s4p] GIAO/ANO[6s5p4d3f/5s4p3d] experimental(1c)c experimental(1c)d experimental(1c)e experimental(1c)f
9.62 9.75 9.70 9.90 9.87 9.86 9.85
CH3F
CH2F2
∆σ1
∆σ2
∆σ1
∆σ2
-8.77 -8.82 -8.55 -8.92 -8.58 -8.75 -8.55 -12.9 ( 1.3 -0.6 ( 0.5 5.2 ( 0.2 -6.1
-4.80 -4.68 -5.17 -4.74 -3.48 -4.85 -5.10
-10.92 -11.11 -11.02 -11.19 -10.98 -11.04 -10.97
0.090 0.176 0.107 0.071 0.053 0.095 0.130
CHF3 ∆σ 7.20 7.35 7.20 7.41 7.20 7.27 7.14
9.8 ( 0.5
∆σ ) σ| - σ⊥, ∆σ1 ) 2σaa - σbb - σcc, ∆σ2 ) 2σbb - σaa - σcc, where σaa < σbb < σcc. b Hartree-Fock calculations. c See ref 66. TMS is used as an internal reference. d See ref 66. CH4 is used as an internal reference. e See ref 61. f See ref 67. a
TABLE 9: Electron Correlation Effects on Nuclear Shielding Constants of CH4 (in ppm) σC
method
a
σH
∆σH
GIAO/HF/ANO[6s5p4d/5s4p] GIAO/1000CAS4220/ANO[6s5p4d/5s4p] GIAO/1000CAS6331/ANO[6s5p4d/5s4p] GIAO/1000RAS4220 5442/ANO[6s5p4d/5s4p] GIAO/1000RAS4220 8553/ANO[6s5p4d/5s4p]
193.5 198.0 200.6 197.4 197.3
31.47 31.37 31.29 31.35 31.37
9.86 9.81 10.28 9.87 9.90
IGLO/1000CAS4220/HIV[8s7p3d1f/5s3p1d]b GIAO/1000CAS4220/HIV[8s7p3d1f/5s3p1d]c GIAO/10CAS83/HIV[8s7p3d1f/5s3p1d]c GIAO/MP2/QZ2Pd GIAO/CCSD/[pz3d2f/pz3p]e GIAO/CCSD(T)/[pz3d2f/pz3p]e
198.39 198.1 198.2 201.5 198.7 198.9
31.13 31.28 31.26
experimental, σ0 (300 K) experimental, σe
194.8 ( 0.9f 198.1 ( 0.9f
30.611 ( 0.024g
31.5 31.6
∆σ ) σ| - σ⊥. b See ref 70. Quoted in ref 20. c See ref 20. d See ref 32. e See ref 71. f See refs 36, 57. g See ref 69.
TABLE 10: Electron Correlation Effects on Nuclear Shielding Constantsa (in ppm) and the Dipole Moment (in Debye) of the CH3F Molecule method
σC
∆σC
σF
∆σF
µ
HF/ANO[4s3p2d/3s2p] 30 CAS84/ANO[4s3p2d/3s2p] 30 42 21RAS21/ANO[4s3p2d/3s2p] 20 42 31RAS31/ANO[4s3p2d/3s2p]
124.0 127.0 126.9 123.7
92.9 90.3 90.4 95.3
477.6 522.8 522.3 478.2
-72.8 -144.9 -144.1 -76.5
2.04 1.83 1.83 1.94
31 42 20RAS31ANO[6s5p4d/5s4p] MP2/QZ2Pb
123.3
97.4
481.8
-72.0
1.92
experimental, σ0(300 K) experimental, σe experimental experimental experimental experimental
121.8 116.4 ( 0.9c 68 ( 30f 90 ( 20h 87.4 ( 3.5g 113.5 ( 0.7k
471.0 ( 6d 473.1 ( 6e
-90 ( 4g -159.2 ( 0.6i -66 ( 8j
a ∆σ ) σ - σ . b See ref 32. c See refs 56, 57. d See ref 3. e See refs 3, 38. f See ref 59. g See ref 61. h See ref 60. i See ref 66. j See ref 65. k See | ⊥ ref 62.
V. Magnetic Properties in a Dielectric Medium We have calculated the effects of a dielectric medium on magnetizabilities and nuclear shielding constants of the fluoromethanes at the Hartree-Fock level. Methane has been studied in a previous work using the same approach.7 The dielectric constants for the following solvents have been used: 1,4-dioxane ( ) 2.209), ethyl acetate ( ) 6.02), 1-hexanol ( ) 13.3), acetone ( ) 20.7), methanol ( ) 32.63), and water ( ) 78.54). A spherical cavity with a radius of 5.08 a0 is used for all molecules. This radius corresponds to the CF bond distance plus the van der Waals radius of the fluorine atom, which is 1.35 Å.72 The dependence of the results with respect to the cavity radius has been investigated in detail elsewhere.7 Molecular dipole moments calculated at the Hartree-Fock level with an accurate basis set are normally 10-15% too high
compared to experiments (see, for example, refs 73, 74), which is also noted in Tables 10 and 11. The interaction with the medium will therefore be slightly overestimated, but will not change the general trends. Consequently, we shall focus more on the trends than on the individual numbers. A. The CH3F Molecule. The dependence of the geometry and the dipole moment on the order of the multipole expansion of the charge distribution, lmax, has been investigated for the CH3F molecule. The effects are small, and the lmax g 6 no further change is noticed. For the magnetizability, the solvent effect is positive for lmax e 2 but then becomes negative. The shielding constants as well as the magnetizability are converged with respect to lmax for lmax g 6. Because of changes in the paramagnetic term, the effects on the fluorine shielding is twice as big for lmax g 6 than for the dipole approximation, i.e. lmax
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19776 J. Phys. Chem., Vol. 100, No. 51, 1996
TABLE 11: Electron Correlation Effects on Nuclear Shielding Constantsa (in ppm) and Dipole Moment (in Debye) of the CH2F2 Molecule σC
method GIAO/HF/ANO[4s3p2d/3s2p] GIAO/4210CAS4422/ANO[4s3p2d/3s2p] 2200 GIAO/4210 1111RAS1111/ANO[4s3p2d/3s2p] 2100 GIAO/3221RAS2200 1111/ANO[4s3p2d/3s2p] 2200 RAS GIAO/2100 3221 3232/ANO[4s3p2d/3s2p] 2100 GIAO/3221RAS2200 5332/ANO[4s3p2d/3s2p]
93.0 92.0 92.3 90.9 91.4 91.0
experimental, σ0(300 K) experimental σe
77.2 ( 0.9b
∆σC1
∆σC2
-31.78 -45.68 -45.71 -45.29 -47.32 -47.93
-22.78 -13.64 -13.69 -14.73 -15.58 -14.87
σF
∆σF1
359.5 359.0 359.5 358.9 361.0 359.6
-348.2 -320.4 -319.5 -319.0 -319.2 -326.6
339.1 ( 6c 343.9 ( 6d
-335 ( 3.5e
∆σF3 101.3 108.13 106.89 108.41 103.03 103.18
µ 2.21 2.01 2.02 1.99 2.06 2.06
9 ( 13e
a ∆σ ) σ - σ , ∆σ ) 2σ - σ - σ , ∆σ ) 2σ - σ - σ , ∆σ ) σ - σ , where σ > σ > σ . b See refs 55, 57. c See ref 64. d See | ⊥ 1 cc bb aa 2 bb cc aa 3 aa bb aa bb cc refs 38, 64. e See ref 47.
) 1. The 13C and 1H shieldings change little with increasing lmax. We have chosen to use lmax ) 10 in the remaining calculations since the extra computational effort is negligible. One should keep in mind that the diamagnetic and paramagnetic contributions depend separately on the gauge origin, here chosen to be the center of mass, which affects the comparison of the absolute values of the paramagnetic and diamagnetic contributions. In principle, the gauge dependence also affects the comparison of the paramagnetic and diamagnetic contributions at different dielectric constants, but this effect is expected to be small. A test calculation on the CH3F molecule where the gauge origin is moved 0.01 a0 from the center of mass toward the carbon atom shows effects that are about 0.15 ppm for the carbon and proton paramagnetic shieldings and about 0.05 ppm for the fluorine paramagnetic shielding. A surrounding medium affects a molecule mainly in two ways: it polarizes the electronic charge distribution and it alters the geometry of the molecule. For the CH3F molecule, we have carried out two sets of calculations, one set with the geometry optimized for each dielectric constant and one set where the gas phase geometry has been employed for all dielectric constants. We thus study both the polarization and the geometry effects in the first set and only the polarization effect in the second set. If the geometry is optimized for each dielectric constant (see Figure 1 and Table 12), the solvent effect on the magnetizability (Figure 1a) is rather small since the changes in the diamagnetic and paramagnetic contributions tend to cancel. The effect on the anisotropy of the magnetizability is, however, around 20% for the highest dielectric constant. The dielectric effects are approximately 2 ppm for the isotropic shielding constants (Figure 1b,d): the carbon shielding is lowered by about 2 ppm and the fluorine shielding is increased by the same amount. Note that the diamagnetic and paramagnetic contributions change in the same direction. The anisotropies of the 13C and 19F shielding constants (Figure 1c,e) increase about 5 ppm, and here it is mainly the paramagnetic term that is altered. The effects on the proton shieldings are much smaller (Figure 1f), and the paramagnetic and diamagnetic contributions shift in different directions. The total shielding is gauge-invariant if the GIAO method is employed, but the different contributions are not. To test the gauge-origin dependence of the paramagnetic and diamagnetic terms, we have carried out a set of calculations where the gauge origin is placed at the fluorine atom (Figure 2). In contrast to the calculations with the gauge origin at the center of mass (Figure 1), the magnitudes of the individual contributions change markedly. It is therefore not possible to discuss the magnitude of the different contributions. Nonetheless, since the solvent effects on the paramagnetic and diamagnetic contributions correspond to different kinds of changes in the charge distribu-
tion, it will be interesting to investigate whether the paramagnetic and diamagnetic terms increase or decrease compared to the gas phase value. In the second set of calculations (Figure 3) we have used the optimized gas phase geometry. Note that the dielectric contribution to the isotropic part of the magnetizability (Figures 1a and 3a) changes sign compared to the first set and so do both the paramagnetic and diamagnetic contributions. On the other hand, the change of the anisotropy of the magnetizability is mainly a polarization effect. For the isotropic carbon and fluorine shieldings, the geometry distortions lower the shielding constants. Consequently, the polarization and the geometry terms add up for the carbon shielding, whereas they change in different directions for the fluorine shielding. For the anisotropies, it is noted that whereas the shift of ∆σC (Figures 1c and 3c) is mainly a polarization effect, the shift of ∆σF (Figures 1e and 3e) is mainly due to the distortion of the geometry. This is expected since the relative distance to the medium decreases much more for the fluorine atom than for the carbon atom when the C-F bond is stretched. From Figures 1f and 3f it is concluded that the shift of the proton shielding constant arising from a dielectric medium is mainly a polarization effect. In Table 12 it is observed that the only significant distortion of the geometry when the solvent becomes more polar is that the C-F bond length increases. This is expected since this is the most efficient way of increasing the dipole moment of the CH3F molecule. B. The CH2F2 Molecule. Results for the CH2F2 molecule are presented in Table 13 and Figure 4. As for CH3F (Table 12), it is mainly the C-F bonds that become longer when the dielectric constant is increased. One might expect that also the FCF angle would become smaller in order to increase the dipole moment further. However, this does not happen since the higher order terms, such as the quadrupole moment, oppose such a change. The magnetic properties of CH2F2 in Figure 4 show the same trends as for CH3F in Figure 1. The solvent shifts on the magnetizabilities of the CH2F2 molecule are slightly larger than for CH3F (Figures 1a and 4a), whereas the solvent shifts of the shieldings behave in the same way as for the CH3F molecule. For the carbon shielding (Figure 4b), both the paramagnetic and the diamagnetic contributions decrease with increasing dielectric constant, and for the fluorine shielding (Figure 4c) both contributions increase with the dielectric constant. For the proton shielding (Figure 4d), the paramagnetic contribution increases and the diamagnetic contribution decreases with the dielectric constant. The dielectric effects on the anisotropies of the 13C and 19F nuclear shielding constants are between 5 and 10 ppm except for the second anisotropy of the fluorine shielding, which is almost unaffected. The first anisotropy of the carbon shielding increases, whereas the second anisotropy
Magnetic Properties of Fluoromethanes
J. Phys. Chem., Vol. 100, No. 51, 1996 19777
Figure 1. Magnetic properties of the CH3F molecule as a function of the dielectric constant. Rcav ) 5.08 au, lmax ) 10. The geometry is optimized. The difference with respect to the gas phase value is given. The gas phase values are given in parentheses. (a) Magnetizability (ξ ) -18.986 cgs, ξd ) -58.200 cgs, ξp ) 39.214 cgs, ∆ξ ) -7.828 cgs), (b) 13C shielding constant (σC ) 129.57 ppm, σCd ) 320.37 ppm, σCp ) -190.80 ppm), (c) anisotropy of the 13C shielding constant (∆σC ) 90.88 ppm, ∆σCd ) -20.67 ppm, ∆σCp ) 111.57 ppm), (d) 19F shielding constant (σF ) 487.91 ppm, σFd ) 508.77 ppm, σFp ) -20.86 ppm), (e) anisotropy of the 19F shielding constant (∆σF ) -78.69 ppm, ∆σFd ) -37.03 ppm, ∆σFp ) -41.66 ppm), (f) 1H shielding constant (σH ) 28.365 ppm, σHd ) 26.773 ppm, σHp ) 1.592 ppm).
TABLE 12: Optimized Geometries of CH3F as a Function of the Dielectric Constanta b
EHF/au
µ/D
1 2.209 13.3 32.63 78.54
-139.086 486 -139.087 724 -139.089 141 -139.089 361 -139.089 454
2.023 2.158 2.312 2.336 2.346
a
rCF/Å rCH/Å ∠HCF/deg ∠HCH/deg 1.364 1.368 1.374 1.375 1.375
1.081 1.081 1.081 1.080 1.080
108.7 108.7 108.6 108.5 108.5
110.2 110.3 110.4 110.4 110.4
GIAO/HF/6-311++G(2d,2p) b Rcav ) 5.08 au, lmax ) 10.
decreases, and the first anisotropy of the fluorine shielding decreases with increasing dielectric constant. C. The CHF3 Molecule. For the CHF3 molecule (Table 14 and Figure 5), the stretching of the C-F bond is only half
as large as for the CH3F and CH2F2 molecules. On the other hand, small effects on the FCF angle are noticed that did not appear for the CH3F and CH2F2 molecules. The isotropic magnetizability (Figure 5a) exhibits similar trends as for the previous molecules. In contrast, the anisotropy behaves differently since the magnetizability tensor is rod-shaped in CH3F, but disk-shaped in CHF3. For the carbon shielding (Figure 5b), the effects from the dielectric medium are smaller for the CHF3 molecule than for CH3F and CH2F2. For the fluorine shielding, the same trend as for the CH3F and CH2F2 molecules is observed (see Figure 5c), although the dielectric effect is smaller. As for the other molecules, it is noted that the solvent effects are larger for the anisotropy than for the corresponding isotropic
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19778 J. Phys. Chem., Vol. 100, No. 51, 1996 TABLE 13: Optimized Geometries of CH2F2 as a Function of the Dielectric Constanta
a
b
E/au
µ/D
rCF/Å
rCH/Å
∠FCF/deg
∠FCH/deg
∠HCH/deg
1 6.02 20.7 32.63 78.54
-237.979 951 -237.983 661 -237.984 590 -237.984 745 -237.984 906
2.151 2.465 2.544 2.557 2.571
1.334 1.340 1.342 1.342 1.343
1.079 1.078 1.078 1.078 1.078
107.2 107.5 107.3 107.3 107.3
108.9 109.0 109.0 109.0 109.0
113.8 113.3 113.4 113.4 113.4
GIAO/HF/6-311++G(2d,2p). b Rcav ) 5.08 au, lmax ) 10.
D. The CF4 Molecule. Due to the absence of molecular dipole and quadrupole moments in CF4, the dielectric effects are much smaller for this molecule than for the other molecules in this study. The effects are therefore about 1 order of magnitude smaller than for the other fluoromethanes. VI. Discussion
Figure 2. Magnetic properties of the CH3F molecule as a function of the dielectric constant. Rcav ) 5.08 au, lmax ) 10. The geometry is optimized. The gauge origin is placed at the fluorine atom. (a) 13C shielding constant, (b) 19F shielding constant, (c) 1H shielding constant.
part. The anisotropy of the carbon shielding increases, whereas both anisotropies of the fluorine shielding decrease with increasing dielectric constant. The trend is clear for the proton shielding constant (see Figure 5d). The diamagnetic and paramagnetic contributions more or less cancel each other even though the dielectric effect on the proton shielding constant of the CHF3 molecule is slightly larger than on the other two molecules.
Some trends are clear from these calculations of magnetic properties of molecules embedded in a dielectric medium. The magnetizability is lower (more diamagnetic) in solution than in the gas phase both for the molecules included here and for the molecules (H2O, H2S, CH4, and HCN) studied in our previous work.7 It is interesting to note that in a recent work by Rizzo et al.75 all components of the hypermagnetizability of the HCN molecule are positive, whereas the change of the magnetizability is negative when the HCN molecule is put into a dielectric medium.7 This apparent discrepancy may be understood if we keep in mind that the potential surface is also perturbed by an electric field,76 as is illustrated by the calculations on the CH3F molecule. Thus, the magnetizability of the CH3F molecule decreases as a function of the dielectric constant if the geometry of the molecule is optimized for each dielectric constant, but it increases if the geometry is fixed. Consequently, rovibrational effects are important for a complete description of the gas-to-liquid shift of the magnetizability. The analysis is more complex for the behavior of the nuclear shielding. The 13C nuclear shielding constants become smaller and the 19F nuclear shielding constants become larger for all the fluoromethanes as the dielectric constant of the solvent is increased. For the polar molecules (CH3F, CH2F2, and CHF3), this behavior is understood from the observation that the charge distribution of the molecules is polarized in such a way that the molecular dipole moment is increased. Consequently, the charge density is shifted away from the carbon atom close to the center of the molecule toward the fluorine atoms. As a result, the diamagnetic contribution to the fluorine shielding is increased and the diamagnetic contribution to the carbon shielding is decreased. Analogously, the dielectric distortion of the geometry of the molecules lowers the shielding of all atoms. For the paramagnetic contribution, the changes may be rationalized from the observation that the paramagnetic contribution is zero for a closed-shell atom. For the fluoromethanes, the charge distribution is polarized in such a way that the fluorine atom becomes more like a closed-shell atom and the paramagnetic term is reduced. In contrast, the carbon atom becomes less like a closed-shell atom and the paramagnetic contribution is increased (the shielding is decreased). The increased anisotropies of the shielding constants in the dielectric medium are easily understood since the polarization in the medium makes the charge distribution more anisotropic. The unpolar methane molecule behaves differently from the fluoromethanes; the carbon shielding of methane increases as the dielectric constant becomes larger.7 Due to the symmetry of the CH4 and CF4 molecules, it is the molecular octopole moment that governs the response to the surrounding medium. As a consequence of the very different charge distributions of the CH4 and CF4 molecules, the 13C nuclear shielding constants
Magnetic Properties of Fluoromethanes
J. Phys. Chem., Vol. 100, No. 51, 1996 19779
Figure 3. Magnetic properties of the CH3F molecule as a function of the dielectric constant. Rcav ) 5.08 au, lmax ) 10. The gas phase geometry is employed. The difference with respect to the gas phase value is given. The gas phase values are given in Figure 1. (a) Magnetizability, (b) 13C shielding constant, (c) anisotropy of the 13C shielding constant, (d) 19F shielding constant, (e) anisotropy of the 19F shielding constant, (f) 1H shielding constant.
shift in different directions. This is realized by representing the charge distribution of the molecules with atomic dipole moments,77 since the hydrogen dipole moment of methane and the fluorine dipole moment of the CF4 molecule have different signs. The proton shielding constants all become smaller, which is in line with the model presented by Buckingham.8 It is, however, important to keep in mind that if we would like to compare with experimental gas-to-liquid chemical shifts, the remaining terms in eq 1 must also be considered. The importance of these terms becomes obvious when our calculated shifts are compared to the experimental fluorine shifts (δF ) F F - σgas ) of the CH3F and CHF3 molecules,3,78 which are σsolvent both negative (-7.7 ppm for CH3F and -3.2 ppm for CHF3), whereas our estimates of σE are about +2 ppm for both molecules.
The effect from the bulk magnetizability, σb, is approximately -2 to -4 ppm. This term is often included in experimental gas-to-liquid shifts,6 but for the molecules considered here it is not stated whether the term is included or not.3,78 The van der Waals term, σw, normally gives a negative contribution.6 If the van der Waals forces are regarded as being equivalent to a mean square electric field, E2, then the van der Waals contribution to the shielding may be written as79
σw ) -B〈E2〉
(5)
where B in general is a tensor and has been calculated for the CH3F molecule by Packer and Raynes,80 where they found that both B| and B⊥ are positive. σw has been calculated for neon
A° strand et al.
19780 J. Phys. Chem., Vol. 100, No. 51, 1996
Figure 4. Magnetic properties of the CH2F2 molecule as a function of the dielectric constant. Rcav ) 5.08 au, lmax ) 10. The geometry is optimized. The difference with respect to the gas phase value is given. The gas phase values are given in parentheses. (a) Magnetizability (ξ ) -22.67 cgs, ξd ) -104.79 cgs, ξp ) 82.13 cgs, ∆ξ1 ) -4.373 cgs, ∆ξ2 ) 0.708 cgs), (b) 13C shielding constant (σC ) 98.14 ppm, σCd ) 366.65 ppm, σCp ) -268.52 ppm), (c) 19F shielding constant (σF ) 370.56 ppm, σFd ) 520.44 ppm, σFp ) -149.88 ppm), (d) 1H shielding constant (σH ) 27.371 ppm, σHd ) 40.235 ppm, σHp ) -12.864 ppm).
in different solvents to be in the range -12 to -24 ppm,81 which means that σb + σw + σE most probably will become negative. As discused elsewhere, the contribution from the anisotropy of the magnetizability tensor of the neighboring molecules, σa, will be positive if the magnetizability tensor of the solvent molecules is disk-shaped and negative if it is rod-shaped.6 In our cases σa will give a positive contribution to σsolvent for the CHF3 molecule and a negative contribution to σsolvent for the CH3F molecule. This effect is enhanced for a disk-shaped solute in a disk-shaped solvent and for a rod-shaped solute in a rodshaped solvent, respectively.6 The σa term may be estimated from the approximate formulas by Buckingham et al.,6 which for a disk-shaped solvent is given by
σa )
-2n∆ξ 3R3
(6)
and for a rod-shaped solvent by
σa )
n∆ξ 3R3
(7)
where n is the number of molecules in a relevant range of R. An upper estimate of σa (for example n ) 4 and R ) 3 Å) would give contributions that are less than 0.5 ppm, which means that this term can hardly explain the difference between experiment and theory. We thus conclude that an accurate description of the van der Waals term in addition to the electrostatic term may model the experimental gas-to-liquid shifts for the fluoromethanes. However, the van der Waals term
TABLE 14: Optimized Geometries of the CHF3 Molecule as a Function of the Dielectric Constanta b
E/au
µ/D
1 6.02 20.7 32.63 78.54
-336.883 261 -336.886 286 -336.887 049 -336.887 176 -336.887 309
1.791 2.062 2.129 2.140 2.152
a
rCF/Å rCH/Å ∠FCF/deg ∠FCH/deg 1.311 1.314 1.315 1.315 1.315
1.076 1.076 1.076 1.076 1.076
108.4 108.0 107.9 107.9 107.9
110.9 111.0 111.0 111.0
GIAO/HF/6-311++G(2d,2p) b Rcav ) 5.08 au, lmax ) 10.
must be investigated in more detail before any definitive conclusions can be drawn, which is most conveniently carried out by means of molecular dynamics simulations.81 The conclusion by Chesnut and Rusiloski that a dielectric medium fails to reproduce the solvent effects of nuclear shielding constants4 does not seem to be correct since these authors compare their calculated σE with the total solvent effect. Nonetheless, strong direct interactions may affect a nuclear shielding constant in such a way that a continuum model would be too crude, but this is also true for any other molecular property. An example of this is the hyperpolarizability82 or the shielding and magnetizability83 of the water molecule. VII. Conclusions and Summary We have presented an investigation of the magnetizabilities and nuclear shielding constants of the fluoromethanes in gas phase and solution. Discrepancies between the calculated gas phase fluorine shieldings and experiments still persist. As discussed elsewhere,5 the discrepancies are probably not due to either incomplete basis sets or electron correlation and the
Magnetic Properties of Fluoromethanes
J. Phys. Chem., Vol. 100, No. 51, 1996 19781
Figure 5. Magnetic properties of the CHF3 molecule as a function of the dielectric constant. Rcav ) 5.08 au, lmax ) 10. The geometry is optimized. The difference with respect to the gas phase value is given. The gas phase values are given in parentheses. (a) Magnetizability (ξ ) -28.41 cgs, ξd ) -154.29 cgs, ξp ) 125.88 cgs, ∆ξ 1.551 cgs), (b) 13C shielding constant (σC ) 91.40 ppm, σCd ) 422.50 ppm, σCp ) -331.09 ppm), (c) 19F shielding constant (σF ) 309.76 ppm, σFd ) 535.28 ppm, σFp ) -225.52 ppm), (d) 1H shielding constant (σH ) 26.836 ppm, σHd ) 55.130 ppm, σHp ) -28.294 ppm).
experimental rovibrational contributions38,39 are not that large. However, the accuracy of the geometries adopted still remains to be investigated. The effets of a dielectric medium on magnetic properties have been calculated and discussed. It is shown that the multipole expansion of the charge distribution may be truncated at lmax ) 6 without loss of accuracy. The dipole approximation, lmax ) 1, gives in some cases qualitatively different results as compared to lmax g 6. The solvent shift of the magnetizability is negative (diamagnetic) in all cases studied here and elsewhere.7 Furthermore, we find that the solvent shift of the carbon shielding is negative, whereas the corresponding fluorine shift is positive, and that the effects on the proton shielding are small. To explain the experimental gas-to-liquid chemical shifts, van der Waals effects have to be included. The effects from a dielectric medium may be partitioned into a pure polarization term, which in a firstorder approximation may be described with a hypermagnetizability and a geometry distortion term. How these two terms alter the shielding constants may be explained by simple arguments that are based on how the charge distribution is affected. It is demonstrated that it is crucial to optimize the geometry for each dielectric constant, since both the isotropic magnetizability and the anisotropic part of the fluorine shielding of the CH3F molecule change sign as compared to the change observed if a fixed geometry is employed. References and Notes (1) Nuclear magnetic shieldings and molecular structure; Tossell, J. A., Ed.; NATO ASI Series C; Kluwer: Dordrecht, 1993; Vol. 386. (2) Jameson, C. J. Chem. ReV. 1991, 91, 1375.
(3) Jameson, C. J.; Jameson, A. K.; Burrell, P. M. J. Chem. Phys. 1980, 73, 6013. (4) Chesnut, D. B.; Rusiloski, B. E. J. Mol. Struct. 1994, 314, 19. (5) Fleischer, U.; Schindler, M. Chem. Phys. 1988, 120, 103. (6) Buckingham, A. D.; Schaefer, T.; Schneider, W. G. J. Chem. Phys. 1960, 32, 1227. (7) Mikkelsen, K. V.; Jørgensen, P.; Ruud, K.; Helgaker, T. J. Chem. Phys., accepted. (8) Buckingham, A. D. Can. J. Chem. 1960, 38, 300. (9) Mikkelsen, K. V.; Dalgaard, E.; Swanstrøm, P. J. Phys. Chem. 1987, 91, 3081. (10) Mikkelsen, K. V.; A° gren, H.; Jensen, H. J. A.; Helgaker, T. J. Chem. Phys. 1988, 89, 3086. (11) Mikkelsen, K. V.; Ratner, M. A. J. Phys. Chem. 1989, 93, 1759. (12) Mikkelsen, K. V.; Ratner, M. A. J. Chem. Phys. 1989, 90, 4327. (13) Mikkelsen, K. V. Z. Phys. Chem. 1991, 170, 129. (14) Wolinski, K.; Hinton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (15) Helgaker, T.; Jørgensen, P. J. Chem. Phys. 1991, 95, 2595. (16) London, F. J. Phys. Radium 1937, 8, 397. (17) Ditchfield, R.; Ellis, P. D. In Topics in carbon-13 NMR; Levy, G. C., Ed.; Wiley: New York, 1974; Vol. 1, p 1. (18) Ramsey, N. F. Phys. ReV. 1950, 78, 699. (19) Ruud, K.; Helgaker, T.; Bak, K. L.; Jørgensen, P.; Jensen, H. J. Aa. J. Chem. Phys. 1993, 99, 3847. (20) Ruud, K.; Helgaker, T.; Kobayashi, R.; Jørgensen, P.; Bak, K. L.; Jensen, H. J. Aa. J. Chem. Phys. 1994, 100, 8178. (21) Ruud, K.; Helgaker, T.; Bak, K. L.; Jørgensen, P.; Olsen, J. Chem. Phys. 1995, 195, 157. (22) Helgaker, T.; Jensen, H. J. Aa.; Jørgensen, P.; Koch, H.; Olsen, J.; Agren, H.; Andersen, T.; Bak, K. L.; Bakken, V.; Christiansen, O.; Dahle, P.; Dalskov, E. K.; Enevoldsen, T.; Halkier, A.; Heiberg, H.; Jonsson, D.; Kirpekar, S.; Kobayashi, R.; de Meras, A. S.; Mikkelsen, K. V.; Norman, P.; Packer, M. J.; Ruud, K.; Saue, T.; Taylor, P. R.; Vahtras, O. DALTON, an electronic structure program. (23) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (24) Widmark, P.-O.; Malmqvist, P. A.; Roos, B. O. Theor. Chim. Acta 1990, 77, 291.
A° strand et al.
19782 J. Phys. Chem., Vol. 100, No. 51, 1996 (25) Roos, B. O. In Ab initio methods in quantum chemistry; Lawley, K. P., Ed.; Wiley: Chichester, 1987. (26) Olsen, J.; Roos, B. O.; Jørgensen, P.; Jensen, H. J. A. J. Chem. Phys. 1988, 89, 2185. (27) Malmqvist, P.-Å.; Rendell, A.; Roos, B. O. J. Phys. Chem. 1990, 94, 5477. (28) Chesnut, D. B.; Moore, K. D. J. Comput. Chem. 1989, 10, 648. (29) Chesnut, D. B.; Rusiloski, B. E.; Moore, K. D.; Egolf, D. A. J. Comput. Chem. 1993, 14, 1364. (30) Dahle, P.; Ruud, K.; Helgaker, T.; Bak, K. L.; Jørgensen, P. Manuscript. (31) Gauss, J. Chem. Phys. Lett. 1992, 191, 614. (32) Gauss, J. J. Chem. Phys. 1993, 99, 3629. (33) Gauss, J. Chem. Phys. Lett. 1994, 229, 198. (34) van Wu¨llen, C.; Kutzelnigg, W. Chem. Phys. Lett. 1993, 205, 563. (35) Chesnut, D. B.; Phung, C. G. J. Chem. Phys. 1989, 91, 6238. (36) Jameson, C. J.; Osten, H. J. Annu. Rep. NMR Spectrosc. 1986, 17, 1. (37) Fowler, P. W.; Grayson, M.; Lazzeretti, P.; Raynes, W. T.; Sadlej, A. J.; Zanasi, R. International NMR Symposium, Cambridge, 1985. (38) Jameson, C. J.; Osten, H. J. Mol. Phys. 1985, 55, 383. (39) Jameson, C. J.; Osten, H. J. Mol. Phys. 1985, 56, 1083. (40) A° strand, P.-O.; Mikkelsen, K. V. J. Chem. Phys. 1996, 104, 648. (41) Roos, B. O.; Fu¨lscher, M. P.; Malmqvist, P.-Å.; Mercha´n, M.; Serrano-Andre´s, L.; In Quantum mechanical electronic structure calculations with chemical accuracy; Langhoff, S. R., Ed.; Kluwer: Dordre˘ cht, 1995. (42) Reed, A. E.; Schleyer, P. v. R. J. Am. Chem. Soc. 1987, 109, 7362. (43) Barter, C.; Meisenheimer, R. G.; Stevenson, D. P. J. Chem. Phys. 1960, 64, 1312. (44) Blickensderfer, R. P.; Wang, J. H. S.; Flygare, W. H. Chem. Phys. Lett. 1993, 205, 563. (45) Flygare, W. H.; Benson, R. C. Mol. Phys. 1971, 20, 225. (46) Mohanty, S.; Bernstein, H. J. J. Chem. Phys. 1971, 54, 2254. (47) Kukolich, S. G.; Nelson, A. C. J. Chem. Phys. 1972, 56, 4446. (48) Norris, C. L.; Pearson, E. F.; Flygare, W. H. J. Chem. Phys. 1974, 60, 1758. (49) Landolt-Bo¨ rnstein, Zahlenwerte und Funktionen, Neue Serie; Hellwege, K. H., Ed.; Springer: Berlin, 1973; Vol. II/6. (50) Appleman, B. R.; Dailey, B. P. AdVan. Magn. Reson. 1974, 7, 231. (51) Oldenziel, J. G.; Trappeniers, N. J. Physica A 1976, 82A, 565, 581. (52) Schindler, M.; Kutzelnigg, W. J. Am. Chem. Soc. 1983, 105, 1360. (53) Keith, T. A.; Bader, R. F. W. Chem. Phys. Lett. 1992, 194, 1. (54) Ruud, K.; Skaane, H.; Helgaker, T.; Bak, K. L.; Jørgensen, P. J. Am. Chem. Soc. 1994, 116, 10135. (55) Jackowski, K.; Raynes, W. T. J. Chem. Res. Synop. 1977, 66.
(56) Jameson, A. K.; Jameson, C. J. Chem. Phys. Lett. 1987, 134, 461. (57) Raynes, W. T.; McVay, R.; Wright, S. J. J. Chem. Soc., Faraday Trans 2 1989, 85, 759. (58) Facelli, J. C.; Grant, D. M.; Bouman, T. D.; Hansen, A. E. J. Comput. Chem. 1990, 11, 32. (59) Appleman, B. R.; Tokuhiro, T.; Fraenkel, G.; Kern, C. W. J. Chem. Phys. 1974, 60, 2574. (60) Zilm, K. W.; Grant, D. M. J. Am. Chem. Soc. 1981, 103, 2913. (61) Jokisaari, B.; Hiltunen, Y.; Lounila, J. J. Chem. Phys. 1986, 85, 3198. (62) Hiltunen, Y. Mol. Phys. 1987, 62, 1187. (63) Hindermann, D. K.; Cornwell, C. D. J. Chem. Phys. 1968, 48, 4148. (64) Jameson, C. J.; Jameson, A. K.; Hornarbakhsh, J. J. Chem. Phys. 1984, 81, 5266. (65) Hunt, E.; Meyer, H. J. Chem. Phys. 1964, 41, 353. (66) Bernheim, R. A.; Krugh, T. R. J. Am. Chem. Soc. 1967, 89, 6784. (67) Bernheim, R. A.; Hoy, D. J.; Krugh, T. R.; Lavery, B. J. J. Chem. Phys. 1969, 50, 1350. (68) Emsley, J. W.; Feeney, J.; Sutcliffe, L. H. High resolution nuclear magnetic resonance spectroscopy; Pergamon Press: New York, 1968; Vol. 2. (69) Raynes, W. T. Nucl. Magn. Reson. 1978, 7, 1. (70) van Wu¨llen, C., Doctoral Thesis, Ruhr-Universita¨t Bochum, 1992. (71) Gauss, J.; Stanton, J. F. J. Chem. Phys. 1996, 104, 2574. (72) Handbook of Chemistry and Physics, 62nd ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, 1981. (73) Wallqvist, A.; Karlstro¨m, G. Chem. Scr. 1989, 29A, 131. (74) A° strand, P.-O.; Wallqvist, A.; Karlstro¨m, G.; Linse, P. J. Chem. Phys. 1991, 95, 6395. (75) Rizzo, A.; Helgaker, T.; Ruud, K.; Barszczewicz, A.; Jaszun´ski, M.; Jørgensen, P. J. Chem. Phys. 1995, 102, 8953. (76) Bishop, D. M. ReV. Mod. Phys. 1990, 62, 343. (77) Port, G. N. J.; Pullman, A. FEBS Lett. 1973, 31, 70. (78) Jameson, C. J.; Jameson, A. K.; Parker, H. J. Chem. Phys. 1979, 70, 5916. (79) Raynes, W. T.; Buckingham, A. D.; Bernstein, H. J. J. Chem. Phys. 1962, 36, 3481. (80) Packer, M. J.; Raynes, W. T. Mol. Phys. 1990, 69, 391. (81) Lau, E. Y.; Gerig, J. T. J. Chem. Phys. 1995, 103, 3341. (82) Mikkelsen, K. V.; Luo, Y.; A° gren, H.; Jørgensen, P. J. Chem. Phys. 1995, 102, 9362. (83) Mikkelsen, K. V.; Ruud, K.; Helgaker, T. Chem. Phys. Lett. 1996, 253, 443.
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