- Email: [email protected]
Basis set and correlation effects in the calculation of selenium NMR shieldings
29 July 1994
CHEMICAL
PHYWCS ELSEVIER
225 ( 1994) 280-284
Basis set and correlation effects in the calculation of selenium NMR shieldings GAbor Magyarfalvi ‘, Peter Pulay Department of Chemistryb&i Biochemistry, UniversityofArkansas, Fayetteville,AR 72701. USA Received 18 April 1994;in fmal form 9 May 1994
Accurate ab initio GIAO calculations of “Se chemical shieldings in SeHs, SeHCH3 and Se(CH,)2 are reported. The calculations closely reproduce the experimental relative chemical shifts of these molecules. The extension of the basis sets with p, d and f functions on the selenium atom improves the chemical shifts at the SCF level values, but quantitativeness is only achieved at the MP2 level. The effect of conformation on the chemical shieldings is also discussed.
1. Inlroduction Ab initio calculation of NMR shieldings is rapidly becoming an important new structural tool (see the recent reviews in Ref. [ 1 ] ) . Only a few comparisons between experiment and accurate theory have been reported beyond the second row of the periodic table so far. Perhaps the most conclusive ofthese is the work of Ellis et al. [ 21. These workers have measured the chemical shifts of hydrogen selenide and methyl selenol with respect to dimethyl selenide and performed GIAO SCF calculations for these molecules. However even the best calculation of Ref. [ 2 ] differs significantly from the experimental shifts. For future applications, it is important to explore which of the following causes is responsible for the deviation: electron correlation, basis set deficiencies or relativistic effects. Ellis et al. suggested electron correlation. Since selenium has an atomic number of 34, relativistic calculations should not be required to produce ’ Part of a Diploma Thesis to be submitted to the E&&s University, Budapest.
accurate shieldings. We tried to carry out a thorough study on the effect of the basis set. To incorporate correlation effects, shielding calculations at the second-order Moller-Plesset (MP2) level of theory, developed recently by Gauss [ 3 1, were also performed. MP2 is expected to recover most of the dynamical correlation energy [ 41 and, as shown by the excellent results of Gauss [ 51, should work well for these molecules. Another efficient approach to correlation effects is density functional theory (DFI’). Salahub and co-workers have performed IGLO-type DFT shielding calculations for these molecules [ 61. Calculations using the GIAO DFT formalism are also in progress in this laboratory.
2. Calculations Calculated geometries were used for all three molecules. The optimizations were carried out at the SCF level with the TX90 program, using basis set I of Table 1, described below. The shielding calculations were performed using the GIAO method. The pro-
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(94)00604-O
281
G. Magyarfalvi, P. Pulay /Chemical Physics Letters 225 (1994) 28&284 Table 1 The contraction patterns of the basis sets used ’ basis set
s
P
d
f
I II III IV V VI VII
62111111 62111111 62111111 62111111 62111111 62111111 62111111
331211 331211 331211+1 11x1 11x1+11 311111111+1 311111111+1
411+1 6x1+1 411+11 6x1+1 6x1+111 411+11 411+11
lb
a The functions after the plus sign are diffuse functions added to the original basis of Schtier et al. [ 71. The notation 11 X 1 uncontracted functions. The exponent the f function was
grams used were: TX90 [ 81 on the SCF level and the MP2 GIAO module [ 91 of the ACESII program [
] for selenium, and the TZP basis sets of the same authors for carbon and hydrogen. In the uncontracted/contracted notation, the composition of these basis sets is (14s, 12p, 6d/8s, 6p, 3d), (lOs6pld/6s3pld) and (5slp/3slp), respectively. The selenium basis was modified in several ways in all calculations. The modifications included the addition of p- and d-type diffuse functions, the partial decontraction of p and d shells and the addition of f-type functions. The contraction patterns of seven basis sets employed can be found in Table 1. New exponents for the polarization functions were obtained simply by dividing the last exponent by 3. The ACESII program uses Cartesiantype basis functions, e.g. 6 d and 10 f functions. TX90 can use both canonical and Cartesian-type basis functions, nevertheless the Hartree-Fock-type calculations were performed using canonical basis functions. When an MP2 calculation was also performed with the basis set in question, HF results are reported for both types of functions to allow comparison.
11
3. Results There is an important difference between the geometries used by Ellis et al. and the ones we calculated. During their optimization of Se( CH3)2, the molecule was forced to remain in a staggered conformation around one Se-C bond and in an eclipsed around the other one. Chemical intuition would suggest that the staggered-staggered conformation should be the global minimum on the potential energy surface. Indeed an ab initio study using 3-2 1G* basis already had established this point [ 111 correcting a previous result of the same group [ 121 which suggested that the eclipsed-staggered one is the preferred conformation. Our calculations on the SCF level with basis set I indicate that the CzVstructure is lower in energy by 1S43 kcal/mol than the eclipsedstaggered one. There is also experimental evidence supporting the staggered-staggered structure for Se(CH&. The microwave spectroscopical results of both Beecher [ 13 ] and Pandey and Dreizler [ 14 ] are only consistent with the CzVequilibrium structure. The geometry parameters used are listed along the experimental values in Table 2. The conformation of SeHCH3 was also staggered. The results of the shielding calculations are shown in Table 3 and in Fig. 1. The results show that the partial decontraction of the p functions, the addition of further p and d diffuse functions and an f function have all distinctly improved the SCF shielding val-
G. Magyarfalvi, P. Pulay /Chemical Physics Letters 225 (1994) 280-284
282 Table 2 Geometry parameters
Parameter
SeH2 b
l
SeHCHs ’
1.454 (1.460)
Me-W
1.454 (1.473) 1.956 (1.959) 1.081 1.079
r(Se-C) r(C-K) r(C-H.) angles X-Se-X H.-C-Se H.-C-Se H&-H,
93.0 (90.9)
96.4 (95.5) 106.3 110.5 109.3
-
WCHA
d
1.948 (1.945) 1.081 (1.088) 1.080 (1.096) 98.0 107.3 110.5 109.2
(96.3) (105.0) (110.3) (110.6)
.
l Bond lengths in A,angles in deg. Experimental values are in brackets. b Experimental values from Ref. [ 15 1. cExperimental values from Ref. [ 161. dExperimental values from Ref. [ 12 1.
Table 3 Calculated 77Seshielding values in ppm Basis set ’
@eHz)
a(SeMer)
ues. Further d and functions, either hard or exponents and decontraction of d shell not have substantial effect difference over ppm) on shieldings. (These are not ported.) Therefore best results be apthe Hartree-Fock However, the provement with change of basis did lead to Only the results are to
a( SeMeH )
a(SeHs)
the results. The of Se CHs ) 2 do not appear to change with the change to the higher theoretical level. This is only fortuitous, the changes in the individual tensor components are significant. The principal components of the shielding tensors calculated with basis VII are collected in Table 4 for comparison with future experimental and theoretical work. A calculation on Se ( CH3 ) 2 using basis set I was
G. iWagyar@lvi,P. Pulay /Chemical PhysicsLetters 225 (1994) 280~284
+Sd-I2I-F
%
+SeMeHHF
*seH2MP2 SeMeHMP2
283
in agreement with values. Ab initio calculations can be an adequate model for gas phase results. In view of the sensitivity of Se shieldings on isotopic [ 18 ] and temperature [ 19 1, taking the vibrational effects in consideration would be necessary to reach the experimental precision.
Acknowledgement A
/ I
II
III
IV
v
VI VII
basis set Fig. 1. “Se chemical shifts relative to dimethyl selenide calculated using different basis sets and different levels of theory.
GM would like to thank the Peregrinatio Foundation (E&v& L. University, Budapest) for a travel grant. This work was also supported by the US National Science Foundation Grant CHE-88 14 143. We would like to thank Dr. J. Gauss and Professor R.J. Bartlett for generously providing the GIAO-MP2 part of ACES11 and Mr. Quingping Chen in Professors Ellis’ group for useful assistance.
References Table 4 The principal values of the shielding tensors of SeH2, SeHCHx and Se(CH,)z calculated using basis VII (in ppm)
SeH2 MP2
1844.11 2043.00
2065.85 2130.37
2624.85 2653.51
SeHCH3 SCF SeHCH3 MP2
1747.76 1872.84
1863.03 1888.29
2520.59 2517.76
Se(CH3)2 Se(CH3)2
1687.34 1684.46
1716.12 1764.48
2371.48 2317.80
SeH2 SCF
SCF MP2
a In the axially symmetric molecules, the orientation of this principal axis coincides with the symmetry axis, in SeHCH3 it is in the symmetry plane of the molecule tilted from the H-Se-C bisector towards the Se-H bond by 0.64” in the SCF case and by 5.26” in the MP2 case. b This principal axis is always perpendicular to the X-Se-X plane.
performed with the geometry optimized in the eclipsed-staggered The change in the geometry caused a change of over 30 ppm in the shieldings. That emphasizes the well-known importance of the accurate geometries in the calculation of the chemical shieldings [ 17 1. In summary,
the “Se shieldings
can be calculated
[ 1] J.A. Tossell, ed., Nuclear magnetic shieldings and molecular structure, NATO ASI Series, Series C, No. 386 (Kluwer, Dordrecht, 1993). [2]P.D. Ellis, J.D. Gdom, A.S. Lipton, Q. Chen and J.M. Gulick, in: Nuclear magnetic shieldings and molecular structure, NATO AS1 Series, Series C, No. 386, ed. J.A. Tossell (Kiuwer, Dordrecht, 1993) p. 539. [3] J. Gauss, Chem. Phys. Letters 191 (1992) 614. [4] R.J. Bartlett, Ann. Rev. Phys. Chem. 32 (1981) 359. [ 51 J. Gauss, J. Chem. Phys. 99 (1993) 3629. [6] V.G. M&in, O.L. Malkina, M.E. Casida and D.R. salahub, J. Am. Chem. Sot., submitted for publication. [7] A. Schiifer, H. Horn and R. Ahlrichs, J. Chem. Phys. 97 (1992) 2571. [ 81 K. Wolinski, J.F. Hinton and P. Pulay, J. Am. Chem. Sot. 111 (1990) 8251. [9] J. Gauss, Chem. Phys. Letters 191 (1992) 614. [ lo] J.F. Stanton, J. Gauss, J.D. Watts, W.J. Lauderdale and R.J. Bartlett, Intern. J. Quantum Chem. Symp. 26 (1992) 879. [ 111 V.K. Yadav, A. Yadav and R.A. Poirier, J. Mol. Structure (THEOCHEM) 186 (1989) 101. [ 121 R.A. Poirier and LG. Csizmadia, in: The chemistry of organic selenium and tellurium compounds, Vol. 1, eds. S. Patai and Z. Rappoport (Wiley, New York, 1986). [ 131 J.F. Beecher, J. Mol. Spectry. 4 (1966) 414. [ 141 G.K. Pandey and H. Dreizler, Z. Natuforsch 32 a (1977) 482. [ 151 Landolt-Bornstein Zahlenwerte und Funktionen, Vol. NS II/ 15 (Springer, Berlin, 1987) p. 115. [ 161 C.H. Thomas, J. Chem. Phys. 59,70 (1973.
284
G. Magyatfdvi, P. Pday /Chemical PhysicsLetters225’(1994) 280-284
[ 17) C.J. Jameson and A.C. de Dios, in: Nuclear magnetic shieldings and molecular structure, NATO ASI Series, Series C, No. 386, ed. J.A. Tossell (Kluwer, Dordrecht, 1993) p. 95.
[ 181 H.J. Jakobsen, A.J. Zozulen, P.D. Ellis and J.D. Odom, J. Magn. Reson. 38 ( 1980) 2 19. [ 191 N.P. Luthra, R.B. Dunlap and J.D. Odom, J. Magn. Reson. 52 (1983) 318.
CHEMICAL
PHYWCS ELSEVIER
225 ( 1994) 280-284
Basis set and correlation effects in the calculation of selenium NMR shieldings GAbor Magyarfalvi ‘, Peter Pulay Department of Chemistryb&i Biochemistry, UniversityofArkansas, Fayetteville,AR 72701. USA Received 18 April 1994;in fmal form 9 May 1994
Accurate ab initio GIAO calculations of “Se chemical shieldings in SeHs, SeHCH3 and Se(CH,)2 are reported. The calculations closely reproduce the experimental relative chemical shifts of these molecules. The extension of the basis sets with p, d and f functions on the selenium atom improves the chemical shifts at the SCF level values, but quantitativeness is only achieved at the MP2 level. The effect of conformation on the chemical shieldings is also discussed.
1. Inlroduction Ab initio calculation of NMR shieldings is rapidly becoming an important new structural tool (see the recent reviews in Ref. [ 1 ] ) . Only a few comparisons between experiment and accurate theory have been reported beyond the second row of the periodic table so far. Perhaps the most conclusive ofthese is the work of Ellis et al. [ 21. These workers have measured the chemical shifts of hydrogen selenide and methyl selenol with respect to dimethyl selenide and performed GIAO SCF calculations for these molecules. However even the best calculation of Ref. [ 2 ] differs significantly from the experimental shifts. For future applications, it is important to explore which of the following causes is responsible for the deviation: electron correlation, basis set deficiencies or relativistic effects. Ellis et al. suggested electron correlation. Since selenium has an atomic number of 34, relativistic calculations should not be required to produce ’ Part of a Diploma Thesis to be submitted to the E&&s University, Budapest.
accurate shieldings. We tried to carry out a thorough study on the effect of the basis set. To incorporate correlation effects, shielding calculations at the second-order Moller-Plesset (MP2) level of theory, developed recently by Gauss [ 3 1, were also performed. MP2 is expected to recover most of the dynamical correlation energy [ 41 and, as shown by the excellent results of Gauss [ 51, should work well for these molecules. Another efficient approach to correlation effects is density functional theory (DFI’). Salahub and co-workers have performed IGLO-type DFT shielding calculations for these molecules [ 61. Calculations using the GIAO DFT formalism are also in progress in this laboratory.
2. Calculations Calculated geometries were used for all three molecules. The optimizations were carried out at the SCF level with the TX90 program, using basis set I of Table 1, described below. The shielding calculations were performed using the GIAO method. The pro-
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(94)00604-O
281
G. Magyarfalvi, P. Pulay /Chemical Physics Letters 225 (1994) 28&284 Table 1 The contraction patterns of the basis sets used ’ basis set
s
P
d
f
I II III IV V VI VII
62111111 62111111 62111111 62111111 62111111 62111111 62111111
331211 331211 331211+1 11x1 11x1+11 311111111+1 311111111+1
411+1 6x1+1 411+11 6x1+1 6x1+111 411+11 411+11
lb
a The functions after the plus sign are diffuse functions added to the original basis of Schtier et al. [ 71. The notation 11 X 1 uncontracted functions. The exponent the f function was
grams used were: TX90 [ 81 on the SCF level and the MP2 GIAO module [ 91 of the ACESII program [
] for selenium, and the TZP basis sets of the same authors for carbon and hydrogen. In the uncontracted/contracted notation, the composition of these basis sets is (14s, 12p, 6d/8s, 6p, 3d), (lOs6pld/6s3pld) and (5slp/3slp), respectively. The selenium basis was modified in several ways in all calculations. The modifications included the addition of p- and d-type diffuse functions, the partial decontraction of p and d shells and the addition of f-type functions. The contraction patterns of seven basis sets employed can be found in Table 1. New exponents for the polarization functions were obtained simply by dividing the last exponent by 3. The ACESII program uses Cartesiantype basis functions, e.g. 6 d and 10 f functions. TX90 can use both canonical and Cartesian-type basis functions, nevertheless the Hartree-Fock-type calculations were performed using canonical basis functions. When an MP2 calculation was also performed with the basis set in question, HF results are reported for both types of functions to allow comparison.
11
3. Results There is an important difference between the geometries used by Ellis et al. and the ones we calculated. During their optimization of Se( CH3)2, the molecule was forced to remain in a staggered conformation around one Se-C bond and in an eclipsed around the other one. Chemical intuition would suggest that the staggered-staggered conformation should be the global minimum on the potential energy surface. Indeed an ab initio study using 3-2 1G* basis already had established this point [ 111 correcting a previous result of the same group [ 121 which suggested that the eclipsed-staggered one is the preferred conformation. Our calculations on the SCF level with basis set I indicate that the CzVstructure is lower in energy by 1S43 kcal/mol than the eclipsedstaggered one. There is also experimental evidence supporting the staggered-staggered structure for Se(CH&. The microwave spectroscopical results of both Beecher [ 13 ] and Pandey and Dreizler [ 14 ] are only consistent with the CzVequilibrium structure. The geometry parameters used are listed along the experimental values in Table 2. The conformation of SeHCH3 was also staggered. The results of the shielding calculations are shown in Table 3 and in Fig. 1. The results show that the partial decontraction of the p functions, the addition of further p and d diffuse functions and an f function have all distinctly improved the SCF shielding val-
G. Magyarfalvi, P. Pulay /Chemical Physics Letters 225 (1994) 280-284
282 Table 2 Geometry parameters
Parameter
SeH2 b
l
SeHCHs ’
1.454 (1.460)
Me-W
1.454 (1.473) 1.956 (1.959) 1.081 1.079
r(Se-C) r(C-K) r(C-H.) angles X-Se-X H.-C-Se H.-C-Se H&-H,
93.0 (90.9)
96.4 (95.5) 106.3 110.5 109.3
-
WCHA
d
1.948 (1.945) 1.081 (1.088) 1.080 (1.096) 98.0 107.3 110.5 109.2
(96.3) (105.0) (110.3) (110.6)
.
l Bond lengths in A,angles in deg. Experimental values are in brackets. b Experimental values from Ref. [ 15 1. cExperimental values from Ref. [ 161. dExperimental values from Ref. [ 12 1.
Table 3 Calculated 77Seshielding values in ppm Basis set ’
@eHz)
a(SeMer)
ues. Further d and functions, either hard or exponents and decontraction of d shell not have substantial effect difference over ppm) on shieldings. (These are not ported.) Therefore best results be apthe Hartree-Fock However, the provement with change of basis did lead to Only the results are to
a( SeMeH )
a(SeHs)
the results. The of Se CHs ) 2 do not appear to change with the change to the higher theoretical level. This is only fortuitous, the changes in the individual tensor components are significant. The principal components of the shielding tensors calculated with basis VII are collected in Table 4 for comparison with future experimental and theoretical work. A calculation on Se ( CH3 ) 2 using basis set I was
G. iWagyar@lvi,P. Pulay /Chemical PhysicsLetters 225 (1994) 280~284
+Sd-I2I-F
%
+SeMeHHF
*seH2MP2 SeMeHMP2
283
in agreement with values. Ab initio calculations can be an adequate model for gas phase results. In view of the sensitivity of Se shieldings on isotopic [ 18 ] and temperature [ 19 1, taking the vibrational effects in consideration would be necessary to reach the experimental precision.
Acknowledgement A
/ I
II
III
IV
v
VI VII
basis set Fig. 1. “Se chemical shifts relative to dimethyl selenide calculated using different basis sets and different levels of theory.
GM would like to thank the Peregrinatio Foundation (E&v& L. University, Budapest) for a travel grant. This work was also supported by the US National Science Foundation Grant CHE-88 14 143. We would like to thank Dr. J. Gauss and Professor R.J. Bartlett for generously providing the GIAO-MP2 part of ACES11 and Mr. Quingping Chen in Professors Ellis’ group for useful assistance.
References Table 4 The principal values of the shielding tensors of SeH2, SeHCHx and Se(CH,)z calculated using basis VII (in ppm)
SeH2 MP2
1844.11 2043.00
2065.85 2130.37
2624.85 2653.51
SeHCH3 SCF SeHCH3 MP2
1747.76 1872.84
1863.03 1888.29
2520.59 2517.76
Se(CH3)2 Se(CH3)2
1687.34 1684.46
1716.12 1764.48
2371.48 2317.80
SeH2 SCF
SCF MP2
a In the axially symmetric molecules, the orientation of this principal axis coincides with the symmetry axis, in SeHCH3 it is in the symmetry plane of the molecule tilted from the H-Se-C bisector towards the Se-H bond by 0.64” in the SCF case and by 5.26” in the MP2 case. b This principal axis is always perpendicular to the X-Se-X plane.
performed with the geometry optimized in the eclipsed-staggered The change in the geometry caused a change of over 30 ppm in the shieldings. That emphasizes the well-known importance of the accurate geometries in the calculation of the chemical shieldings [ 17 1. In summary,
the “Se shieldings
can be calculated
[ 1] J.A. Tossell, ed., Nuclear magnetic shieldings and molecular structure, NATO ASI Series, Series C, No. 386 (Kluwer, Dordrecht, 1993). [2]P.D. Ellis, J.D. Gdom, A.S. Lipton, Q. Chen and J.M. Gulick, in: Nuclear magnetic shieldings and molecular structure, NATO AS1 Series, Series C, No. 386, ed. J.A. Tossell (Kiuwer, Dordrecht, 1993) p. 539. [3] J. Gauss, Chem. Phys. Letters 191 (1992) 614. [4] R.J. Bartlett, Ann. Rev. Phys. Chem. 32 (1981) 359. [ 51 J. Gauss, J. Chem. Phys. 99 (1993) 3629. [6] V.G. M&in, O.L. Malkina, M.E. Casida and D.R. salahub, J. Am. Chem. Sot., submitted for publication. [7] A. Schiifer, H. Horn and R. Ahlrichs, J. Chem. Phys. 97 (1992) 2571. [ 81 K. Wolinski, J.F. Hinton and P. Pulay, J. Am. Chem. Sot. 111 (1990) 8251. [9] J. Gauss, Chem. Phys. Letters 191 (1992) 614. [ lo] J.F. Stanton, J. Gauss, J.D. Watts, W.J. Lauderdale and R.J. Bartlett, Intern. J. Quantum Chem. Symp. 26 (1992) 879. [ 111 V.K. Yadav, A. Yadav and R.A. Poirier, J. Mol. Structure (THEOCHEM) 186 (1989) 101. [ 121 R.A. Poirier and LG. Csizmadia, in: The chemistry of organic selenium and tellurium compounds, Vol. 1, eds. S. Patai and Z. Rappoport (Wiley, New York, 1986). [ 131 J.F. Beecher, J. Mol. Spectry. 4 (1966) 414. [ 141 G.K. Pandey and H. Dreizler, Z. Natuforsch 32 a (1977) 482. [ 151 Landolt-Bornstein Zahlenwerte und Funktionen, Vol. NS II/ 15 (Springer, Berlin, 1987) p. 115. [ 161 C.H. Thomas, J. Chem. Phys. 59,70 (1973.
284
G. Magyatfdvi, P. Pday /Chemical PhysicsLetters225’(1994) 280-284
[ 17) C.J. Jameson and A.C. de Dios, in: Nuclear magnetic shieldings and molecular structure, NATO ASI Series, Series C, No. 386, ed. J.A. Tossell (Kluwer, Dordrecht, 1993) p. 95.
[ 181 H.J. Jakobsen, A.J. Zozulen, P.D. Ellis and J.D. Odom, J. Magn. Reson. 38 ( 1980) 2 19. [ 191 N.P. Luthra, R.B. Dunlap and J.D. Odom, J. Magn. Reson. 52 (1983) 318.