6468
J. Phys. Chem. 1995,99, 6468-6471
Calculation of Proton Affinities Using the G2(MP2,SVP) Procedure Brian J. Smith*@ and Leo Radom*9lb Biomolecular Research Institute, Parkville, Victoria 3052, Australia, and Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia Received: November 15, 1994; In Final Form: February 7, 1 9 9 9
The G2(MF'2,SVP) method, which uses an additivity scheme similar to that of G2(MP2) but with QCISD(T) contributions calculated using the split-valence plus polarization 6-3 1G(d) basis in place of the 6-3 1lG(d,p) basis, is shown to reproduce proton affinities for a set of reference molecules to within the G2 target accuracy of 10 kJ mol-' but at significantly lower computational cost. Application to additional systems leads to the suggestion that the experimental proton affinities of methyl vinyl ether, ethyl cyanide, and hydrogen isocyanide may need revision.
Introduction The Gaussian-2 (G2) method? recently introduced by Pople and co-workers, has been f0und~9~ to consistently provide estimates of proton affinities to within a target accuracy of 10 kJ mol-'. In a subsequent search4 for computationally less demanding means of determining reliable proton affinities, we found that the more economical G2(MP2) method5 also consistently yields proton affinities within this target accuracy, with values very close to those obtained by the G2 level. We were also able to obtain accurate proton affinities with procedures such as MP4 and F4, but this required the use of a large basis set (of the size of the ultimate basis set in G2 theory), the calculations being carried out using correlationhasis set additivity approximations. We found that computationally efficient density functional methods such as B-LYP and Becke3-LYP give proton affinities which often lie within the G2 target accuracy. However, large and unpredictable errors exceeding 20 kJ mol-' occasionally occur, a clearly undesirable state of affairs. The G2(MP2) method was originally introduced5 to extend the range of systems amenable to a G2-type approach because of its lower computational cost. In order to further extend the range of systems that can be handled with currently available computational resources, we introduce here the G2(MP2,SVP) procedure. We evaluate its performance with respect to the calculation of proton affinities.
Method Standard ab initio molecular orbital calculations6 were performed at a number of levels of theory using the GAUSSIAN 92 p r ~ g r a m .G2 ~ theory corresponds effectively to QCISD(T)/ 6-3 11+G(3df,2p)//MP2/6-3 1G(d) calculations with zero-point vibrational and "higher-level" corrections. In the G2(MP2) approach, this level of theory is obtained using the additivity approximation, E(QCISD(T)/6-31 l+G(3df,2p)) X E(QCISD(T)/6-31lG(d,p)) E(MP2/6-3 1 1+G(3df,2p)) - E(MP2/6-3 1lG(d,p))
+
The computationally most demanding component of a G2(MP2) calculation for large systems arises from the QCISD(T) contribution. By reduction of the size of the basis set in this part @
Abstract published in Advance ACS Abstracts, April 1, 1995.
0022-3654/95/2099-6468$09.00/0
of the calculation, substantial savings can be realized. We have therefore introduced an alternative additivity approximation, E(QCISD(T)/6-31l+G(3df,2p)) E(QCISD(T)/6-3 lG(d)) E( MP2/6-31 1+G( 3df,2p)) - E(MP2/6- 3 1G(d))
+
to achieve the same effective level of calculation as the G2 or G2(MP2) methods. Energies obtained at this level are labeled G2(MP2,SVP), reflecting the relationship with the G2(MP2) additivity scheme and the use of the split-valence plus polarization (SVP) 6-31G(d) basis set for the QCISD(T) component. We have not attempted to determine any empirical higher-level correction term (as required in general for a G2type procedure) since, when calculating proton affinities, the higher level correction cancels; the resulting proton affinity is thus purely ab initio. The bromine basis we have used in these calculations is one originally recommended for use in G1 theory.8 Zero-point vibrational corrections and enthalpy corrections based on the scaled HF/6-3 1G(d) vibrational frequencies have been applied to obtain proton affinities at 298 K. Standard statistical thermodynamics formulas were used, the harmonic oscillator approximation being employed for all vibrations, unless otherwise noted. Replacing the standard harmonic oscillator temperature corrections by the value appropriate for a free rotor (RT/2) for low-frequency torsions (i.e., below 260 cm-I) has an effect at 298 K smaller than 1 kJ mol-', except for the proton affinity of isobuteqe which is increased by 1.3 kJ mol- I .
Results and Discussion Comparisons of 6 2 , G2(MP2), GZ(MPZ,SVP), and Experimental (SMT Data Set) Proton Affinities. We have evaluated the performance of the G2(MP2,SVP) method by making comparisons both with results obtained with the more accurate G2 and G2(MP2) theoretical procedures and with the recent experimentally determined proton affinities of Szulejko and McMahon9 and Traeger'O (SMT data set4). We note that the theoretical proton affinities refer to a temperature of 298 K. The Szulejko and McMahon proton affinitiesg are also nominally 298 K values, being referenced to a 298 K proton affinity for CO, but the experimental proton-transfer energies from which their proton affinity scale was constructed were obtained at a variety of temperatures. It is useful to assess the 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 17, 1995 6469
Calculation of Proton Affinities
TABLE 1: Calculated and Experimental Proton Affinities (kJ mol-', 298 K) G2"
-+ -+ -+ +
(CH3)2NH2+ (CH3)2NH H+ CH3NH3' CH3NH2 Hf N&+ NH3 H+ CH3CO' CH2CO H+ (CH3)zCOH' (CH3)2CO H+ (CH3)3CC (CH3)zCCHz H+ (CH&OH+ (CH3)20 H+ HC(OH)OCH3+ HC(O)OCH3 H+ CH3CHOH' CH3CHO H+ CH3OHz' CH3OH H+ CH3CHCH3+ CHzCHCH3 H+ CH20H' CH20 H+ H3S+ HzS H+ H3O' HzO H+ HSCS+-CS2 H+ CH3CH2' CHzCH2 H+ HCO+ CO H+ CH5' C& H+ HOCO' C02 H+ HNN' N2 H+ +
-
-.
+
+
+
-+
-
+
-++
--
-
+
-+
+ + -+ + --- ++ + +
G2(MP2)b G2(MP2,SVP)
expt:
93 1.7
932.2
928.2
93 1
901.0
901.3
900.4
90 1
853.6 825.0
853.5 826.1
852.8 823.5
85 1 825d
811.96
812.7
813.2
810
802.1
800.9
799.2
802
792.0
792.5
792.0
793
782.26
783.5
783.2
787
TABLE 2: Comparison of Calculated - Experimental Proton Affinity Differences" (kJ mol-', 298 K)
- ++ -- + + --- +++ -
(CH3)2NHz+ (CH&NH H+ CH3NH3+ CH3NH2 H+ N&+ NH3 H+ CH2CO H+ CH3CO' (CH3)2COH+ (CH3)zCO H+ (CH3)3C+ (CH3)2CCHz H+ (CH3)20Hf (CH3)zO H+ HC(OH)OCHj+ HC(O)OCH3 H+ CH3CHOHf-CH3CH0 H+ CH30Hz+ -.+CH3OH Hf CH3CHCH3' CH2CHCH3 H' CHIOH' CH2O H' H3S' HzS H+ H30+ H20 H+ HSCS+ CS2 H+ CH3CH2+ CHzCHz H+ HCO+ CO H+ CH5' CH4 H+ COz H+ HOCO' HNN+ N2 H+ Idevlc
+
+
+
+
+
-+
+
-- +++ -+ + -- + + - +
+
770.2
770.8
771.3
76gd
754.3
754.9
754.4
760
744.3
743.5
741.6
746, 747d
711.8
712.8
712.2
713d
707.7 688.4 681.9 68 1.9
711.0 688.4 682.7 681.6
709.3 687.8 684.2 679.1
706 690 675 680, 678d
593.0 539.8 539.3 493.9
593.3 540.5 540.0 494.5
597.1 541.3 539.3 494.0
594,594d 545 541, 537d 497
From ref 3 unless otherwise noted. From ref 4. From ref 9 unless otherwise noted. From ref 10.
effect of such temperature variation. In previous work,3 we found that proton affinities at 600 K were systematically higher than those at 298 K by an average of 3.7 kJ mol-', the maximum and minimum differences being 5.2 and 2.3 kJ mol-', respectively. However, because the energies of proton-transfer reactions correspond formally to differences in proton affinities (PA), the systematic nature of the PA temperature correction leads to a temperature dependence for proton-transfer energies smaller than that for absolute proton affinities. As a result, the uncertainity introduced into the proton affinity scale by using a variety of temperatures in the proton-transfer experimentsg is relatively small (up to 3 kJ mol-' but generally significantly less). Calculated and experimental proton affinities for the 20 molecules of the SMT set are presented in Table 1. Differences between theoretical and experimental proton affinities, including mean absolute deviations for the three different levels of theory, are shown in Table 2. The G2 and G2(MP2) proton affinities for the 20 systems studied show mean absolute deviations from the SMT values of just 2.3 and 2.4 kJ mol-', respectively; maximum deviations are 6.9 and 7.7 kJ mol-I. The G2(MF'2,SVP) proton affinities are almost as good, with a mean absolute deviation of 2.9 kJ mol-' and a maximum deviation of 9.2 kJ mol-'. Thus, all the calculated proton affinities in this set lie within the G2 target accuracy of 10 kJ mol-'. Notably, all three methods perform least well for the proton affinity of CS2. The next largest deviations are 5.7, 5.1, and 5.6 kJ mol-' for the G2, G2(MP2), and G2(MP2,SVP) methods, respectively. The mean absolute difference between the G2 and G2(MP2) proton affinities is 0.8 kI mol-', while for the G2 and G2(MP2,SVP) levels the difference is 1.6 kJ mol-'. The largest
G2
G2(MP2) G2(MP2,SVP)
0.7 0.0 2.6 0.06 1.9 0.1 -1.0 -4.8
1.2 0.3 2.5 1.16 2.7 -1.1 -0.5 -3.5
-2.8 -0.6 1.8 - 1.5' 3.2 -2.8 -1.0 -3.8
2.2b -5.7 -1.7
2.gb -5.1 -2.5
3.36 -5.6 -4.4
-1.26 1.7 -1.6 6.9 1.9 -1.0 -5.2 -1.7 -3.1 2.3
-0.26 5.0 -1.6 7.7 1.6 -0.7 -4.5 -1.0 -2.5 2.4
-0.8' 3.3 -2.2 9.2 -0.9 3.1 -3.7 -1.7 -3.0 2.9
a Differences from values in ref 9 unless otherwise noted. Differences from values in ref 10. Mean absolute deviation between theory and experiment.
TABLE 3: Calculated and Experimental Proton Affinities (kJ mol-', 298 K) G2(MP2) G2(MP2,SVP) (CH3)3NH+ (CH&N H+ C5H&+ pyridine H+ CHjCH2NH3' CH3CH2NH2 Hf CH3CHOCH3+ CH2CHOCH3 H+ (CH&SH+ (CH3)2S HS HCS+ CS H+ CHjCH2CNH' CH3CHzCN H+ CHzCHCNH' CHzCHCN H+ PH4+ PH3 H+ CH3CNHC CH3CN Hf CH3SH2+ CH3SH H+ HNCH+ HNC H+ CHzSH' CH2S H+ HC(DH)z+ HCOOH H+ HCNH' HCN H+ HzBr+ HBr Hf H2C1+ HCI H' HzF+ HF Hi' H+ H3+-Hz
-+ +
+ +
+
-+
- -+ + -++ -+ ++ -- ++ -+ --- ++ + -. + -+
+
+
expt."
95 1.6
950.6
942
929.8 914.0
928.4 913.2
924 908
849.2
846.4
868
833.9 796.9 794.3
832.4 795.9 793.3
839 787 806
785.4
783.7
794
787.7 781.7 779.4 772.3 769.4 743.9
784.8 780.8 777.9 771.5 770.8 743.7
789 787 784 7846 773 748
713.8 588.6 564.1 484.9 420.0
712.2 587.8 562.9 483.5 420.2
7186 582, 580.7' 571.556.5' 489.5 423.4
From ref 11 unless otherwise noted. See ref 17. From ref 12.
differences are 3.3 kJ mol-I (between G2 and G2(MP2)) and 4.3 kJ mol-' (between G2 and G2(MP2,SVP)). Additional Comparisons of G2(Mp2), G2(Mp2,SVP), and Experimental (LBLHLM) Proton Affinities. As a further test of the performance of the G2(MP2,SVP) procedure and in order to widen the set of molecules being examined, we compare proton affinities obtained using the G2(MP2,SVP) and G2(MP2) methods with experimental for an additional 19 systems in Table 3. Several of these are larger systems for which the reduced computational cost of G2(MP2) and G2(MP2,SVP) compared with G2 makes the calculations more tractable. Calculated differences between the results obtained
Smith and Radom
6470 J. Phys. Chem., Vol. 99, No. 17, 1995
TABLE 4: Comparison of Calculated - Experimental Proton Affinity Difference (kJ mol-', 298 K)
--
+
(CH&NH+ (CH&N H+ CsH&+ pyridine H+ CH3CH2NH3' -.+C H ~ C H ~ N H LH', CH3CHOCH3+ CH2CHOCH3 H+ (CH3)2SH+ (CH3)zS H+ HCS+ CS H+ CH3CHzCN H+ CH3CHzCNH' CH2CHCNH' CHzCHCN H+ PH4+ PH3 H+ CH3CNH' CH3CN H+ CH3SH H+ CH3SH2' HNCH+ HNC -I-H+ CH2S H+ CH2SH' HC(OH)2+ HCOOH H+ HCNH+ HCN H+ H2Brf HBr H+ H2Cl+ HC1+ H+ HF H+ H2F' H3+-H2 H+
+
- + -. - +- -.+- + --- + + + + - + -. - ++ +
a
+ +
+
+
G2(MP2)
GZ(MP2,SVP)
9.6 5.8 6.0 - 18.8 -5.1 9.9 -11.7 -8.6 -1.3 -5.3 -4.6 -11.7 -3.6 -4.1 -4.2 6.6 -6.9 -4.6 -3.4
8.6 4.4 5.2 -21.6 -6.6 8.9 -12.7 -10.3 -4.2 -6.2 -6.1 - 12.5 -2.2 -4.3 -5.8 5.8 -8.1 -6.0
-3.2
Differences from experimental values in ref 11.
by these methods and the experimental values from the compendium of Lias et al. (LBLHLM)" are shown in Table 4. As found above for the initial set of 20 molecules, the G2(MP2,SVP) and G2(MP2) proton affinities are in close agreement. The mean absolute difference between the results for the two methods is just 1.3 kJ mol-'. There is generally good agreement between the calculated and experimental proton affinities. Thus, there are just three cases out of the 19 included in Tables 3 and 4 for which the proton affinities calculated at the G2(MP2) level differ from the experimental values reported in the LBLHLM compendium by more than the 10 kJ mol-' target accuracy. We consider each of these molecules, methyl vinyl ether (CHZCHOCH~), ethyl cyanide (CH~CHZCN), and hydrogen isocyanide (HNC), individually below. We note that the proton affinities calculated for those systems at the upper end of the scale (i.e., with proton affinities greater than NH3 but excluding methyl vinyl ether which we discuss below) are greater than the experimental LBLHLM values while for most of the remaining systems the calculated proton &hities are slightly smaller than the experimental values. This reinforces our earlier argument3 for a small upward adjustment (by 5-10 W mol-') at the upper end of the LBLHLM scale. Our new results also provide further evidence that the scale of Mautner and Sieck (MS)I3requires a somewhat larger downward adjustment (by about 20 kJ mol-'), the MS proton affinities for (CH3)3N, C5H5N, and CH3CH2NH2 being 974,952, and 935 W mol-', respe~tive1y.l~ Analysis of the Cases for which there is Disagreement between G2(MP2) and LBLHLM. The largest difference between G2(MP2) and experimental LBLHLM proton affinities (18.8 kJ mol-') occurs for methyl vinyl ether for which the respective values are 849.2 kJ mol-' and 868 kI mol-'. As a first step in attempting to resolve this discrepancy, we have also calculated the proton affinity of methyl vinyl ether at the G2 1 e ~ e l . IThis ~ gives a result of 848.6 kJ mol-', very close to the G2(MP2) result. In order to probe further whether it is theory or experiment that is likely to be at fault, we have calculated the proton-transfer energy between methyl vinyl ether and ammonia. This has been directly measured by Mautner and Sieck (MS) who obtained a near-zero value at 600 K, indicating that the proton affinity for methyl vinyl ether is very close to that of ammonia. The G2 value (at 600 K) for the protontransfer energy between methyl vinyl ether and ammonia is 3.9
kJ mol-', methyl vinyl ether having the lower proton affinity.I6 We suggest that the proton affinity of 868 kJ mol-' given for methyl vinyl ether in the LBLHLM compendium is probably too high by about 15-20 kJ mol-'. For CH~CHZCN,the G2(MP2) proton affinity (794.3 kJ mol-') differs from the LBLHLM value (806 kT mol-') by 11.7 kJ mol-'. In this case, the proton-transfer energy of CH3CH2CN with methyl formate has been directly measured by MS who obtained a value of 13 kJ mol-' at 600 K. This is in good agreement with the G2(MP2) estimate of 10 kJ mol-'. We again submit the G2(MP2) value as the more reliable estimate of the proton affinity of ethyl cyanide. For HNC, the G2(MP2) and LBLHLM proton affinities are 772.3 and 784 kJ mol-', respectively, a difference of 11.7 kJ There is no significant change at the G2 levells where the calculated proton affinity is 772.6 kJ mol-'. The discrepancy between theory and experiment could arise in principle from a discrepancy in the heat of formation either for HNC or for HNCH+. The G2 AHf 298 values for HCN and HNCH+ are 130.9 and 949.6 W mol-', in reasonable agreement with the experimental" values of 135.1 and 947 W mol-', respectively. On the other hand, the G2 AHf 298 value for HNC is 191.5 kJ mol-' compared with the experimental of 201 f 8 kJ mol-'. We propose that the G2 value provides the more reliable estimate for the AHf 298 of HNC. Concluding Remarks The following conclusions emerge from the present study. (1) The G2(MP2,SVP) method performs very well in determining the gas-phase proton affinities of the 20 systems of the SMT data set and consistently achieves the G2 target accuracy of 10 kJ mol-'. (2) G2(MP2,SVP) produces proton affinities of a quality generally comparable to G2 but at a significantly reduced computational cost. (3) The calculated proton affinities of methyl vinyl ether, ethyl cyanide, and hydrogen isocyanide show significant differences from the literature experimental values. The good agreement between G2 and G2(MP2) proton-transfer energies involving methyl vinyl ether and ethyl cyanide and directly-measured values suggests that the present theoretical proton affinities for these molecules may be more reliable than the literature experimental values. (4) Our calculations suggest a revised AHf 298 for HNC.
Acknowledgment. We gratefully acknowledge a generous allocation of time on the Fujitsu VP-2200 of the Australian National University Supercomputer Facility. References and Notes (1) (a) Biomolecular Research Institute. (b) Australian National University. (2) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem. Phys. 1991, 94, 7221. (3) Smith, B. J.; Radom, L. J . Am. Chem. SOC.1993, 115,4885. (4) Smith, B. J.; Radom, L. Chem. Phys. Lett. 1994, 231: 345. (5) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J . Chem. Phys. 1993, 98, 1293. (6) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A b Initio Molecular Orbital Theory; Wiley: New York, 1986. (7) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S . ; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S . ; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision C ; Gaussian Inc.: Pittsburgh, PA, 1992. (8) McGrath, M. P.; Radom, L. J . Chem. Phys. 1991, 94, 511. Note that the splitting factor for the three d functions in the basis set that corresponds to 6-311+G(3df,2p) is 3 rather than the 4 used for first- and second-row atoms. See: Curtiss, L. A.; McGrath, M. P.; Blaudeau, J. P.; Davis, N. E.; Binning, R. C.; Radom, L. To be published. Note also that standard first- and second-row splitting
J. Phys. Chem., Vol. 99, No. 17, 1995 6471
Calculation of Proton Affinities factors were used for the calculations on HBr and H2Br+ in ref 3, yielding results slightly different to those reported here. (9) Szulejko, J. E.; McMahon, T. B. J . Am. Chem. SOC.1993, 115, 7839. (10) Traeger, J. C. To be published. (11) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J . Phys. Chem. Ref. Data Suppl. I 1988, 17. (12) Adams, N. G.; Smith, D.; Tichy, M.; Javehery, G.; Twiddy, N. D.; Ferguson, E. E. J . Chem. Phys. 1989, 91, 4037. (13) Mautner, M.: Sieck, L. W. J . Am. Chem. SOC.1991, 113, 4448. (14) If the MS proton affinities13 are adjusted downward by 15.3 kJ mol-' to reflect a 600 K proton affinity for isobutene of 804.7 kJ mol-' (G2)3 rather than the original reference value of 820 kJ mol-', and if calculated temperature corrections from 600 to 298 K of 4.5, 4.3, and 4.9 kJ mol-' are applied for (CH3)3N, C~HSN, and CH~CHZNHZ, respectively, then proton affinities at 298 K of 954.2, 932.4, and 914.8 kJ mol-', respectively, are obtained for these molecules. These values are in very good agreement with the calculated G2(MP2) results of 951.6, 929.8, and
914.0 kJ mol-' (Table 3). We thank Dr. Wayne Sieck for bringing this to our attention. (15) The G2 total energies for methyl vinyl ether and its protonated form at 0 K (298 K) are -192.770 95 (-192.765 15) and -193.092 68 (- 193.08602) hartrees, respectively. (16) The enthalpy temperature correction for methyl vinyl ether at 600 K showed the greatest sensitivity (2.7 kJ mol-') of any of the systems examined in the present paper to replacing the harmonic oscillator approximation for low-frequency torsions by the expression for a free rotor. The value of 3.9 kJ mol-' was obtained using the free rotor approximation for frequencies below 524 cm-'. (17) The proton affinities of 784 and 718 kJ mol-' for HNC and HCN, respectively, were calculated using the experimental AHf 298 values for HNC, HCN, HCNH+, and H+, as listed in the LBLHLM compendium." (18) The G2 total energies for HNC and HNCH+ at 0 K (298 K) are -93.262 10 (-93.258 32) and -93.553 88 (-93.550 23) hartrees, respectively. (19) Pau, C.-F.; Hehre, W. J. J . Phys. Chem. 1982, 86, 321. JP943061Q
