Ab initio Prediction of the Structure and Rotational
Ab initio Prediction of the Structure and Rotational Constants of Ground State Methylamine, CH 3 NH 2 David E. Woon
Overview • GOAL: to accurately predict rotational constants and vibrational frequencies to assist spectroscopic studies Ø A e, B e, Ce A 0, B 0, C 0 Ø barrier heights for internal rotation and inversion Ø wi n i • OBJECTIVE: predictions for protonated methanol (CH 3 OH 2+) [see TI 10] • Methylamine is a good choice for benchmarking the efficacy and limitations of state-of-the-art theory. Ø analogous to CH 3 OH 2+ Ø comprehensive data is available
Theoretical Treatment • H 2 O was used to explore methodology and basis set issues. • Equilibrium structures: all-electron CCSD(T) employingaugcc-p. VQZ sets plus sp core-valence functions (C&N) from ccp. CVDZ sets (MOLPRO , 398 basis functions) • Harmonic frequencies: valence-electron CCSD(T) with aug-cc-p. VQZ sets without the H f function (MOLPRO , 320 basis functions) • Anharmonic corrections: as large as B 3 LYP/aug-cc-p. VQZ (GAUSSIAN 03 , 390 basis functions) • Perturbation theory was used for anharmonic shifts: Ø ni = wi + S ( xii, xij ) Ø B 0 = B e – ½ S ai. B (similar for A and C) - anharmonicities - rotation-vibration interaction constants
H 2 O – Frequencies anharmonic shifts (cm-1) B 3 LYP/AVDZ /AVTZ /AVQZ n 1 n 2 n 3 -40. 3 -25. 8 -19. 8 -27. 5 -20. 1 -17. 8 -41. 8 -36. 5 -31. 1 frequency or error (cm-1) n 1 n 2 n 3 Experiment 3657 1595 3756 CCSD(T)/AVTZ /AVQZ-g /AVQZ-f /AVQZ -13. 7 +20. 5 +4. 5 +6. 8 -1. 9 +15. 7 +2. 6 +2. 7 -17. 6 +13. 8 +1. 3 +3. 2
H 2 O – Equilibrium Structure • Benchmarks by Polyansky et al. (Science 299, 539, 2003) and Császár et al. (JCP 122, 214305, 2005): re (Å) MRCI/AV 6 Z ………………. core correlation (D) ……. …. relativistic Breit (D) ……. . …. …. quantum electrodynamics (D). . Best ab initio …. ………………. . • Current work: CCSD(T)/AVQZ+CVDZ ………. CCSD(T)/AVQZ+CVTZ. ………. CCSD(T)/AV 5 Z+CVDZ ………. . qe 0. 95870 -0. 00096 +0. 00016 <0. 00001 104. 411 +0. 134 -0. 074 +0. 003 0. 95782 104. 485 re (Å) 0. 95826 0. 95817 0. 95760 qe 104. 466 104. 475 104. 551
H 2 O – Rotational Constants rotational constant or error (GHz) A 0 B 0 C 0 Experimenta 835. 840 435. 352 278. 138 Variationalb 835. 390 435. 825 278. 699 -0. 450 +0. 473 +0. 561 re: CCSD(T)/AVQZ+CVDZ we: CCSD(T)/AVQZ anh: B 3 LYP/AVQZ 833. 294 434. 215 278. 157 -2. 546 -1. 137 +0. 019 re: CCSD(T)/AV 5 Z+CVTZ 833. 602 434. 239 278. 024 -2. 238 -1. 113 +0. 066 a. De Lucia et al. , Phys Rev A 5, 487, 1972. b. Császár et al.
CH 3 NH 2 – Harmonic Frequencies Mode (A’) Pelegrini et al. a CCSD(T)/ AVQZ-f NH 2 s-str CH 3 d-str CH 3 s-str NH 2 scis CH 3 d-def CH 3 s-def CH 3 rock CN str NH 2 wag 3518 3091 3008 1669 1512 1463 1185 1075 858 3504 3080 2998 1666 1508 1461 1179 1067 853 Mode (A”) NH 2 a-str CH 3 a-def NH 2 twist CH 3 rock torsion Pelegrini et al. a CCSD(T)/ AVQZ-f 3601 3127 1528 1358 978 303 3587 3117 1526 1354 974 296 et al. , CPL 414, 495, 2005: cc-p. VXZ limit with CVTZ a. Pelegrini (rotation) (inversion)
CH 3 NH 2 – Fundamental Frequencies B 3 LYP AVDZ AVTZ AVQZ Mode (A’) w n w n NH 2 s-str CH 3 d-str CH 3 s-str NH 2 scis CH 3 d-def CH 3 s-def CH 3 rock CN str NH 2 wag -157 -153 -121 -33 -29 -18 -46 -27 -74 -158 -99 -163 132 -35 -10 -50 -26 132 -156 -72 -154 184 -34 5 -49 -26 92 CCSD(T)/ AVQZ-H(f) Experiment Error 3361 2961 2820 1623 1473 1430 1130 1044 780 -13 +47 +24 +227 +1 +36 0 -3 +165
CH 3 NH 2 – Fundamental Frequencies B 3 LYP AVDZ AVTZ AVQZ Mode (A’) w n w n NH 2 s-str CH 3 d-str CH 3 s-str NH 2 scis CH 3 d-def CH 3 s-def CH 3 rock CN str NH 2 wag -157 -153 -121 -33 -29 -18 -46 -27 -74 -158 -99 -163 132 -35 -10 -50 -26 132 -156 -72 -154 184 -34 5 -49 -26 92 CCSD(T)/ AVQZ-H(f) Experiment Error 3361 2961 2820 1623 1473 1430 1130 1044 780 -13 +47 +24 +227 +1 +36 0 -3 +165 4 A’ modes have well-behaved anharmonic shifts and small errors.
CH 3 NH 2 – Fundamental Frequencies B 3 LYP AVDZ AVTZ AVQZ Mode (A’) w n w n NH 2 s-str CH 3 d-str CH 3 s-str NH 2 scis CH 3 d-def CH 3 s-def CH 3 rock CN str NH 2 wag -157 -153 -121 -33 -29 -18 -46 -27 -74 -158 -99 -163 132 -35 -10 -50 -26 132 -156 -72 -154 184 -34 5 -49 -26 92 CCSD(T)/ AVQZ-H(f) Experiment Error 3361 2961 2820 1623 1473 1430 1130 1044 780 -13 +47 +24 +227 +1 +36 0 -3 +165 4 A’ modes have well-behaved anharmonic shifts and small errors. 5 A’ modes have ill-behaved anharmonic shifts and large errors.
CH 3 NH 2 – Fundamental Frequencies B 3 LYP AVDZ AVTZ AVQZ Mode (A”) w n w n NH 2 a-str CH 3 a-def NH 2 twist CH 3 rock torsion -170 -161 -34 -49 -29 -51 -168 -130 -53 -44 -20 -49 -161 -180 -44 -39 -15 -43 CCSD(T)/ AVQZ-H(f) Experiment Error 3427 2985 1485 1335 972 268 -1 +48 -3 -20 -13 -15
CH 3 NH 2 – Fundamental Frequencies B 3 LYP AVDZ AVTZ AVQZ Mode (A”) w n w n NH 2 a-str CH 3 a-def NH 2 twist CH 3 rock torsion -170 -161 -34 -49 -29 -51 -168 -130 -53 -44 -20 -49 -161 -180 -44 -39 -15 -43 CCSD(T)/ AVQZ-H(f) Experiment Error 3427 2985 1485 1335 972 268 -1 +48 -3 -20 -13 -15 4 A” modes have well-behaved anharmonic shifts and small errors. 1 A” mode has an ill-behaved anharmonic shift and large error. • Perturbation theory has difficulties treating some modes, but basis set analysis provides a diagnostic.
CH 3 NH 2 – Rotational Constants rotational constant or error (GHz) Ae re: CCSD(T)/AVQZ+CVDZ 104. 151 A 0 Be 22. 803 B 0 Ce 21. 926 C 0 Experimenta 103. 156 22. 169 21. 291 re: CCSD(T)/AVQZ+CVDZ we: CCSD(T)/AVQZ-f anh: B 3 LYP/AVQZ 103. 085 22. 543 21. 666 -0. 071 +0. 374 +0. 375 a. Ilyushin et al. , J Mol Spectrosc 229, 170, 2005.
CH 3 NH 2 – Barrier Heights barrier height (cm-1) rotation Takagi, J Phys Soc Jpn 30, 1145, 1971. . . . Kreglewski, J Mol Spectrosc 133, 10, 1989 …. …. 684. 1 718. 4 B 3 LYP/AVQZ ……. …………. . . CCSD(T)/AVQZ-f, g+CVDZ (zpe: B 3 LYP/AVQZ). . 507. 1 536. 2 inversion Tsuboi, J Mol Spectrosc 22, 272, 1967 …………. Sztraka, Acta Chim Hung 124, 865, 1987 ……… Kreglewski, J Mol Spectrosc 133, 10, 1989 …. …. 1688 2081 1943 B 3 LYP/AVQZ … …. …………. . . CCSD(T)/AVQZ-f, g+CVDZ (zpe: B 3 LYP/AVQZ). . 1082 1366
Concluding Remarks & Acknowledgments • This work predicted fundamental frequencies, rotational constants, and barrier heights for CH 3 NH 2: – Half of the ni’s are within 15 cm-1 of the experimental values, but others are poorly treated. – B 0 and C 0 are within 400 MHz of the experimental values. • Hopefully, predictions from variational methods will be better than those derived from perturbation theory and will be practical to perform within 1 -5 years on species with 7 atoms or more. • THANKS to Prof. Ben Mc. Call and Dr. Susanna Widicus. Weaver for a challenging problem and to Dr. Thom H. Dunning, Jr. for resources and financial support.
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