3.6 Hints for Calculations
151
Q9: How can TS and IRC be obtained?
A9: The procedure to search for the transition state (TS) is generally associated with
that for the structural optimization of molecules. For TS finding is to examine the col
(saddle point) having the local maximum of energy profile (on the potential surface)
along the reaction coordinate assigned by the user. It is noted that, however, the TS
has only one imaginary frequency of the normal vibration suggesting the direction of
molecular deformation leading to the reaction product. This saddle point is equal to
the TS. Hence, that at the saddle point the molecular vibration has only one imaginary
frequency.
The potential energy barrier at the TS setting that of the reactant(s) as zero is
normally estimated to be higher than that found by the experimental estimation. In
this sense, one ought to select the calculation method that can afford the quantitative
energy of the molecular species including also the TS state as much as possible.
The intrinsic reaction coordinate (IRC) is obtained as two routes: one is from the
TS to the product(s) and another to the reactant(s) utilizing the formula defining the
IRC on which the steepest descent path is guaranteed down from the TS. The actual
calculation is performed at finite (discrete) numbers of points on each IRC, so one
has to be careful not to stray off the intrinsic path.
References
C. Adamo, V. Barone, J. Chem. Phys. 110, 6158–6170 (1999)
B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31, 459–466 (1959)
J. Antony, S. Grimme, Phys. Chem. Chem. Phys. 8, 5287–5293 (2006)
C.W. Bauschlicher Jr., H. Partridge, J. Chem. Phys. 103, 1788–1791 (1995)
A.D. Becke, Phys. Rev. A 38, 3098–3100 (1988)
A.D. Becke, J. Chem. Phys. 98, 5648–5652 (1993)
A. D. Becke, J. Chem. Phys. 107, 8554-8560 (1997)
R.C. Bingham, M.J.S. Dewar, D.H. Lo, J. Am. Chem. Soc. 97, 1285–1293 (1975)
S.F. Boys, F. Bernardi, Mol. Phys. 19, 553–566 (1970)
J.-D. Chai, M. Head-Gordon, J. Chem. Phys. 128(084106), 1–15 (2008a)
J.-D. Chai, M. Head-Gordon, Phys. Chem. Chem. Phys. 10, 6615–6620 (2008b)
J. ˇ
Cížek, J. Chem. Phys. 45, 4256–4266 (1966)
A.J. Cohen, P. Mori-Sánchez, W. Yang, Chem. Rev. 112, 289–320 (2012)
E.U. Condon, Phys. Rev. 36, 1121–1133 (1930)
L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople, J. Chem. Phys. 94, 7221–7230 (1991)
J. Del Bene, H.H. Jaffé, J. Chem. Phys. 50, 1126–1129 (1969)
G. Del Re, J. Ladik, G. Biczó, Phys. Rev. 155, 997–1003 (1967)
R. Ditchfield, W.J. Hehre, J.A. Pople, J. Chem. Phys. 54, 724–728 (1971)
T.H. Dunning, J. Chem. Phys. 90, 1007–1023 (1989)
J. Frenkel, Wave Mechanics: Advanced General Theory (Clarendon Press, Oxford, 1934)
D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd
edn. (Academic Press, San Diego, 2001)
K. Fukui, Acc. Chem. Res. 4, 57–64 (1971)
K. Fukui, T. Yonezawa, H. Shingu, J. Chem. Phys. 20, 722–725 (1952)
W.A. Goddard III, L.M. Harding, Ann. Rev. Phys. Chem. 29, 363–396 (1978)
151
Q9: How can TS and IRC be obtained?
A9: The procedure to search for the transition state (TS) is generally associated with
that for the structural optimization of molecules. For TS finding is to examine the col
(saddle point) having the local maximum of energy profile (on the potential surface)
along the reaction coordinate assigned by the user. It is noted that, however, the TS
has only one imaginary frequency of the normal vibration suggesting the direction of
molecular deformation leading to the reaction product. This saddle point is equal to
the TS. Hence, that at the saddle point the molecular vibration has only one imaginary
frequency.
The potential energy barrier at the TS setting that of the reactant(s) as zero is
normally estimated to be higher than that found by the experimental estimation. In
this sense, one ought to select the calculation method that can afford the quantitative
energy of the molecular species including also the TS state as much as possible.
The intrinsic reaction coordinate (IRC) is obtained as two routes: one is from the
TS to the product(s) and another to the reactant(s) utilizing the formula defining the
IRC on which the steepest descent path is guaranteed down from the TS. The actual
calculation is performed at finite (discrete) numbers of points on each IRC, so one
has to be careful not to stray off the intrinsic path.
References
C. Adamo, V. Barone, J. Chem. Phys. 110, 6158–6170 (1999)
B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31, 459–466 (1959)
J. Antony, S. Grimme, Phys. Chem. Chem. Phys. 8, 5287–5293 (2006)
C.W. Bauschlicher Jr., H. Partridge, J. Chem. Phys. 103, 1788–1791 (1995)
A.D. Becke, Phys. Rev. A 38, 3098–3100 (1988)
A.D. Becke, J. Chem. Phys. 98, 5648–5652 (1993)
A. D. Becke, J. Chem. Phys. 107, 8554-8560 (1997)
R.C. Bingham, M.J.S. Dewar, D.H. Lo, J. Am. Chem. Soc. 97, 1285–1293 (1975)
S.F. Boys, F. Bernardi, Mol. Phys. 19, 553–566 (1970)
J.-D. Chai, M. Head-Gordon, J. Chem. Phys. 128(084106), 1–15 (2008a)
J.-D. Chai, M. Head-Gordon, Phys. Chem. Chem. Phys. 10, 6615–6620 (2008b)
J. ˇ
Cížek, J. Chem. Phys. 45, 4256–4266 (1966)
A.J. Cohen, P. Mori-Sánchez, W. Yang, Chem. Rev. 112, 289–320 (2012)
E.U. Condon, Phys. Rev. 36, 1121–1133 (1930)
L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople, J. Chem. Phys. 94, 7221–7230 (1991)
J. Del Bene, H.H. Jaffé, J. Chem. Phys. 50, 1126–1129 (1969)
G. Del Re, J. Ladik, G. Biczó, Phys. Rev. 155, 997–1003 (1967)
R. Ditchfield, W.J. Hehre, J.A. Pople, J. Chem. Phys. 54, 724–728 (1971)
T.H. Dunning, J. Chem. Phys. 90, 1007–1023 (1989)
J. Frenkel, Wave Mechanics: Advanced General Theory (Clarendon Press, Oxford, 1934)
D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd
edn. (Academic Press, San Diego, 2001)
K. Fukui, Acc. Chem. Res. 4, 57–64 (1971)
K. Fukui, T. Yonezawa, H. Shingu, J. Chem. Phys. 20, 722–725 (1952)
W.A. Goddard III, L.M. Harding, Ann. Rev. Phys. Chem. 29, 363–396 (1978)