Advances in Physical Chemistry

Review Article

Potential Energy Surfaces Using Algebraic Methods Based on Unitary Groups

Table 3

Force constants for H2O. In the first column is indicated the order that should be considered in order to obtain the corresponding force constant.
Order Force constant This workaJensenb Halonen and Carrington Jr.c Lemus et al.d Ab initio e
1 𝛽 𝑠 / Å − 1 2.1573    2.053 2.1542 
1 𝐷 𝑠 / a J 0.8694  0.999 0.9050 
1 𝛽 𝑏 / Å − 1 0.8279   0.7296 
1 𝐷 𝑏 / a J 0.5190   0.7055 
1 𝑓 𝑟 𝑟 / a J Å − 2 8.093 8.4393 8.428 8.401 8 . 4 4 3
1 𝑟 2 𝑒 𝑓 𝜙 𝜙 / a J 0.652 0.7070 0.699 0.688 0 . 7 9 2 1
1 𝑓 𝑟 𝑟 ′ / a J Å − 2 −0.1571−0.1051−0.101−0.11 − 0.100
√ 1 / 𝜅 𝑟 𝑒 𝑓 𝑟 𝜙 / a J Å − 1 −1.0578 0.3064 0.219  0.2743
√ 1 / 𝜅 𝑓 𝑟 𝑟 𝑟 / a J Å − 3 −35.880−55.40−51.91  − 56.400
√ 1 / 𝜅 𝑟 𝑒 𝑓 𝑟 𝑟 ′ / a J Å − 2 −3.098−0.447 0.414  − 0.505
√ 1 / 𝜅 𝑓 𝑟 𝑟 𝑟 ′ 𝜙 / a J Å − 3 −0.358−0.318 0.645  − 0.076
1 𝑟 2 𝑎 𝑓 𝑟 𝜙 𝜙 / a J Å − 1 −2.6243−0.3383−0.314−0.51 − 0.3210
√ 1 / 𝜅 𝑟 𝑒 𝑓 𝑟 𝑟 𝜙 / a J Å − 2 21.442−0.252 1.341 −0.084
√ 1 / 𝜅 𝑟 3 𝑒 𝑓 𝜙 𝜙 𝜙 / a J −8.4312−0.7332−0.918  − 0.7482
1 𝑓 𝑟 𝑟 𝑟 𝑟 / a J Å − 4 130.87 306.0 248.7 275.39 3 3 8
1 𝑟 2 𝑒 𝑓 𝑟 𝑟 𝜙 𝜙 / a J Å − 2 −15.89−0.950−2.0 −15.699 − 0.28
1 𝑓 𝑟 𝑟 𝑟 𝑟 ′ / a J Å − 4 7.861 2.57  3.728 − 0 . 3 0
1 𝑟 2 𝑒 𝑓 𝑟 𝑟 ′ 𝜙 𝜙 / a J Å − 2 2.3910 0.1150 −0.632 0.62
1 𝑓 𝑟 𝑟 𝑟 ′ 𝑟 ′ / a J Å − 4 − 9.843 1.93−12.68 0.52
1 𝑟 4 𝑒 𝑓 𝜙 𝜙 𝜙 𝜙 / a J 23.349 −0.238 −0.1 2.32 − 0.74
√ 1 / 𝜅 𝑟 𝑒 𝑓 𝑟 𝑟 𝑟 𝜙 / a J Å − 3 − 100.98 −6.14   − 1.2
√ 1 / 𝜅 𝑟 𝑒 𝑓 𝑟 𝑟 𝑟 ′ 𝜙 / a J Å − 3 3.5584 −3.22  0.2
√ 1 / 𝜅 𝑟 3 𝑒 𝑓 𝑟 𝜙 𝜙 𝜙 / a J Å − 1 8.955 0.87   0.648
aFrom [58]. bFrom [138]. cFrom [109]. dFrom [57]. eFrom [139].