2.2 Chemical Bonds
25
Table 2.6 Hydrogen bond with the bond strength E and its decomposition obtained by HF/4-31G.
Energies are in kcal/mol
Proton donor
X–H
Proton acceptor Y R (X · · · Y)
(in Å) a
E
ES
EX PL
CT
MIX
FH
NH 3
2.68
−16.3 −25.6 16.0 −2.0 −4.1 −0.7
FH
OH 2
2.62
−13.4 −18.9 10.5 −1.6 −3.1 −0.4
HOH
NH 3
2.93
−9.0 −14.0
9.0 −1.1 −2.4 −0.4
HOH
OH 2
2.88
−7.8 −10.5
6.2 −0.6 −2.4 −0.5
FH
FH
2.71
−7.6
−8.2
4.5 −0.4 −3.2 −0.3
H 2 NH
NH 3
3.30
−4.1
−5.7
3.6 −0.6 −1.3 −0.2
H 3 CH
NH 3
4.02
−1.1
−0.6
0.5 −0.3 −0.7 −0.0
Adapted with permission from Morokuma (1977). Copyright 1977 American Chemical Society
See text as to the decomposition expressions
a All the (X − H · · · Y) bonds are linear
Weak bonds such as H-bond are often analyzed by energy decomposition into
various ingredients so as to understand the “hidden” nature of the bonds. The way
of decomposition is not unique but the most popular one seems to come from
Morokuma’s work (Kitaura and Morokuma 1976; Morokuma 1977) by decomposing
the interaction energy into electrostatic (ES), exchange repulsion (EX), polarization
(PL), charge transfer (CT), and higher order coupling (MIX) energies in terms of
employment of the intermediary wavefunctions. Examples of the energy decomposition as to the interaction energy of H-bond are also listed in Table 2.6. The ES term
is either repulsive or attractive in general and it originates in electrostatic interaction between the two moieties involving, respectively, X–H and Y under undistorted
electron distribution without formation of the H-bond. In the H-bond ES becomes
mostly negative signifying an attractive electrostatic interaction. The EX term signifies contribution from electron exchange between the undistorted two moieties. Value
of EX is always repulsive and is also mentioned exchange repulsion term. The PL
term comes from the polarization representing distortion of electron distribution in
a moiety under influence of another one and vice versa without electron exchange.
This distortion is caused by electron excitation from the occupied MO to the unoccupied MO within the same moiety accompanied with charge distortion therein. The
PL term causes a slight stabilization and hence its value is slightly negative. The CT
term originates in electron delocalization from a moiety to another, the phenomenon
of which is called charge transfer. The CT is associated with the electron transfer
from the occupied MO of one moiety to the unoccupied MO of the other. The CT term
always results in energetical stabilization and hence its value is negative. The MIX
term summarizes the difference of the total interaction energy and the summation
of the decomposed energies mentioned above, and it involves all the other coupling
term of various components. The absolute value of the MIX term is not large in
general. It is seen from Table 2.6 contribution from ES is generally the largest and
25
Table 2.6 Hydrogen bond with the bond strength E and its decomposition obtained by HF/4-31G.
Energies are in kcal/mol
Proton donor
X–H
Proton acceptor Y R (X · · · Y)
(in Å) a
E
ES
EX PL
CT
MIX
FH
NH 3
2.68
−16.3 −25.6 16.0 −2.0 −4.1 −0.7
FH
OH 2
2.62
−13.4 −18.9 10.5 −1.6 −3.1 −0.4
HOH
NH 3
2.93
−9.0 −14.0
9.0 −1.1 −2.4 −0.4
HOH
OH 2
2.88
−7.8 −10.5
6.2 −0.6 −2.4 −0.5
FH
FH
2.71
−7.6
−8.2
4.5 −0.4 −3.2 −0.3
H 2 NH
NH 3
3.30
−4.1
−5.7
3.6 −0.6 −1.3 −0.2
H 3 CH
NH 3
4.02
−1.1
−0.6
0.5 −0.3 −0.7 −0.0
Adapted with permission from Morokuma (1977). Copyright 1977 American Chemical Society
See text as to the decomposition expressions
a All the (X − H · · · Y) bonds are linear
Weak bonds such as H-bond are often analyzed by energy decomposition into
various ingredients so as to understand the “hidden” nature of the bonds. The way
of decomposition is not unique but the most popular one seems to come from
Morokuma’s work (Kitaura and Morokuma 1976; Morokuma 1977) by decomposing
the interaction energy into electrostatic (ES), exchange repulsion (EX), polarization
(PL), charge transfer (CT), and higher order coupling (MIX) energies in terms of
employment of the intermediary wavefunctions. Examples of the energy decomposition as to the interaction energy of H-bond are also listed in Table 2.6. The ES term
is either repulsive or attractive in general and it originates in electrostatic interaction between the two moieties involving, respectively, X–H and Y under undistorted
electron distribution without formation of the H-bond. In the H-bond ES becomes
mostly negative signifying an attractive electrostatic interaction. The EX term signifies contribution from electron exchange between the undistorted two moieties. Value
of EX is always repulsive and is also mentioned exchange repulsion term. The PL
term comes from the polarization representing distortion of electron distribution in
a moiety under influence of another one and vice versa without electron exchange.
This distortion is caused by electron excitation from the occupied MO to the unoccupied MO within the same moiety accompanied with charge distortion therein. The
PL term causes a slight stabilization and hence its value is slightly negative. The CT
term originates in electron delocalization from a moiety to another, the phenomenon
of which is called charge transfer. The CT is associated with the electron transfer
from the occupied MO of one moiety to the unoccupied MO of the other. The CT term
always results in energetical stabilization and hence its value is negative. The MIX
term summarizes the difference of the total interaction energy and the summation
of the decomposed energies mentioned above, and it involves all the other coupling
term of various components. The absolute value of the MIX term is not large in
general. It is seen from Table 2.6 contribution from ES is generally the largest and