3478
J. Phys. Chem. 1995, 99, 3478-3486
A Simple Functional Representation of Angular-Dependent Hydrogen-Bonded Systems. 1. Amide, Carboxylic Acid, and Amide-Carboxylic Acid Pairs Kyoung Tai No,*st Oh Young Kwon, and Su Yeon Kim D e p a m e n t of Chemistry, Soong Si1 University, Sang Do 5 Dong 1-1, Dong Jak Gu, Seoul, 156-743, Korea
Mu Shik Jhont Department of Chemistry, Korea Advanced Institute of Science and Technology, 373-1 Kusung-dong Yusung-gu, Taejon 305-701, Korea
Harold A. Scheraga* Baker Laboratory of Chemistry, Cornel1 University, Ithaca, New York, 14853-1301 Received: September 19, I994@
For describing the angular dependence of the energy of hydrogen bonds, especially for amide, carboxylic acid, and amide-carboxylic acid molecular pairs, four interatomic distances are used instead of the conventional internal coordinates (the hydrogen bond distance, two bond angles, and one dihedral angle). With the new representation, the angular dependence of the energy of hydrogen bonds can be well described with only 6-12 type potential functions without additional functions involving bond or dihedral angles. In the new model, the repulsion between 1-3 atomic pairs proved to be the most important for describing the angular dependence of the energy of hydrogen bonds. The parameters of these empirical hydrogen bond potential functions were optimized with the 6-3 1G** ab initio potential energy surfaces of 11 hydrogen-bonded molecular pairs. The empirical potential functions reproduce the a b initio potential surfaces very well.
Introduction Hydrogen bonds in biological systems, especially the N - H - 0 4 and O-H-O=C pairs, play a central role in determining the structure and activity of biomolecules.1-3 For this reason, many hydrogen bond potential functions have been proposed for conformational and energetic studies of such molecules.4-19 Some of the potential functions were determined by using crystal structures and heats of sublimation of molecular crystals containing hydrogen bonds. Statistical analysis of the geometrical parameters of hydrogen bonds, viz., the distribution of hydrogen bond lengths and bond angles in molecular crystals, shows that both the bond length and bond angle are very dependent on the e n ~ i r o n m e n t . * ~Both - ~ ~ bond length and bond angle work cooperatively and depend on the environment in which they are located. In crystals, the hydrogen bond lengths, m in the X-H-A-B system, are compressed or expanded up to 20% from their equilibrium distances, compared with an average hydrogen bond length. Since the bond lengths, m, m, and QH, and the bond angles, especially 0- and O w , work cooperatively in determining the hydrogen bond energy, all of these geometrical parameters must be involved in a description of a hydrogen bond potential energy function. McGuire et aL7 suggested that a general hydrogen bond (GHB) function, with no special angular dependence, could reproduce the angular dependence when combined with other components of a nonbonded potential function. More recent calculations, however, have suggested that the GHB function may have to be augmented by a specific angular-dependent term. Two dipoles in a hydrogen-bonded system, Le., the X-H bond dipole and the A-B bond dipole, tend to be collinear. This tendency is partly responsible for the stability of linear hydrogen bonds. Therefore, without a O m term in the potential function, Member of the Center for Molecular Science, Korea. @Abstractpublished in Advance ACS Abstracts, February 15, 1995.
0022-365419512099-3478 $09.00/0
a linear hydrogen bond is stable. Several hydrogen bond potential functions have been proposed in the hope that the dipole-dipole interaction could account for most or all of the hydrogen-bonding structure and energy. In the case of h4M2,11 for example, about 1-3 kcallmol is not accounted for by the dipole-dipole interaction. Also, the dependence of the hydrogen bond energy on OXHA or O m cannot be accounted for by the dipole-dipole interaction. Some investigators3J do supplement the hydrogen bond interaction with a specific function and m,or to m,m,and O m . Hagler related to m,to et al. proposed an angular-dependent hydrogen bond potential function for amides using an attenuating function,6aA@);the Lennard-Jones interactions between N and 0, and between H and 0, are attenuated so that, for a “perfect” hydrogen bond, the nonbonded interaction becomes zero. Lippincott and Schroedefi-Cproposed a linear hydrogen bond model for the 0-H-0 hydrogen bond system. In this model, the hydrogen atom is located along the line of centers of the two oxygen atoms and the covalent bond length rO-H and the weak -0 bond length work cooperatively. The van der Waals repulsion between the two oxygen atoms also plays an important role in describing the hydrogen bond. This model was extended and reparametrized by Van Zandt and Schrol14 and by Schroll et al.& It must be pointed out that repulsion between the electronegativeatoms, e.g., 0-0, in a hydrogen-bonded system, is very important for describing the potential energy surface. The purpose of this work is to develop a simple hydrogen bond potential function that is a good representation of its potential energy surface, especially its angular dependence. In our new hydrogen bond model, an explicit angular-dependent function is not included. The energy calculated with the new hydrogen bond model is balanced with the other energy components, electrostatic and nonbonded energies, which were calculated with the methods that we developed earlier.32s33 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 11, 1995 3479
Angular-Dependent Hydrogen-Bonded Systems
(qsq
TABLE 1: Hydrogen-Bonding Pairs Investigated in This Study
A
rm
amide-amide dimer
acid-acid dimer
amide-acid dimer ~
bm, rm
exm
b
X
H
Figure 1. Coordinate system,
~~
formamide-formamide formic acid-formic acid" acetamide-acetic acidb formamide-acetamide formic acid-acetic acid" acetamide-acetamide acetic acid-acetic acid"
Oxm, & M I , and usually used to describe the hydrogen bond system. HA
&C-IAB,
which is
Both open-chain and cyclic types were investigated. Two types of hydrogen bond exist in the acetamide-acetic acid dimer, viz., 0-H-O=C (dimer 1) and N-H-O-C (dimer 2).
TABLE 2: Atomic Species Included in the Description of the Hydrogen Bond Potential classification in ECEPPl2
description
X
H
riM
Figure 2. Coordinate system, m,m,~ B H ,and ~XB,which is introduced in this work for describing the hydrogen bond. 6
I
amide hydrogen hydrogen in COzH carbonyl carbon in carboxylic group carbonyl carbon in amide carbonyl oxygen in carboxylic group carbonyl oxygen in amide sp3 oxygen in CO2H nitrogen in amide
TABLE 3: Sampled Conformations of Each Hydrogen Bond Pair for the ab Initio Calculation of the Potential Energy Surface A?&
hydrogen-bonded pair
interatomic distance (A)
formamide-formamide formamide-acetamide acetamide-acetamide formic acid-formic acidd formic acid-formic acid'
1.6-2.7,O.l 1.8-2.6.0.2 1.6-2.6,0.2 1.6-2.6,0.2 1.7-2.3.0.2
formic acid-acetic acidd formic acid-acetic acid' acetic acid-acetic acidd
1.8-2.6,0.2 1.7-2.3.0.2 1.8-2.6,0.2
acetic acid-acetic acid' acetamide-acetic acidf
1.7-2.3,0.2 1.5-2.5,0.1
acetamide-acetic acidg
1.8-2.8,0.1
ODHA,
hH.4,
A&-' (deg)
A@ (deg)
30-150, 10 30-150,20 30-150,20 30-150, 15 60-150, 15 50-140, 15 30-150, 15 60-150, 15 60-150, 15 30-150, 15 60-150, 15 70-130, 15 63-133, 15 123-183, 15 115-190, 15
30-150, 15 30-150,20 30- 150, 20 30-150, 15 45-135, 15 30-150, 15 45-135, 15 30-150, 20 45-135, 15
Ar, AO, and A 4 represent the grid intervals of r, 0, and 4, respectively. Where the dummy atom D was defined in order that the angle DHX becomes 90°,Figure 4. ~ ~ D H A BA, 4 (in deg) was 0- 180, 30 in all cases. Open-chain conformation. e Cyclic conformation. f 0-H-O=C type conformation. 8 N-H-O=C type conformation. "0
0.5
1
1.5
2
2.S0
3
3.5
interatomic distance (A) Figure 3. Distributions of interatomic distances in hydrogen-bonded systems, taken from experimental crystal structures: (a, top) amideamide pairs. (b, bottom) carboxylic acid-carboxylic acid pairs. In (b), rOH represents the covalent 0-H bond distance and THO represents the hydrogen bond length.
Model Figure 1 shows the geometric parameters for describing the hydrogen-bonded system, X-H-A-B, e.g., N-H-O=C. If the covalent bond distances, ~ X Hand rm, are fixed, then only four degrees of freedom remain, viz., m, 8xm, 8HAB, and b. The geometrical parameters shown in Figure 2 can also be used to describe the configuration of a hydrogen-bonded system. Like the coordinate system of Figure 1, it also has , TXB. For a four degrees of freedom, QIA, ~ X A , m ~ and description of the hydrogen bond potential energy surface with a potential function that includes 8's and 4, the coordinate system of Figure 1 must be used; such a potential energy function is described with the four geometrical parameters.
VHB = A ~ H A ' ~ x H A ' ~ H A B ' ~ x H A B )
(1)
This hydrogen bond potential energy surface, defined by VHB of eq 1, can also be described by the coordinate system of Figure 2.
In order to use the approximation of the additivity of effective two-body potentials, the following form is introduced.
V1-4
= hxB(rxB)
(3c)
where the subscript k represents one of the atomic pairs and the corresponding interatomic distances, QIA. %A, OH, and ~ X B .
No et al.
3480 J. Phys. Chem., Vol. 99, No. 11, I995 Acetamide dimer
Formamide dimer
Formic acid dimer (open-chain)
Formic acid dimer (cyclic)
M
W
Acetamide-Formamidedimer
Acetic acid dimer (open-chain)
Acetic acid-Formic acid dimer (open-chain)
Acetic acid dimer (cyclic)
Acetic acid-Formic acid dimer (cyclic)
%lI.O,Cl.cO
aww
Acetamide-Aceticacid dimer I
RILO,C,*O
Acetamide-Aceticacid dimer 2
n W 4 e Ndl@f+lM.O
Figure 4. Hydrogen-bonded dimers investigated in this work (a) amide dimer; (b) carboxylic acid dimer in the open-chain conformation; (c) carboxylic acid dimer in the cyclic conformation; (d) amide-carboxylic acid dimer, which forms an 0-H-0-C hydrogen bond, dimer 1; and (e amide-carboxylic acid dimer, which forms an N-H-O% hydrogen bond, dimer 2.
Since the functional form of eq 3 is simple and the coordinate system of Figure 2 spans the whole conformational space of the hydrogen-bonding system, we introduce eq 3 to describe such a system and use the following 1-6-12 type function to compute its energy.
or
where rzm is the value of rk at the minimum.
The function Vm contains the r-l, r-6, and r-I2 terms, but no explicit angular-dependent function. As mentioned in the Introduction, the geometrical parameters m and m~ play important roles in describing the potential energy surface. In hydrogen-bonded molecular crystals, the variations of the distances ~ X Aand m~ are smaller than that of m, and ~ X A , m,and ~ B Hbecome important quantities determining whether a hydrogen bond is formed or not. Therefore, in addition to m, the two geometrical parameters ~ X Aand m~ are also important for describing the potential surface. In Figure 3, the experimental probability distributions of IZ[H, m,and m,taken from X-ray data on molecular crystals, are plotted for both amides and carboxylic acids. Since the geometrical parameters
J. Phys. Chem., Vol. 99, No. 11, 1995 3481
Angvlar-Dependent Hydrogen-Bonded Systems
TABLE 4: Optimized Parameters of the Hydrogen Bond Potential Energy Function interacting conformations atomic pairs" D; E; €y 2 690 158.2 2.325 976 358 412.2 0.043 262 468 118.70 0.013 7 516 288.3 2.764 491 722 318.9 0.052 245 891 118.7 0.014 4.186 2 470 203.4 318.9 0.141 180 790 0.017 211 238 118.7 3.519 10 288 380.5 0.061 418 988 318.9 0.015 241 139 118.7 2.790 98.4 867 0.032 412.2 1 328 720 0.015 118.7 235 682
rtHB(A) 1.80 4.10 4.05 1.95 3.82 4.01 1.70 3.23 3.91 1.95 3.71 3.99 1.61 4.31 3.98
Ekd"
4 (A)
0.138 0.187 0.102 0.135 0.213 0.100 0.135 0.213 0.100 0.135 0.213 0.100 0.138 0.187 0.102
2.69 3.22 2.89 2.70 3.01 2.90 2.70 3.01 2.90 2.70 3.01 2.90 2.69 3.22 2.89 a The atom types are described in Table 2. In kcal AIz/mol. In kcal A6/mol. In kcdmol. e The depth of the nonbonded potential of the kth atomic pair. f The minimum energy distance of the nonbonded potential of the kth atomic pair.
TABLE 5: ODtimized Dimer Conformations Calculated with Various Potential Enerw Functions potential energy conformations functions ro-n (A) e m (deg) (de@ 4xHAB (deg) Am-Am ab initio 2.10 172.09 157.21 180.00 - 14.80 CVFF" 1.99 168.00 130.87 AMBER" 1.87 168.23 172.62 -4.70 ECEPP/2 1.89 165.45 172.27 180.00 this work 1.96 169.21 163.96 180.00 Ac-Ac (open chain) 1.98 162.89 132.84 180.00 1.69 179.30 124.30 66.90 5.06 1.85 171.52 119.19 1.67 179.92 154.40 180.00 1.98 171.22 128.17 180.00 Ac-Ac (cyclic) 1.87 177.32 132.14 0.00 1.70 171.68 135.62 0.00 1.84 167.11 143.64 0.00 1.67 175.66 156.57 180.00 1.71 173.49 147.69 180.00 Am-Ac dimer lb 1.88 170.01 136.95 179.43 - 171.50 1.69 176.67 125.92 1.84 171.60 126.65 -1.60 1.91 178.08 148.10 180.00 1.94 174.85 144.20 180.03 Am-Ac dimer 2c 2.18 176.74 152.78 180.00 1.98 175.31 148.31 180.00 1.88 164.08 172.48 0.00 2.66 164.83 164.55 180.00 2.10 176.74 152.77 180.00 ~~~
(1
~~~~
~
Calculated with DISCOVER Ver. 3.1 For 0 - H - 0 4 hydrogen bond pairs, Figure 4d. For N-H-O%
and are strongly c o ~ p l e d ~in~the - ~ description of the potential energy surface of the hydrogen bond, the functional form of the hydrogen bond potential is complicated if both geometrical parameters are introduced as variables. For a simple functional ex ression, we have fixed ~-XHat the optimum bond length, 0.99 for amides and 0.95 A for carboxylic acids.
!.
~~
E- (kcal/mol) -6.22 -3.83 -6.94 -4.88 -6.99 -6.74 -5.95 -2.67 -8.05 -6.54 -15.33 -11.18 -11.77 -9.60 -12.57 -10.37 -7.87 -7.89 -10.12 -9.15 -4.45 -4.43 -5.69 -2.13 -4.43
hydrogen bond pairs, Figure 4e.
The potential parameters were determined with eq 6 so that the empirical potential functions could reproduce the ab initio potential energy surfaces well at every configuration. The stationary points, especially the global mininum, in the parameter space that satisfy the following conditions were obtained.
Computations In this work, the hydrogen bond potential function for three types of hydrogen bonds will be investigated. These are amideamide, carboxylic acid-carboxylic acid, and amide-carboxylic acid. In Table 1, the hydrogen-bonding molecular pairs investigated in this work are summarized. In Table 2, the atomic species in these hydrogen-bonding systems are classified. For the calculation of the potential energy surfaces, ab initio molecular orbital calculations were carried out with the 6-3 1G** basis set34at several conformations for each hydrogen-bonding molecular pair. In Table 3, the sampling points are summarized for each molecular pair. Figure 4 shows the geometries of the dimers, which were optimized with the 6-31G** basis set, starting with the X-ray geometry.
where j31 and {Pj} represent the lth potential parameters and a set of potential parameters to be optimized (Bk's and Dk'S), respectively. Qi, VBb(Qi), and V(Qi,{&}) represent the ith conformation, the ab initio energy at Qi, and the calculated energy from the empirical potential energy function at Qi, respectively. The dimer energy V(Qi,{Pj})was expressed as follows.
where Vm and Vel represent the nonbonded and electrostatic
No et al.
3482 J. Phys. Chem., Vol. 99, No. 11, 1995
-Electrostatic Energy
or---
/!
1-2 pair Energy 1-3 pair Energy -.-Total Energy .*I..’.
--
4
h
10-
: d Y
w
_ _-.#*-;__j/’’ ---
... .......................,, ... I.
I....
-,,< ..........................
.---_---
=HC
Figure 5. Repulsive cores, UNO and UHC, of the 1-3 atomic pairs for the N-H-O--C hydrogen-bonded system.
t
interactions between the two interacting molecules. These do not include the atom pairs that are included in the Vm expression (e¶ 4).
180 190 200 210 220 230 240 250 260 270
N-H...0 angle (degree) Figure 6. Energy components of the N-H-O% hydrogen-bonded system, Vel, VI-2, VI-3, and V+,,plotted against the variable hydrogen bond angle, emo. In the computation, the hydrogen bond length ~ H O was fmed at 2.06 8, (vertical dashed lines in Figure 7).
It was assumed that the net atomic charges are located at the atomic centers, and they were calculated with the M-PEOE method. The point charges calculated with the M-PEOE method give good dipole moments and reproduce the electrostatic potentials obtained from ab initio molecular orbital calculations with the 6-31G** basis set very well.32
0.. IJ = r92lJ6
(9a)
6-12 type functions were used for the nonbonded interactions, and the Cii’s were calculated with the Slater-Kirkwood f0rmula3~~
where the effective atomic polarizabilities ai of atoms i were calculated with the charge-dependent effective atomic polarizability (CDEAP) method proposed by No et al.33bN represents the number of effective electrons, and the other symbols have their usual meaning. The Aii’s (or ai))were determined from crystal packing studies.35 The following relations are used to convert from (A, 0 to (f,
€1: 0 12 Aii = eii(rii)
(11)
0 6 Cii= 2eii(rii)
(12)
ri was obtained as the arithmetic mean of r: and obtained as the geometric mean of ~ i and i Cjj. r: = (ri
+ r3/2
ri, and €0 was (13)
Results and Discussion In Table 4, the potential parameters for VHBare summarized for amides, carboxylic acids, and amide-carboxylic acid pairs.
Bk and Dk were determined for both the 1-2 and 1-3 terms of VHB, viz. and by the optimization procedure of eq 6. for the atomic pairs located at Since the Bk’s and Dk.s of 1-4 positions, N3-C4, 03-C3, 03HB’sof the terms are larger than ri, the equilibrium distance of the nonbonded potential of atomic pair k, except for 0 3 - 0 1 of the cyclic carboxylic acid form. In the case of the cyclic carboxylic acid dimer, four oxygen atoms are crowded into a small area, and the large 1-3 r>HBwill break the cyclic conformation. The last two columns of Table 4 show the minimum energy and the equilibrium separation of the nonbonded potential function for the atom pair k. The r:HB’s of the 1-3 H-C pairs, H2 r&, (cf. r:= in Table 4 with r0-H in Table 5 ) ; e.g., for Am-Am, r:HB = 1.80 A and ~O-H= 1.96 A. Since the cyclic dimer is not frequently found in biomolecules, the parameters obtained for the open-chain dimer will be used in subsequent papers. The minimum energy structures of the dimers were calculated with the 6-31G** ab initio molecular orbital theory and with the CVFF,6 Ah4BER,14 ECEPP/2,36 and our new potential
e3e4
e3
1
e3,
rg
rE;
J. Phys. Chem,, Vol. 99, No. 11, 1995 3483
Angular-Dependent Hydrogen-Bonded Systems
1
P
-0
P
Y
v
s
B
CD
CD
2.1
2.4
2.7
rHo 270-
249
3.0
-L 3.3
3.3
(A) 270
7
-
s
240
I
20-
1 3
20
1P
18)-
v
B
CD
150
CD
-
150
I
120-
90-
1 .a
i
2.1
1 2.4
2.7
120
3.0
3.3
sn --
1.8
2.1
2.4
2.7
3.0
3.3
fHo (A) rHo (A) Figure 7. Contours of the energy components of the N-H-O% hydrogen-bonded system, Vel, 111-2, VI-3, and Vtot,mapped on the ~ 0 - 0 ~plane 0 (a, top left). Electrostatic energy, (b, bottom left) VI-2, (c, top right) VI+, and (d, bottom right) VtOt= Vel VI-2 VI-3.
+
functions, and the results are summarized in Table 5 . For CVFF and AMBER, the computer simulation software DISCOVER version 3.1 was used. During the optimization of the dimer geometry, the structures of the monomers were fixed at their minimum energy conformation of each force field. Since the physical basis of each of these potential functions differs, a simple comparison of the optimized conformation does not have much meaning. Figure 5 shows the repulsive cores, u's, of N-O and H-C at the equilibrium position for the N-H-O=C hydrogen-bonded system. The hydrogen atom is located inside the repulsive core of the H-C 1-3 potential, and the oxygen atom is located inside the repulsive core of the N-0 1-3 potential. The equilibrium is larger than by 0.16 8,for hydrogen bond distance, is 1.96 A. The vi-3 the amide dimer; r:? is 1.80 A and and Vi-2 terms work in opposite directions in locating the equilibrium hydrogen bond distance, cg. The energy components, VI-?, Vi-3, and Vel, of the hydrogenbonded system N-H-O=C are plotted in Figure 6. roH was
e,
rg
r:p
+
e,
fixed at its equilibrium distance, of the open-chain conformation, and the angle N-H-O, Omo, was scanned from 180" to 270". The curves correspond to the planar sections of Figure 7 indicated by the dashed lines at mo = 2.06 A. The magnitudes of VI-2 (VHO), which are commonly regarded as the hydrogen bond potential, remain constant because mo is fixed and Vel favors the linear hydrogen bond, but the slope, aVel/aO"o, is too small to describe the rapid change of the hydrogen bond energy as Om0 changes. VI-3 is the term that is primarily responsible for the stability of the linear hydrogen bond. Therefore, the model that introduces the Vi-3 terms into Vm for the description of the angular dependence is physically realistic. In Figure 7, the contour maps of (a) Vel (b) VI-2, (c) VI-3, and (d) Vel Vi-2 VI-3 are drawn for the N - H - O e hydrogen-bonded system, in which only these four atoms are considered for the acetamide dimer. The electrostatic energy favors the linear hydrogen bond but the slope is too small, even in the repulsive region (Figure 7a). VI-2 does not show any
+
+
No et al.
3484 J. Phys. Chem., Vol. 99,No. 11, 1995
1
--This work
-Abinitio
15
3
2
Hydrogen Bond Length
-10
'
15
35
4
(A)
15
2
2s
1
3
Hydrogen Bond Length
35
4
(A)
' '
2
5.2
3
Hydrogen Bond Length
35
4
(A)
Figure 8. Potential energy curves plotted as a function of the hydrogen bond length: (a) acetamide dimer (top left); (b) acetic acid open-chain dimer (bottom left); (c) acetamide-acetic acid, dimer 1 (0-H-0-C type; top right); and (d) acetamide-acetic acid, dimer 2 (N-H-0type; bottom right). All the other geometrical parameters were fixed at their equilibrium values, given in Figure 4.
angular dependence (Figure 7b). Vi-3 is the main source of the angular dependence (Figure 7c). The shape of the linear hydrogen bond potential energy surface (Figure 7d) is quite similar to Figure 7c. By adding Vel and VI-2 (Figure 7a,b) to Figure 7c, the contours (Figure 7d) become denser and steeper. It is clearly evident again that the 1-3 terms contribute the most to the angular dependence of the hydrogen bond potential. Therefore, the fine tuning of the parameters in Vi-3 is the most important step in describing the angular dependence of the potential energy surfaces. The potential energy curves of Figure 8 were obtained by varying the hydrogen bond distances, m,from their equilibrium values, while all the other geometrical parameters (given in Figure 4) were fixed. The equilibrium hydrogen bond distance, g, is sensitive to both VI-2 and v1-3 (these two terms work in the opposite direction in locating E).As shown in Figure
8a, calculated with our new potential function is a little shorter compared with that obtained from ab initio calculations, and the curve is relatively steeper in the region of high potential energy than the ab initio potential curve. Both curves agree well throughout the whole range of m. In the case of the acetic acid open-chain dimer, Figure 8b, the equilibrium position agrees well with the ab initio results but the curve is too steep in the repulsive region compared with the ab initio curve. For the acetamide-acetic acid pair, two types of hydrogen bonds are possible. For the 0-H-O=C hydrogen bond type dimer, the minimum energy of our potential function is a little higher, by about 1 kcdmol, than the ab initio result, and the curve is too steep in the repulsive region compared with the ab initio curve. The potential curve for the N-H-O=C type hydrogen bond dimer shows good agreement with the ab initio result. As shown in parts a and d of Figure 8, the N-H-O-C type
J. Phys. Chem., Vol. 99, No. 11, 1995 3485
Angular-Dependent Hydrogen-Bonded Systems
40
60
80
loo
120
80
140
120
100
160
140
0-H...0 angle (degree)
N-H...0 angle (degree)
--r=2.4
t 40
60
80
loo
120
140
60
N-H...0 angle (degree)
80
100
1u)
140
160
0 - H...0 angle (degree)
Figure 9. Potential energy curves calculated with both ab initio and the empirical potential function are plotted as a function of the hydrogen bond (a) acetamide dimer, ab initio (top left); (b) acetamide dimer, this work (bottom left); (c) acetic acid dimer (open chain), ab initio (top angle, e-: right); and (d) acetic acid dimer (open chain), this work (bottom right). All the other geometrical parameters were fixed at their equilibrium values, Q given in Figure 4.
hydrogen bond can be well described by 6- 12 type potential functions, but for the 0-H-0-C type hydrogen bond, the 6-12 type potential function gives too steep a curve in the repulsive region. The distance dependence of the N-H-O-C type hydrogen bond is relatively well described by the 6-12 type VI-2potential function. In Figure 9, the potential curves are plotted as a function of the hydrogen bond angle Omo, at three hydrogen bond lengths, mo, of 1.8, 2.1, and 2.4 A, with all the other geometrical parameters fixed at their equilibrium values, given in Figure 4. Comparison of Figure 9a, from ab initio, and Figure 9b, from the empirical potential function, shows that the empirical potential function describes the angular dependence of the ab initio potential energy curves well. The minimum energies in Figure 9b are somewhat different from those of Figure 9a because the potential energy curves of Figure 8a show some difference at those three ~0 values. The potential curves of Figure 9c and d, the acetic acid open-chain dimer, are quite similar in their shapes except that the empirical curves are a little steeper than the ab initio curves, especially at short QO.
Conclusions A simple hydrogen bond model is proposed, in which the 1-3 atomic pairs in the hydrogen-bonded system proved to be the most important terms in the description of the angular dependence of the hydrogen bond potential surfaces. The hydrogen bond potential parameters of the model were obtained for amides, carboxylic acids, and carboxylic acid-amide pairs. The angular dependence of the hydrogen bond energy of these molecular pairs can be described well with the optimized potential functions. By introducing the 1-3 atomic pairs in describing the hydrogen bond potential surfaces, the angular dependence of the ab initio hydrogen bond potential surface can be successfully reproduced without introducing additional angular-dependent terms.
Acknowledgment. This work was supported by research grants from the National Science Foundation (DMB90-15815, INT93-06345), by the Center for Molecular Science, by the Korea Science and Engineering Foundation (9 1-0300-lo), and by Soong Si1 University (93).
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