Investigation of the CH,CN-CO, 

Potential Energy Surface (PES) 

Using Symmetry-Adapted 

Perturbation Theory (SAPT) 

by Hayes L. Williams, Betsy M. Rice, and Cary F. Chabalowski 

ARL-l-R-2301 September 2000 
The fiidings in this report are not to be construed as an official 

Department of the Amy position unless so designated by other 

authorized documents. 

Citation of manufacturer’s or trade names does not constitute an 

offkial endorsement or approval of the use thereof. 

Destroy this report when it is no longer needed. Do not retum 

it to the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 2 1005-5066 

ARL-TR-2301 September 2000 

Investigation of the CH,CN-CO, 

Potential Energy Surface (PES) 

Using Symmetry-Adapted 

Perturbation Theory (SAPT) 

Hayes L. Williams, Betsy M. Rice, and Cary F. Chabalowski 

Weapons and Materials R&arch Directorate, ARL 

Approved for public release; distribution is unlimited. 
Abstract 

Symmetry-adapted perturbation theory (SAPT) has been used to investigate the 

intermolecular potential energy surface (PES) of CH,CN-CO,. A SAPT computation was 

performed for approximately 200 geometrical configurations using both a coarse grid in the 

five intermolecular coordinates as well as selected representative cuts. Four near-local minima 

are located on the PES. The deepest of these is -2.90 kcal/mol. 

ii 
Acknowledgments 

This work was partially supported by the Strategic Environmental Research and Development 

Program (SERDP), Project PP-695. The authors gratefully acknowledge the computer resources 

made available for this study on the Silicone Graphics Inc. (SGI) Power Challenge Array by the 

Department of Defense high-performance computing site at the U.S. Army Research Laboratory 

(ARL), Aberdeen Proving Ground, MD. This research was performed while Hayes Williams was 

a National Research Council postdoctoral associate at ARL, and he wishes to thank both 

organizations for their support. The authors would also like to thank Krzysztof Szalewicz and 

Bogumil Jeziorski for reading and commenting on the manuscript. 

. . . 

111 
bIT.BNTIONALLY LEFT BLANK. 

iv 
Table of Contents 

, Acknowledgments . . . . . . . . . . . . . . . . . . . . ..~.......................... 

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

2. Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

3. Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

4. Results and Discussion . . . . ..0....*..0............................... 

5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . ..~~~........................... 

6. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Appendix: Supporting Information for Investigation of the CH,CN-CO, 

Potential Energy Surface (PES) Using Symmetry-Adapted 

Perturbation Theory (SAPT) ..e........................... 

Distribution List . . . . . . . . . ..0.~~.~.~0............................... 

Report Documentation Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

. . . 

111 

vii 

ix 

1 

2 

6 

14 

38 

41 

45 

77 

79 

. 

V 
. 

. 

vi 
List of Figures 

Figure 

1. 

2. 

3. 

4a. 

4b. 

5a. 

5b. 

6. 

7a. 

7b. 

8a. 

8b. 

The Four Local Minimum Geometries Labeled as Gl, G2, G3, and G4 

inTable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Graphical Representation of the Coordinate System Used to Specify the Dimer 

Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Cuts in R Through the PES for the Four Local Minimum Geometries Detailed 

in Table 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

SAPT Components Used in Equation (9) for a Range of R Values at and Around 

the Local Minimum Geometry Gl ,...............................*..... 

EE and the SAPT Components Included in Equation (8) at and Around 

Geometry Gl as a Function of R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

The Interaction Energy and Individual Components Indicated in Equation (9) 

Are Shown in Histogram Format to Illustrate the Relative Importance of the 

Various Energy Contributions at the Gl, G2, G3, and G4 Minima . . . . . . . . . . . . . 

A Histogram Is Shown Containing EE and the SAPT Components Included 

inEquation(8)attheGl,G2,G3,andG4Minima . . . . . . . . . . . . . . . . . . . . . . . . . 

,!Zzp”b’ as a Function of pi Is Shown for R = 4.0 and R = 4.75 A, With the 

Remaining Coordinates Taken From Gl ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

The Interaction Energy E zf”’ and Its Components According to Equation (9) 

Shown as a Function of p, for R = 4.0 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

The HF Interaction Energy E E and Its Components According to Equation (8) 

Shown as a Function of pr for R = 4.0 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

The Interaction Energy E Lf”’ and Its Components According to Equation (9) 

ShownasaFunctionof pi forR =4.75A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

The HF Interaction Energy E E and Its Components According to Equation (8) 

Shown as a Function of p, for R = 4.75 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

7 

10 

19 

25 

26 

28 

29 

33 

34 

35 

36 

37 

vii 
bWENTIONALLY LEFT BLANK. 

1.. 

Vlll 
List of Tables 

. Table 

b 1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

A-l. 

A-2. 

A-3. 

A-4. 

A-5. 

Nuclear Coordinates in A for the CH,CN Monomer Geometry ............... 

The Coordinates for the Local Minimum Geometries Gl, G2, G3, and G4 ...... 

Comparison of the SAPT Interaction Energy Components for the CH,CN-CO, 

Interaction Using a MC +BS and the Analogous DCBS at the Two Local 

Minimum Geometries Gl and G4 ...................................... 

Comparison of SM Results With SAPT Results at Three Local Minimum 

Geometries.. ...................................................... 

Contribution of Basis Functions of Different Angular Syrnmetry Placed at the 

Midbond Position to the E gi Energy in kcal/mol ......................... 

Potential Cuts in R Through the Two Local Minimum Geometries Gl and G2 ... 

Potential Cuts in R Through the Local Minimum Geometry G3 ............... 

Potential Cuts in R Through the Local Minimum Geometry G4 ............... 

Potential Cuts in PI at Geometry Gl for Two Different R Values ............. 

Potential Cuts in PI at Geometry Gl for R = 4.75 8, ........................ 

The Supplementary Tables Complement Tables 6-10 and Provide a Complete 

Description of All Single-Point Symmetry-Adapter Perturbation Theory (SAPT) 

Computations Used in the Present Work ................................. 

Supplementary Tables Continued ...................................... 

Supplementary Tables Continued ...................................... 

Supplementary Tables Continued ...................................... 

Supplementary Tables Continued ...................................... 

Page 

6 

8 

15 

16 

18 

20 

22 

23 

31 

32 

47 

49 

51 

53 

55 

ix 
Table Paae 

A-6. Supplementary Tables Continued ...................................... 57 

A-7. Supplementary Tables Continued ...................................... 59 

A-8. Supplementary Tables Continued ...................................... 61 

A-9. Supplementary Tables Continued ...................................... 63 

A-10. Supplementary Tables Continued ...................................... 65 

A- 11. Supplementary Tables Continued ...................................... 67 

A- 12. Supplementary Tables Continued ...................................... 69 

A- 13. Supplementary Tables Continued ...................................... 71 

A- 14. Supplementary Tables Continued ...................................... 73 

A- 15. Supplementary Tables Continued ...................................... 75 
1. Introduction 

. 

Weak intermolecular interactions play a particularly important role in the computer simulation 

of liquids [ 11. An excellent example of a process which displays this characteristic is supercritical 

fluid (SCF) CO, extraction [2]. When SCFs are compressed to liquid-like densities, their solvent 

strength dramatically increases. A closed system can then be built to extract materials of interest 

from a more general mixture. Carbon dioxide (CO,) proves to be an excellent choice for this process 

because of both its nondestructive character and because it is environmentally benign. Some 

industrial processes, such as caffeine extraction, already make profitable use of this procedure. 

The Department of Defense (DOD) community sets a priority on developing an environmentally 

beneficial and cost-effective way to recycle solid energetic materials which have reached the end of 

their rated lifetime. Significant environmental and economic advantages could result from an 

industrial scale, closed-system recycling procedure based on supercritical CO, for this particular 

application. Unfortunately, certain components in composite propellants are not sufficiently soluble 

in pure SCF CO, to make this extraction process viable. The solubility characteristics of these 

components can be enhanced with the addition of so-called modifier molecules. These typically 

polar molecules increase the solubility strength of the SCF, but little is known about the detailed 

molecular interactions accounting for the increased solubility. The first step towards simulating the 

entire system is knowledge of accurate intermolecular potentials for all dimer interactions in the 

system-the solvent-solute, solvent-modifier, modifier-solute, and each with itself (e.g., 

solvent-solvent). Methyl cyanide (CHJN) has been shown to be an effective polar modifier for 

enhancing the dissolution of one of the important solid energetic materials, 

cyclotrimethylenetrinitramine (RDX), in SCF CO, [3]. This work will focus on mapping the detailed 

potential energy surface (PES) of CO, interacting with CH,CN. 

Symmetry-Adapted Perturbation Theory (SAPT) [4,5] is a natural choice to find the interaction 

energy of the CH,CN-CO, system or any two closed-shell weakly interacting atomic or molecular 

systems. SAPT directly and naturally separates the interaction energy into four physically 
interpretable components: (1) electrostatics, (2) exchange, (3) dispersion, and (4) induction. Each 

component has distinct radial and angular dependence for each system and can be fitted to an 

analytical form independently of the other components. This can lead to significant physical insight 

about the interaction in contrast to the currently more popular supermolecular (SM) method which 

returns only a single number. SAPT has been used to successfully investigate a variety of systems 

includingAr-H,[6],He-HF[7],He-CO[8],Ar-HF[9],He-C,H,[lO], HZ-CO[ll],and(H,O),[12]. 

Section 2 introduces definitions necessary for analyzing SAPT results. Section 3 describes the 

computational details. Section 4 investigates some representative cuts of the PES for the 

CH,CN-CO, system and specifies the coarse grid used for the majority of the geometrical 

configurations investigated. Section 5 presents conclusions. 

2. Method 

Jeziorski, Moszynski, and Szalewicz [4] and Szalewicz and Jeziorski [5] present recent reviews 

of SAPT and provide an excellent overview of the method. Further details on the explicit derivation 

of the theory and implementation can be found in section 6 [ 13-201. We present only a necessary 

amount of notation to interpret the results of the present work. 

The dimer Hamiltonian is decomposed by SAPT into three general parts. The first two, the Fock 

operator F, and the Moller-Plesset-type intramonomer correlation operator IV, have separate 

contributions from both systems A and B and are written as F = FA + FB and W = WA + WB, 

respectively. The third part of the Hamiltonian is the intermolecular interaction operator V which 

mediates interactions between the two systems. The total Hamiltonian is then written as 

6-I =F + V + W. The wave function used with this Hamiltonian is the product of the system A and 

B wave functions. This product wave function does not obey the Pauli principle. The correct 

permutational symmetry of the electrons between systems is imposed on the product wave functions 

using an antisymmetrizer described in more detail in Jeziorski, Moszynski, and Szalewicz [4 ] and 

Szalewicz and Jeziorski [S]. 

2 
The intermolecular interaction energy E,, within the SAPT framework can then be expanded 

in powers of the intermolecular interaction operator V as 

(1) 

where the first two terms on the right-hand side of equation (1) can be interpreted as the classical 

electrostatic (coulomb) and exchange energies, respectively. The exchange components are the 

result of the antisymmetrization previously mentioned. They can also be viewed as an effect of 

resonance tunneling of electrons between the interacting systems. 

The second-order terms in equation (1) naturally separate into dispersion and induction 

components as 

and analogously for the exchange component 

(2) 

The dispersion energy is a result of the interactions of the two monomers’ instantaneous electric 

moments. The induction energy describes the interactions of the permanent and induced multipole 

moments of the two monomers. The second-order exchange-dispersion and exchange-induction 

energies result from electron tunneling between systems related to the dispersion and induction 

components of the wave function. 

Equation (1) implicitly indicates the inclusion of full intramonomer electron correlation. Within 

the SAPT framework, this is only currently possible in the case of four-electron systems [21,22]. 

To describe the intramonomer electron correlation for larger systems, we also perturbationally 

3 
expand each of the components in equation (1) in powers of W. For example, the first-order 

polarization energy is now expanded in a double perturbation series as 

E(l) = 5 Eg, elst 

k=O 

(4) 

where k indicates the order in W. It is conveniento split expansions like equation (4) into terms 

which include and neglect intramonomer correlation. This is written explicitly for the first-order 

polarization energy as 

(5) 

where the second term sums all terms of order one and above in Win equation (4). The sum of these 

terms through the kth order in W will be indicated by the notation r$Lt (k). Similar definitions are 

assumed for the other components as well. 

The first-order polarization and second-order induction components are calculated with the 

inclusion of the coupled Hartree-Fock (I-W)-type response of a perturbed system. Components 

computed in this manner will be indicated with the subscript “resp” as in Erd&,. The 

irmamonomer correlation effects in induction interactions will be approximated by ‘Egj9 the 

so-called “true” correlation contribution which collects those parts of the E Ei’ correction that are 

not included in E rdjmp. Note that E F$ = E fi/9),, . 
The t&22) exch-ind component which partially quenches the corresponding induction component is not 

currently coded. We have estimated it by scaling ,?T~~~-~~ by the ratio of the correlated to 

uncorrelated induction components by 

. 

tE (22) s E'20' _ 

tE (22) 

ind 

exch -ind exch ind,mp c c20j * (7) 

There exists the following relation between the SM HF interaction energy and the SAPT 

expansion [23,24]: 

where 6HF indicates the sum of higher order induction and exchange terms. The first- and 

second-order terms in equation (8) are those calculated in the current implementation of SAPT. 6nr 

is detied as the difference between the sum of these SAPT terms and the supermolecule HF energy, E g e 

In order to include some of the higher order induction terms currently not available in SAPT, we use 

a hybrid method which includes the SM HF energy and the correlated portion of the SAPT 

components indicated in equation (6). The total interaction energy in the present work will then be 

approximated by combining equation (6) and equation (8) to give 

(9 

For more discussion about this relationship and further references, see Szalewicz and Jeziorski [5]. 

The Boys-Bernardi [25] counterpoise (CP) scheme is always used to compute E g and other SM 

quantities of interest in order to eliminate basis set superposition error (BSSE) [5,26]. 

5 
3. Computational Details 

We used Dunning’s correlation-consistent basis augmented with diffise functions labeled 

aug-cc-PVDZ 127-291 as a starting point for all calculations with modifications. The CH,CN 

monomer geometry was determined by a QCISD [30-321 calculation with the full inclusion of inner 

shell electrons optimizing the monomer’s total energy. The nuclear coordinates for this monomer 

are presented in Table 1. For carbon dioxide, a carbon-oxygen distance of 1.162047 8, was taken 

from Sadleg, Szczesniak, and Chalasinslci 1331. Both monomer geometries were then futed for all 

further study. Gaussian 94 [34] and Atmol [35] were both used to perform the necessary SCF 

calculations. Both programs are interfaced to the SAPT suite of codes 1361. 

Table 1. Nuclear Coordinates in 8, for the CH,CN Monomer Geometry. Each HCCN Angle 

Is 109.731504”. The Center of Mass for the System is 0.68927 A From the Inner 

Carbon Between the Two Carbon Atoms. 

Optimizations of the full dimer energy in the full dimer basis set with fured internal monomer 

geometries were then performed at the MP2 level of theory again with full inclusion of inner core 

electrons. Four local minimum geometries were located with this procedure and will be designated 

Gn, n = 1,2,3, or 4. These geometries, shown in Figure 1, serve as starting points for investigating 

interesting portions of the PES. Since a CP-corrected optimization procedure was not used for the 

minimizations, BSSE may affect the positions of the local minima. No attempt to quantify this error 

was made since the minimum geometries were used only for the purpose previously mentioned. 

6 
7 
Subsequent discussion of these geometries refers to the SAPT computations which are not biased 

by BSSE. 

. 

The coordinates of the MP2 local minimum geometries are provided in Table 2. A description 

. 

of the coordinate system is given in the next paragraph. In configuration Gl, the CO, axis is in a 

slipped, nearly parallel position (away from the CH, group) with respecto the C, axis of the CH,CN 

molecule (see Figure 1). In configuration G2, the CO, is oriented along and nearly perpendicular 

to the major axis of CH,CN toward the CH, group. Configuration G4 has the CO, in a similar 

location, but the CO, major axis is nearly aligned with the CH,CN axis. Finally, configuration G3 

is oriented in the same way as G2 except toward the nitrogen atom. 

Table 2. The Coordinates for the Local Minimum Geometries Gl, G2,63, and 64 (The Units 

for Distance and Angles Are 8, and Degrees, Respectively.) 

Geometry R PI Yl P2 cl, 

Gl 3.327156 107.746148 119.852998 116.669519 359.978866 

G2 4.652572 7.954955 59.997536 95.612989 359.87068 1 

G3 4.276012 179.643584 60.183120 89.771324 170.272920 

G4 5.572889 0.012626 6 1.490949 179.921826 1.518053 

The dimer configuration has been specified by coordinates consisting of a separation distance 

R and two sets of Euler angles as given in Brink and Satchler [37]. A pictorial representation of 

these coordinates as applied to this system can be seen in Figure 2. R is defined as the length of the 

vector connecting the centers of mass between the two monomers. Each center of mass is located 

at the origin of a system of Cartesian coordinate axes, and these two sets of axes remain fixed and 

parallel to the space-fixed coordinate system. The vector R coincides with the Z axis and points in 

the positive Z direction. One set of Euler angles is assigned to each of the molecules and is defined 

with respect to the Cartesian coordinate axes associated with that molecule. The angles are given 

by the variables (aI, PI, yl) for the orientation of CH,CN, and (CQ, &, yJ for CO,. 

8 
The dimer configurations are obtained from the independent Euler angles by rotating CH,CN 

about yr, followed by rotating each monomer through its respective PI angle, and finally rotating the 

CO, molecular axis through its CL, angle. y1 is the angle of rotation of CH,CN about its C, axis 

(hereafter referred to as its “molecular axis”). This can be further defined as a rotation about the 

CCN molecular axis between a half plane and the stationary XZ plane. The half-plane is formed by 

the CH,CN molecular axis and one of the CH bonds. yr is taken to be zero when the half-plane 

containing the CH bond coincides with the XZ plane and lies in the positive X hemisphere (see 

Figure 2). yr is then allowed to vary between 0 and 120”, with the sense of rotation always being 

done such that the CH bond lies in the positive Y hemisphere. With this definition of yr, one can 

take advantage of the C,, symmetry of CH,CN. y2 would be the angle of rotation for CO2 about its 

molecular axis, but due to its cylindrical symmetry, it is undefined and allows us to reduce the 

coordinates from six independent coordinates to five. 

PI is the simple angle between the positive Z axis and the vector drawn from the COM of CH,CN 

to the methyl carbon. Likewise, pz is the angle between one of the CO bonds and the part of the Z 

axis where Z > R. Both PI and p2 are allowed to vary from 0 to 180”. cq! is an angle of rotation 

between two half planes, both of which have their edge coincidental with the Z axis. The first half 

plane, which is taken to remain stationary, is formed by the Z axis and the positive X axis. The 

second half plane (i.e., the rotating plane) is formed by the Z axis and the CO bond involved in the 

definition of p2. a;! can vary from 0 to 360”, but is zero when the half plane containing the CO is 

coincidental with the XZ plane and pointing in the +X direction. The sense of rotation is clockwise 

when viewed down the Z axis from -Z to +Z. The final Euler angle, a,, would rotate the molecular 

axis for CH,CN out of the XZ plane. This corresponds to the rotation of the entire dimer system, 

in a fixed configuration, about the Z axis. Thus, aI is not involved in the definition of the relative 

positions of the two molecules, and thus can be fixed to zero. The results of this are that the CCN 

molecular axis always lies in the XZ plane, and the PI angle always lies in the positive X direction. 

There are a few symmetries within this system which can be exploited to reduce the total number 

of grid points that need to be considered. The linearity of the CO, molecule eliminates the need to 

9 
(Fixed) 

Figure 2. Graphical Representation of the Coordinate System Used to Specify the Dimer Configuration. The Vector R Is 

Coincidental With the Z Axis and Connects the Centers of Mass of the Two Dimers. Associated With Each Monomer 

Is a Set of Euler Angles as Given in Brink and Satchler [37]. The Orientation of CH,CN Is Given by the Angles a,, pl, 

and yl, Where 01, Is Held Fixed at 0, and the Orientation of CO, Is Given by a, and pz. Due to the Cylindrical Symmetry 

of CO,, yz Is Undefined, Which Reduces the Number of Independent Variables to 5. (See the Text for Further 

Explanation.) 
consider the sixth coordinate necessary for describing general rigid two-body interactions. 

Describing Eht as a potential function of five coordinates by 

the symmetries can be concisely written as 

WR,P,,r,,P2,aZ) = V(R,P1,yI,71-P2,1t+az), and 

W$1,y1$29a2) = V(R,P1,-y1,11-P2,~--a,); 

further symmetries in special cases can be written as 

WR,w,,P,,a,) = V(R,dAP,,a, +yJ, 

WW,y,,O,~,) = WCWU40), and 

11 

(11) 

(12) 

(13) 

(14) 

(17) 

(18) 

(19) 
Including these symmetry constraints significantly reduced the total number of points needed for our 

coarse grid covering of the total PES. 

A total of 187 points on the PES were computed for various combinations of R, PI, yl, f&, and 

%. The first group of points chosen was based on the four geometries presented in Table 2. For each 

of these geometries, we varied only the R coordinate and computed enough points to show the depth 

and shape of the local minimum well. This required 27 points total for all four geometries 

investigated, and the results are shown in Tables 6-8. Next, we covered a coarse grid in R, PI, and 

y1 while fixing the remaining coordinates to those of geometry Gl . For this collection of points, we 

selected values for R from the set (Gl, 3.5,3.75,4.0,4.25,4.5,4.75 A). For PI, we selected from 

the set (0,45,90,135,180”) and for yl, either the Gl value or Gl + 60”. A subset of these points, 

where only R and /3r vary, is given in Tables 9 and 10 for the purpose of discussion, and the 

remainder of the data points are included in Tables A12-A15 in the appendix. A clarification is 

required concerning the coordinates for the points in Tables A12-A15. For these four tables, the 

algorithm written to transform from internal coordinates to Cartesian coordinates (used as input to 

the SAPT procedure) unintentionally caused a reflection through the XZ plane of the y1 value in 

structure Gl. This generated Gl -like structures that differ from Gl by only +0.294’ in the y1 torsion 

angle. Accordingly, the starting yr value used in Tables A12-A15 is not 119.853 ‘,but rather 

119.853” + 0.294”, or taking into account the C,, axis, y1 = +0.147’. The coordinates in 

Tables Al 2-A15 include this difference in yl. Finally, we selected a coarse grid covering the entire 

PES withvaluesfor R = (3,4,5,6&, PI = (0,45,90, 135, 18O"),y, = (0,60"), pz = (0,45"), and 

cl, = (0,45,90"). 

Since SAPT interaction energies are rigorously free of BSSE, there is no a priori need to 

compute the SAPT components in a dimer-centered basis set (DCBS) as is necessary in the SM 

CP-corrected approach. Williams et al. [38] investigated some alternate schemes for the placement 

of basis functions for effkient computation of SAPT components, called monomer-centered and 

monomer-centered plus basis sets (MCBS and MC+BS), respectively. In a “pure” MCBS, eaclh 

monomer uses only those basis functions that are placed on its own nuclear centers. The “plus” in 

the MC+BS case indicates basis functions used in addition to the monomers’ original basis set. 

12 
The location for these additional functions in the MC+BS are the original locations of the basis 

functions on the ghost monomer. Eventually, adding functions to the MCBS in this manner would 

produce the full DCBS. The goal, however, is to reduce the computational effort below that required 

for the full DCBS while retaining acceptable accuracy. A MC+BS that best balances the goals of 

computational tractability and accuracy in SAFT calculations is one in which only the valence basis 

functions are retained on the ghost monomer. Explicitly, when a CH,CN, SAPT computation is 

being performed, only s- and p-type functions are included in the CO, ghost basis set. Likewise, 

when the CO, computation is being performed, only s and p functions are placed on the C or N 

atoms of CH,CN, and only s-type functions are placed on the H atoms. This arrangement allows a 

20-30% reduction in the size of the basis compared to the equivalent DCBS, with almost no sacrifice 

in accuracy. This significantly reduces the computational effort because the most computationally 

expensive SAFT component, E Efi, scales as n&,” where PZ,’ and n,” are the numbers of occupied 

and virtual orbitals, respectively. In this manner, the full DCBS size of 165 basis functions was 

reduced to a MC+BS size of 135 and 117 basis functions for monomer CH,CN and CO,, 

respectively. 

A separate computation was performed for the EEfj component, which is variational in 

character. The MC+BS was augmented with a large midbond set of 2s2pUlflg placed at the 

midpoint of the line segment defining the coordinate R. The orbital exponents are 0.15 and 0.6 for 

s, p, and d functions and 0.3 for thefand g functions. These functions were selected by optimizing 

one basis function of each type to one digit accuracy with the goal of maximizing the absolute value 

of the E zii energy. The s, p, and d functions were then each split into two basis functions using the 

“even scaling rule” [39] producing the orbital exponents given previously. This new value for E gfj 

was then used in place of the one which was computed using the basis set described in the previous 

paragraph. The addition of midbond functions for this component will be indicated with a 

superscript “( +mb)” for both the leading term in the second-order dispersion energy and for the total 

interaction energy as E E$+mb) and Eint(*mb), respectively. 

13 
4. Results and Discussion 

To check the quality of the atomic orbital (AO) basis set used on the monomers, we report the 

calculated electric dipole and quadrupole moment of CO, and CH,CN, respectively. The theoretical 

values are calculated at the QCISD level with the aug-cc-pvdz basis set used on the monomers 

throughout this work. The electric dipole moment of CH,CN is predicted to be 3.95 debye, while 

experimenting gives 3.92 debye [41]. Values for the CO2 experimental quadrupole moment [42-45] 

vary between - 1.34 and 1.5 x 10-l’ coulomb A2, while the calculated value lies at the upper end of 

this range with a value of - 1.5 14 x 10-l’ coulomb A2. 

Table 3 compares the SAPT components computed using the MC +BS described in section 3 with 

the equivalent DCBS at the two geometries Gl and G4. The difference in the fast-order components 

between a MC+BS and the equivalent DCBS is less than about 0.01 kcal/mol. Aside from Egj, 

which will be replaced as previously described, the second-order components differ by no more than 

0.04 kcal/mol. Further, the second-order differences at least partially offset each other for the 

geometries shown, though this cannot be relied upon over the entire PES. This level of error should 

be substantially smaller than other sources of error in the present work. Further, the reduction in the 

number of basis functions decreases the computational cost at each geometrical configuration by 

more than a factor of three. For the most time-consuming component, the triples portion of Egi, 

this cost is cut by 3.5 times by using a MC+BS rather than a DCBS. 

Table 3 further shows that the largest components in absolute magnitude for Gl and G4 are 

p) 

elst 9 &~;,and Eg;. Previous experience [38] and Table 3 indicate that the first two components 

converge very quickly with basis set and are sufficiently converged with the current MC +BS. More 

attention must be paid to Egfj since small percentage errors in this component can translate into 

relatively large absolute errors in the final energies. With this in mind, the convergence properties 

of this component with respect to basis set saturation will be studied in more detail later. 

14 
Table 3. Comparison of the SAPT Interaction Energy Components for the CH,CN-CO, 

Interaction Using a MC +BS and the Analogous DCBS at the Two Local Minimum 

Geometries Gl and 64 (The Units for the Energies Are kcal/mol.) 

E (10) I 3.88 I 3.88 

exch I 1.09 I 1.09 

E;;ch(2> 1 0.25 1 0.26 1 0.20 1 0.21 

E (20) -3.07 -3.22 - 1.21 -1.26 

dlsp 

$;sp(2) 

E (2) 

disp 

-0.03 -0.05 -0.08 -0.10 

-3.09 -3.28 - 1.30 -1.36 

E !20) -2.01 -2.05 -0.26 -0.26 

md.resp 

(E (2% 

ind 

0.05 0.05 -0.03 - 0.03 

E (20) _ exch dlsp 0.32 0.36 0.07 0.08 

E c20) _ 

exch ind,resp I 

1.57 1 1.57 1 0.15 1 0.15 

E a int 1 -2.38 1 -2.51 1 -1.06 1 -1.12 

Computed according to equation (9). 

Table 4 compares the best currently coded SAPT approximation to each SM energy (HP, MP2, 

MP3, and MP4), with the appropriate sums detailed in the footnotes to this table. At the Gl 

geometry sHF, the difference between the four-term SAPT approximation to E z and E E itself is 

less than 0.2 kcal/mol. While this is a small difference in absolute magnitude, it represents a large 

percentage ofE 2. This large percentage ismisleading, though, since it occurs near the point where E E 

15 
16 

Table 4. Comparison of SM Results With SAPT Results at Three Local Minimum Geometries 

(The SM Interation Energies Are Computed Using the Boys-Bernardi [25] CP 

Scheme; the SAPT Components Use a MC+BS. The DCBS Values Available for 

Geometries Gl and 64 Are Displayed in the Footnotes if They Differ by More Than . 

0.02 kcal/mol From the MC +BS Value.) 

’ DCBS value is - 1.84 kca.l/mol. 

d DCBS value is -0.84 kcal/mol. 

g DCBS value is -0.83 kcal/mol. 

h Computed according to equation (9). 
crosses zero. The absolute values of Es’ and EL:: g iven in Table 3 are nearly 4 kcal/mol at Gl , 

but are opposite in sign and cancel to within a fraction of a kcal/mol. The comparison to SM-MP2 

is quite good at all three geometries, probably indicating reasonably good agreement over the entire 

PES. The SM-MP3 energies show a small difference in absolute values of less than 0.1 kcal/mol. 

The SM-MP4 energy comparison shows the largest deviation of 0.3 kcal/mol from the SAPT 

approximation at geometry Gl . This deviation is probably due to accumulation of errors resulting 

from the neglect of EL;:&, and E~~_,i,. 

Table 5 investigates the effect on Egrj of adding basis functions with different angular 

symmetries placed at the midbond position as described in section 3. The value for this component 

using the DCBS from Table 3 is repeated in Table 5 for comparison. The addition of the full 

midbond 2s2p2dlflg set lowers this energy component by 0.53 (17%) and 0.18 (15%) kcal/mol for 

the geometries Gl and G4, respectively, from its MC+BS value. This results in a 22% and 16% 

lowering of the final value of E,, for these geometries. By adding only s and p functions at the 

midbond, the value of ZZE:j is already lower than the corresponding DCBS value while using 22 

fewer basis functions. This indicates that midbond functions are helping to converge this component 

faster than nuclear-centered basis functions of higher angular symmetry placed at the other nuclear 

centers. The increase in the computational cost of treating only Egfi with the full set of midbond 

basis functions is rather minor, yet provides a significant increase in accuracy for this component. 

Using this set of midbond functions in the computation of all SAPT components would not have 

improved the accuracy of the results in proportion to the amount of additional computer time needed. 

Figure 3 displays a cut in R for each of the four geometries, Gl, G2, G3, and G4. Tables 6,7, 

and 8 provide the individual SAPT components and total interaction energy for each of the points 

shown in Figure 3. Geometry Gl, with CO, roughly parallel to the CCN axis, has a total interaction 

17 
Table 5. Contribution of Basis Functions of Different Angular Symmetry Placed at the 

Midbond Position to theE (20) disp Energy in kcal/mol (The Table Indicates the Successive 

Inclusion of Each of the Symmetries, e.g., Row g Includes the Full 2s2p2dlf lg Set. 

The Numerical Values of the Eiponents Used for Each Symmetry Are Found in 

Section 3. The Number of Basis Functions Refers to the CH,CN Monomer Including 

Midbond Functions and Ghost Functions Placed on the CO, Nuclear Centers. The 

Values Computed Without Midbond Functions Are Taken From Table 3.) 

lr~~--~ Basis Type Midbond Basis Size Geometry II 

Number Symrretry Gl G4 

DCBS - - - 165 -3.22 - 1.26 

MC+BS - - - 135 -3.07 -1.21 

MC+BS 2 - s 137 -3.17 - 1.23 

MC+BS 2 -P 143 -3.35 -1.31 

I II MC+BS 2 -d 153 1 -3.47 1 -1.36 I II I MC?BS 1 -f 160 -3.55 - 1.38 

1 MC+BS 1 1 I-lgl 169 1 -3.60 1 -1.39 11 

energy of Eint(+mb) = -2.90 kcal/mol. This is slightly more stable than G3, where Eint(*mb) = 

-2.82 kcall mol, and the CO, is perpendicular to the CCN axis. The interaction energy of 

- 1.25 kcal/mol at geometry G4 is significantly smaller in magnitude than for the former two 

geometries. Finally, geometry G2 is only weakly bound at -0.43 kcal/mol. 

Figure 4a shows the cut through geometry Gl broken into the components indicated in 

equation (9). The minimum energy for E,, HF is near R = 3.75 A, while the full interaction energy, 

including correlation corrections, predicts the minimum to occur near R = 3.33 8, or 0.4 8, shorter 

than the HF value. This comparison clearly indicates the need to include the intermolecular electron 

correlation effects for this system. At the minimum for the correlated interaction, the HF 

contribution is only - 0.39 kcaVmo1 and is determined by two pairs of large values of opposite signs: 

the first-order interactions EizL + Earn’ = 3.88 - 3.62 = +0.26 kcal/mol and the second-order 

18 
. 

-3 

3 4 5 

Figure 3. Cuts in R Through the PES for the Four Local Minimum Geometries Detailed in Table 2. The Final Energies Were 

Computed Using Equation (9) and Include E disp (20)(+mb) o The Solid Line Is a Spline Fit to the Single-Point SAPT Energies 

for Each Cut and Is Only to Guide the Eye. 

Separation Between the Two Monomers in A. 

Energies Are in kcal/mol, and Distances Refer to the Center-of-Mass 
Table 6. Potential Cuts in R Through the Two Local Minimum Geometries Gl and 62 (All Energies Are in kcal/mol and Distances 

in A.) 

0.09 0.00 -0.03 -0.03 -0.03 -0.02 -0.01 0.00 -0.30 -0.15 -0.11 -0.06 

E :ip (2) -9.00 -5.62 -3.55 -3.09 - 2.28 -1.49 -0.99 -0.47 -5.42 -2.07 -1.57 -0.86 

. . 
. 

Table 6. Potential Cuts inR Through the Two Local Minimum Geometries Gl and 62 (All Energies Are in kcal/mol and Distances 

in A.) (continued) 

I R 1 2.75 1 3.00 1 3.25 1 3.33 1 3.50 1 3.75 1 4.00 1 4.50 1 4.00 1 4.50 1 4.65 1 5.00 I I 

E (20) 

exch-disp 

E;,q” 

E int 

E(20)(+mb) 

disp 

E (+mb) int 

..- - .--- 

1.70 0.84 0.41 0.32 0.19 0.09 0.04 0.01 0.72 0.14 0.08 

-5.32 -3.45 -2.26 -1.98 - 1.47 -0.96 -0.62 -0.26 -4.21 -1.91 -1.52 

4.28 -0.66 -2.22 -2.37 -2.41 -2.14 -1.76 -1.11 4.73 0.01 -0.22 

-10.92 -6.69 -4.14 -3.60 -2.62 -1.69 -1.12 -0.52 -6.11 -2.23 -1.67 

2.45 - 1.72 -2.84 -2.90 -2.78 -2.36 - 1.89 -1.16 3.73 -0.29 -0.43 
Table 7. Potential Cuts in 22 Through the Local Minimum Geometry 63 (All Energies Are in 

kcal/mol and Distances in 8.) 

R 

EE 

E(‘o) 

elst 

E (lo) 

exch 

E !20) 

md,resp 

E 120) _ 

exch ind,resp 

tF 

& (1) c3) 

elst,resp 

$;& c2) 

‘E g 

‘E zL+,,j 

E t20) 

disp 

E’Tl’ 

dlsp 

E (T2) 

dlsp 

Efisp (2) 

E:;,(2) 

E c20) 

exch -disp 

EEm 

Eixlt 

E$(+mW 

E (+mb) int 

3.75 4.00 4.28 4.50 4.75 5.00 -5.50 

5.03 0.54 -1.13 -1.44 -1.39 - 1.20 -0.82 

-11.29 -6.16 -3.52 -2.43 -1.72 -1.28 -0.79 

18.84 7.87 2.96 1.32 0.53 0.21 0.03 

-9.30 -3.71 -1.42 -0.69 -0.33 -0.18 -0.07 

7.48 2.84 0.96 0.40 0.14 0.05 0.01 

-0.70 -0.29 -0.10 - 0.04 -0.02 -0.01 0.00 

-0.30 0.01 0.15 0.18 0.17 0.16 0.11 

2.13 1.14 0.53 0.28 0.13 0.06 0.01 

- 1.17 -0.51 -0.19 -0.08 -0.03, -0.01 0.00 

0.94 0.39 0.13 0.05 0.01 0.00 0.00 

-5.91 -3.55 -2.06 -1.36 -0.87 -0.58 -0.28 

1.51 0.87 0.50 0.33 0.22 0.15 0.07 

-1.72 -1.03 -0.61 -0.40 -0.26 -0.17 - 0.08 

-0.21 -0.16 -0.11 -0.07 - 0.04 -0.02 -0.01 

-6.12 -3.71 -2.17 -1.43 -0.92 - 0.60 -0.28 

1.15 0.54 0.23 0.11 0.04 0.02 0.00 

-3.37 -2.14 -1.33 -0.90 -0.58 -0.38 -0.15 

1.66 - 1.60 -2.45 -2.34 - 1.97 -1.58 -0.97 

-7.13 -4.24 -2.43 -1.58 - 1.00 -0.66 -0.30 

0.44 - 2.29 -2.82 - 2.57 -2.10 -1.66 -1.00 

22 
Table 8. Potential Cuts in R Through the Local Minimum Geometry 64 (All Energies Are in 

kcal/mol and Distances in A.) 

. 

R 4.75 5.00 5.25 5.57 5.75 

JG!T 14.29 5.11 1.43 -0.15 -0.43 

E (10) elst 

E (10) exch 

- 8.55 -3.89 - 2.00 -1.08 -0.85 

24.74 9.84 3.82 1.09 0.54 

E (20) 

ind, resp 

- 6.43 - 2.22 -0.81 -0.26 -0.15 

E t20) 

exch ind, resp 

_ 5.67 1.92 0.64 0.15 0.07 

II P 1 -1.15 1 -0.53 1 -0.21 1 -0.05 1 -0.02 

I p 

elst, resp c3) 

-0.48 -0.12 0.04 0.11 0.12 

E:;,h (2) 

‘E (22) 

ind 

2.16 1.15 0.56 0.20 0.11 

- 0.99 -0.38 -0.14 -0.03 -0.01 

II I I I fEzj,-hd 

E (20) 

disp 

0.88 0.33 0.11 0.02 0.01 

-6.38 -3.74 -2.25 -1.21 -0.88 

E (!l) 1.19 0.65 0.38 0.21 0.16 

dlsp 

0.11 I 0.05 

E (22) 

dim 

-1.30 -0.80 -0.50 -0.29 -0.22 -0.15 I- -0.08 

EOsp (2) -0.11 -0.14 -0.12 ‘-0.08 -0.06 

E g;, (2) - 6.49 -3.88 -2.37 -1.30 -0.95 

E c20) 

exch disp 

_ 

E COlT int 

1.12 0.51 0.22 0.07 0.04 

-3.80 -2.39 -1.57 -0.92 -0.68 

II Eillt 1 10.49 1 2.73 1 -0.14 1 -1.07 1 -1.11 

II ,d$f~C+mb) I -7.94 1 -4.55 ( -2.66 1 -1.39 1 -0.99 -0.64 I -0.29 

E (+mb) 8.93 1.92 -0.55 -1.25 - 1.22 illt -1.04 1 -0.68 

-0.66 1 -0.46 

0.20 I 0.03 

-0.08 1 -0.04 

0.02 I 0.00 

-0.01 I 0.00 

0.12 I 0.09 

0.05 0.01 

~ 

0.00 0.00 

0.00 0.00 

-0.58 I -0.27 

-0.04 I -0.02 

-0.62 I - 0.29 

0.62 0.00 

-0.44 -0.19 

23 
E (20) 

exch-ind,resp + E!20’ md,resp = 1.57 - 2.01 = -0.44 kcal/mol. The resulting two values of opposite signs, 

plus the residual E = -0.18 [see equation (S)], produce the comparatively small -0.39 kcal/mol 

contribution by the EE. Therefore, the correlated interaction terms account for most of the 

- 2.90 kcal/mol stabilization energy E ht(+mb) near the minimum. It is worth pointing out that even 

though the net I-IF induction energy is only -0.44 kcal/mol, it still represents 15% of the total 

E int (+mb) = -2.90 kcal/mol. 

Closer examination of Figure 4a shows that almost all of the stabilizing energy comes from the 

dispersion energy. The intramonomer electron cotrelation contributions, E zfj and E gj, essentially 

cancel one another, making a very small net attractive contribution [the sum is labeled as e(iip(2)]. 

Table 6 shows that at the Gl conformation, ~($)~~(2) contributes only 1% of the total dispersion 

energy. In general, eTisp(2) accounts for no more than about 10% of the leading-order component, 

E?$+mb), and for about two-thirds of all of the points computed, this contribution is less than 5%. 

The primary source of the stabilization of the Gl complex can be pinpointed to the leading-order 

dispersion term E gjtqrnb) o 

Moving away from the Gl minimum to larger intermolecular distances, the stabilization energy 

at R = 3.75 8, (see Figure 4a) is composed of nearly equal contributions from the dispersion term and 

the HF energy. The delicate balance between the first- (E 2' and E izi) and second- (E Esp and 

EgA-,,,,) order interactions contributing to E E 1s ' shown in Figure 4b. Table 6 shows that the 

repulsive first-order exchangenergy is a major contributor to E g over most of the cut through Gl 

and counters the large stabilizing interaction arising from the electrostatic term E ziz'. This gives a 

24 
-2 

-3 

-4 

--c- &(l) elstaesp 

---t3- E”’ exch 

(2-4 

-t- tEind 

7 E(2) (+mb) 

disp 

- ES-disp 

- Ert 

+ Eint (+mb) 

3.0 3.5 

R Ml 

Figure 4a. SAPT Components Used in Equation (9) for a Range of R Values at and Around 

the Local Minimum Geometry Gl. The Estimated Component tEz&,,d Is Not 

Included in the Figure. The Numerical Results for This Cut Are Displayed in 

Table 6. The Energies and Distances Are Given in Units of kcal/mol and A, 

Respectively. 

25 
Es3 

3 

4- 

I - 

, 2 

1 

0 

-1 

-2 

-3 

- Egt 

+s Et’@ 

elst 

,+m Et’@ 

exch 

-e- Et”) md.resp 

Figure 4b. EE and the SAPT Components Included in Equation (8) at and Around 

Geometry Gl as a Function of R. 

26 
net HF first-order contribution of E Fi’ + E LzL = -0.93 kcal/mole ,or 39% of the total interaction 

energy at R = 3.75 A. While this is also a general trend, the G2 geometry is a notable exception. 

Table 6 shows the G2 HF electrostatic term ,?I:;:’ to be repulsive, with a value of +0.33 kcal/mol 

near the minimum at R = 4.65 A. Returning to the Gl geometry, the induction energy ( Ezi!ESp) 

accounts for 22% of the stabilization interactions at R =3.75 A, which gives a net HF second-order 

contribution of E!20) md, resp + eLd.resp = -0.19, or 8% of the total interaction energy. 

A summary of the individual components split according to equation (9) for all four geometries, 

Gl, G2, G3, and G4, are shown in histogram format in Figure 5a. A quick inspection shows that the 

EgiP (2prnb’ energy is the largest component in absolute value for each of these configurations. 

Also, it is clear that Eg plays an important role in determining the total interaction energy at two 

of the four minimum geometries, specifically G2 and G3. For all configurations except G2, the Eg 

energy stabilizes the complex. 

A histogram for the components of Ez for these four geometries is given in Figure 5b. The 

repulsive contribution of EE for G2 differs from the other three minima by having a positive 

electrostatic interaction energy (i.e., EL::’ = +0.33 kcaYmo1). Jn the other three minimum 

conformations, E Liz’ is negative and nearly cancels the positive E~~~~ term. Hence, as seen in 

Table 6, the combination of the positive electrostatic term and a large (positive) E d:L account for 

the very weak bond at this geometry. Finally, for configurations Gl and G4, Figure 5b illustrates 

the cancellation within the first-order and second-order HF terms, leaving J?Z~~,(~)(‘~~) as the 

dominant contribution to the total interaction energy. 

27 
r 

0 m 

I 

- 

. 

A 

28 
. 

4 

3 

2 

1 

0 

-1 

-2 

-3 

-4 

I I 

N 

I I t 

I I I 

w 

i I 

I N 

I 

I I 

I 

I n EK 

Gl G2 G3 G4 

Figure 5b. A Histogram Is Shown Containing E E and the SAPT Components Included in Equation (8) at the Gl, G2,63, and 

64 Minima. 
Tables 9 and 10 provide the interaction energies on the PES around geometry Gl as a function 

of PI for three values of R. Figure 6 displays the PI dependence of the total interaction energy at 

R = 4.0 and 4.75 A. Figure 6 clearly shows the asymmetry in PI for the R = 4.0 8, cut due to the 

absence of a oh symmetry plane in CH,CN. At R = 4.75 A, the PES flattens out and is attractive 

everywhere as a function of the single variable PI, albeit weakly bound. These plots predict a 

favorable angle PI of approach in the range 80’ 5 PI I 150’. 

Analyses of the terms defining the total Eint(+mb) are shown in Figures 7 and 8 for R = 4.0 and 

4.75 A, respectively. Figure 7a plots the components of Eint(+mb) [according to equation (9)] as a 

function of PI at R = 4.0 A. Again, I?,,(‘~~) is determined primarily by two terms, EE and 

E&(2) (+mb). The remaining terms from EL? are small in absolute magnitude and essentially 

cancel one another. Table 9 indicates that the leading-order dispersion term, E gi(+mb), accounts 

for most of the net contribution to the total dispersion interaction. The E ,$ii and E gj energies are 

individually 28% or less of the E gi energy, but are nearly equal in magnitude and opposite in sign, 

effectively canceling one another. This cancellation of dispersion components was noted earlier in 

the analysis of Einl(+mb) as a function of R. 

The separation of E E into the components indicated in equation (8) is shown in Figure 7b. The 

second-order terms, E gieind resp and E g;&, , p ractically cancel over the entire range of PI. Thus, 

the general dependence of133: on PI can be assigned to the two first-order terms E Lzi and E yky’. 

As j$ goes to 180”, the atoms of the CO, molecule come into closer proximity with atoms on 

CH,CN. At PI = 180”) an oxygen resides only 1.95 A away from the nitrogen. In this arrangement, 

one would expect a repulsive intermolecular penetration of the electron clouds by the two monomers 

(i.e., a “steric” interaction, and indeed the exchange [repulsion] interaction dominates near 180”). 

30 
Table 9. Potential Cuts in p1 at Geometry Gl for Two Different R Values (All Energies Are 

in kcal/mol and Distances in A. Only Two Angles Are Shown for the R Value Taken 

From Geometry Gl, Since Each of the Others Is Too High on the Exponential Wall.) 

Eint -0.88 0.78 7.43 -1.59 - 1.76 - 2.09 5.97 

,d$b+mb) -4.11 -6.74 -6.04 -1.21 -1.12 -1.95 - 6.75 

E (+mb) -1.41 -0.41 6.52 -1.71 -1.89 -2.4 4.79 int 

31 
Table 10. Potential Cuts in PI at Geometry GI for R = 4.75 %, (All Energies Are in kcal/moI.) 

32 
. 

7 

6: 

I 

4- 

3. 

2: 

1 

1 

O- \ 

B- 

-l- R=4.75 1 

-2: 

Figure 6. E int (+mb) as a Function of p1 Is Shown for R = 4.0 and R = 4.75 A, With the Remaining Coordinates Taken From Gl. The 

Solid Line Is a Spline Fit to the Single Point SAPT Energies for These Two Cuts and Is Only to Guide the Eye. (Data 

Taken From Tables 9 and 10.) 
(~ouI/py) fczm3 

34 
25 

20 

15 

I( 

5 

0 

-5 

E (20) 

exch-ind,resp 

E (20) 

ind,resp 

E (10) 

exch 

q E (10) 

elst 

/ / 

105 120 135 150 165 180 

Figure 7b. The HF Interaction Energy EE and Its Components According to Equation (8) Shown as a Function of p1 for 

R = 4.0 A. The Remaining Coordinates Are Those of the Gl Geometry. (Data Taken From Table 9.) 
1.5' 

1 

n 

.120 

8 

180 

Figure 8a. The Interaction Energy E izpb’ and Its Components According to Equation (9) Shown as a Function of fix for 

R = 4.75 A. The Remaining Coordinates Are Those of the Gl Geometry. (Data Taken From Table 10.) 
. . 

Y 

2 

1.5 

1 

G=? 

2 Oe5 

3 

s 0 

i2 

b 

c-o.5 

w 

-1 

-1.E 

45 60 75 90 

n 

0 E (20) 

exch-ind,resp 

E cm 

ind,resp 

E (10) 

exch 

E (10) 

elst 

A 

+ 

Cl 

105 120 

8 

135 161 

Figure 8b. The HF Interaction Energy E E and Its Components According to Equation (8) Shown as a Function of p1 for 

R = 4.75 A. The Remaining Coordinates Are Those of the Gl Geometry. (Data Taken From Table 10.) 
This strong dependence of Ezz! on PI (indirectly on R) can be seen in Tables 9 and 10 and in 

Figure 7b as changes in PI bring the two molecules closer together. The EiEi term changes from 

a maximum of +20 kcaYmo1 at PI = 180” to 0.4 kcal/mol at 108” (see Table 9). 

As the two molecules separate to a distance of R = 4.75 A, Figure 8a shows a similar relationship 

between the total interaction energy and its components as seen at the shorter R = 4.0 A distance. 

As PI varies over 45” 2 PI 5 180”, Eint(+mb) isonce again seen to be composed primarily of the E 2 

and E&(2)'+mb) contributions, and the dispersion interaction is comprised almost entirely of the 

leading-order term E disp (20)(+ mb) (see Table 10) . E ?r mt is again a balance between the first-order terms E g: 

and Eg:. From the previous discussion, itis clear that the qualitative, if not quantitative, changes 

in E int(+mb) as a function of R and PI can be traced primarily to three interaction terms: E Lil', E d!$!!, 

md ,Zjf$+mb) . 

5. Conclusions 

The CH,CN-CO, PES was investigated using SAPT. Approximately 200 geometrical 

configurations were computed for both selected individual cuts of the PES around the 4 minimum 

energy geometries and a coarse grid spanning the 5 intermolecular coordinates. A separate 

computation with a larger basis set, including midbond functions, was also performed at each point 

for the leading-order dispersion energy. Four representative local minimum geometries were 

investigated to determine the relative strengths of different physical contributions to the interaction 

energy. The leading-order dispersion energy, Egi, contributed a large percentage of the binding 

energy near each of the local minima investigated. Surprisingly, the intramonomer electron 

correlation corrections to the leading-order dispersion component had very little impact on the final 

energies due to cancellation between them-even though, individually, they typically had large 

38 
absolute magnitudes. The SM HF energy, EE , which includes contributions from the leading-order 

SAPT components of polarization, exchange, and induction, also had a large though varying impact 

on the final interaction energy around the local minima investigated. The main contributors to EE 

are the first-order exchange and electrostatic terms, where the importance of the electrostatic term 

is due to the strongly polar nature of the CH,CN monomer. The most strongly bound geometrical 

configuration investigated had an interaction energy of -2.90 kcaVmo1. 

39 
INTENTIONALLY LEFT BLANK. 
6. References 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

Allen, M. P., and D. J. Tildesley. Computer Simulation ofliquids. Oxford: Clarendon Press, 

1987. 

McHugh, M. A., and V. J. Krukonis. Supercritical Fluid Extraction: Principles and Practice. 

Second edition, Butterworth-Heinemann series in chemical engineering, MA, 1994. 

Morris, J. B., M. A. Schroeder, R. A. Pesce-Rodriguez, K. L. McNesby, and R. A. Fifer. 

“Supercritical Fluid Extraction of N&amine-Based Gun Propellant: A Fluid Survey.” 

ARL-TR-885, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, 1995. 

Jeziorski, B., R. Moszynski, and K. Szalewicz. Chemical Review. Vol. 94, p. 1887, 1994. 

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41 
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Appendix: 

Supporting Information for Investigation of the 

CH&N-CO2 Potential Energy Surface (PES) Using 

Symmetry-Adapted Perturbation Theory (SAPT) 

45 
b?TENTIONALLY LEFT BLANK. 

46 
. 

. 

Table A-l. The Supplementary Tables Complement Tables 6-10 and Provide a Complete Description of All Single-Point 

Symmetry-Adapter Perturbation Theory (SAPT) Computations Used in the Present Work (The Units for Energies, 

Distances, and Angles Are kcal/mol, A, and Degrees, Respectively.) 

EE 54.71 76.12 193.89 137.17 160.94 57.99 28.76 21.96 14.37 66.12 

E (lo) - 27.08 - 42.84 125.78 - 48.70 -65.44 - 39.94 - 13.47 -11.21 - 10.02 - 42.75 PO1 

E (lo) 90.10 129.54 374.04 220.37 263.12 110.20 45.59 36.05 26.76 120.85 exch 

E p - 43.57 - 63.54 229.78 159.27 187.28 -56.29 -21.97 -17.16 -11.58 -57.64 md.resp 

E c20) 35.52 49.65 118.29 99.49 110.77 45.98 20.26 15.93 10.57 46.66 

exch -ind,xesp 

6 -0.26 3.30 57.12 25.28 39.77 -1.96 -1.65 -1.65 -1.35 -1.00 

~(p$R.sp (3) -2.40 -1.98 -0.25 -5.54 -4.84 - 1.39 -0.72 -0.56 -0.24 -1.48 

Et;&, c2) 3.45 2.34 - 4.97 - 0.93 -2.88 2.65 -0.06 0.29 1.05 2.24 

‘E g) -2.36 -3.38 -9.46 -3.02 -3.76 -3.66 -0.40 -0.46 -0.66 -3.90 

‘E (2% 1.93 2.64 4.87 1.88 2.22 2.99 0.37 0.42 0.60 3.16 

exch -ind 

E (20) - 17.54 -21.14 -39.97 -28.49 -31.77 - 19.41 - 10.48 -9.28 -8.22 -20.42 

disp 

E c21) 3.87 4.71 10.18 6.22 7.20 6.36 2.95 2.50 2.15 6.44 disp 
Table A-l. The Supplementary Tables Complement Tables 6-10 and Provide a Complete Description of All Single-Point 

Symmetry-Adapter Perturbation Thepry (SAPT) Computations Used in the Present Work (The Units for Energies, 

Distances, and Angles Are kcal/mol, A, and Degrees, Respectively.) (continued) 

E (22) 

disp 

Eosp (2) 

E :ip (2) 

E t20) 

exch -disp 

Eint col? 

E int 

,$$+mb) 

E (+mb) 

int 

-3.69 -4.21 -7.10 -5.48 -5.94 -5.08 -2.25 -1.96 -1.88 -5.18 

0.18 0.50 3.08 0.74 1.25 1.28 0.71 0.54 0.27 1.26 

- 17.36 - 20.64 - 36.89 - 27.75 - 30.52 -18.13 -9.77 -8.74 -7.95 - 19.16 

3.95 5.03 7.47 5.90 6.71 4.69 2.67 2.24 1.69 4.92 

- 12.79 - 15.99 - 39.23 - 29.45 -33.06 - 12.85 -7.91 -6.80 -5.50 - 14.22 

41.92 60.12 154.66 107.71 127.88 45.14 20.86 15.16 8.87 51.90 

-21.72 -25.87 -45.80 -33.51 -37.17 -23.62 - 12.53 - 11.20 -9.99 - 24.96 

37.73 55.40 148.83 102.70 122.49 40.92 18.80 13.24 7.10 47.36 

. 1 
. 

. 

Table A-2. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 
Table A-2. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 
. . 

Table A-3. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

p) 9.34 2.67 2.98 2.51 0.55 0.63 

disp 

1.01 5.71 0.79 0.89 

E (72) - 6.68 -2.44 -2.64 -2.33 -0.67 - 0.77 -1.15 

dlsp 

-4.39 -0.97 -1.07 
Table A-3. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

&(g, (2) 2.66 0.23 0.34 0.18 -0.12 -0.14 -0.14 1.33 -0.19 -0.17 

E :;, (2) -32.74 -13.68 -14.60 -11.67 -3.38 -3.98 -6.04 -22.08 -5.43 -6.01 

E t20) 5.97 3.17 3.40 2.60 0.42 0.57 1.13 3.46 0.96 1.13 

exch-disp 

4nt corr -37.32 -9.76 -10.62 -7.70 -2.82 -3.08 -4.05 -22.95 -4.09 -4.39 

E int 153.16 39.57 44.75 33.19 2.26 3.37 9.09 80.49 8.22 9.97 

E$C+mb) -43.28 -17.02 -18.01 -14.55 -3.92 -3.92 -6.99 -27.02 -6.35 -7.05 

E t+mb) 145.28 36.45 41.68 30.48 1.60 3.29 8.01 76.87 7.11 8.74 

int 

. 
. 

. 

. 

Table A-4. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 4 4 4 4 4 4 4 4 4 4 

P* 45 90 90 90 90 90 90 90 90 135 

Yl 60 0 0 0 0 60 60 60 60 0 

P2 45 0 45 45 45 0 45 45 45 0 

CL, 90 0 0 45 90 0 0 45 90 0 

EE 22.44 1.95 2.19 1.61 0.41 2.38 2.30 1.75 0.60 22.66 

E('O) -13.79 - 1.36 0.94 0.54 -0.42 -1.68 1.08 0.68 -0.41 -11.19 

PO1 

E (lo) 42.27 3.72 1.49 1.27 1.00 4.59 1.49 1.30 1.20 37.08 

exch 

E c20) -18.32 - 1.20 -0.57 -0.47 -0.35 -1.30 -0.57 -0.47 -0.38 - 15.25 

ind,resp 

E (20) 15.20 1.03 0.44 0.36 0.25 1.07 0.41 0.34 0.26 14.08 

exch-ind,resp 

6 -2.92 -0.24 -0.11 -0.09 -0.06 -0.31 -0.12 -0.10 -0.08 - 2.07 

E;;l,resp(3) -o-37 -0.07 -0.33 -0.23 -0.01 -0.08 -0.36 -0.26 -0.03 -0.86 

$;,f, c2) 1.34 0.34 0.07 0.07 0.09 0.41 0.08 0.08 0.11 1.15 

‘E (22) -1.35 -0.05 0.01 0.00 -0.01 -0.08 0.01 0.00 -0.01 -1.16 

ind 

‘E (22) 1.12 0.04 0.00 0.00 0.00 0.06 0.00 0.00 0.01 1.07 

exch -ind 

E c20) -7.96 -2.63 -1.48 -1.40 -1.35 -2.85 - 1.53 -1.45 -1.44 -8.19 

disp 

E t21) 1.33 0.69 0.35 0.33 0.32 0.70 0.35 0.32 0.31 2.52 

disp 

E (T2, -1.42 -0.67 -0.34 -0.32 -0.32 -0.70 -0.35 -0.32 -0.33 -2.08 

dlsp 

&7’sp (2) -0.10 0.02 0.01 0.01 0.00 -0.01 0.00 0.00 -0.02 0.44 
Table A-4. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

E 16.82 -0.09 0.60 0.17 -0.77 0.16 0.63 0.23 -0.68 17.14 int 

Eg$+mb) -9.50 -3.08 -1.72 - 1.63 -1.56 -3.39 - 1.78 - 1.70 -1.68 - 10.07 

E (+mb) 15.27 -0.54 0.36 -0.06 -0.98 -0.37 0.38 -0.01 -0.92 15.25 bit c 
. 

Table A-5. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 

Pl 

Yl 

P2 

a, 

EE 

&lo) 

PO1 

E(‘O) 

exch 

E c20) 

ind,resp 

E (20) 

exch-ind,resp 

6 

&$, resp (3) 

$;,h c2) 

‘E (22) 

ind 

‘E $,-i,,d 

E t20) 

disp 

E t21) 

disp 

E (22) 

disp 

gp (2) 

4 4 4 4 4 4 4 4 4 4 

135 135 135 135 135 135 135 180 180 180 

0 0 0 60 60 60 60 0 0 60 

45 45 45 0 45 45 45 0 45 45 

0 45 90 0 0 45 90 0 0 0 

15.89 11.39 5.11 22.59 15.88 11.39 5.11 193.11 34.87 34.87 

-5.79 - 4.28 - 2.94 -11.16 -5.78 - 4.26 -2.92 116.65 -21.29 -21.29 

23.87 17.30 8.91 36.99 23.85 17.29 8.89 335.28 60.58 60.58 

-9.00 -6.48 -3.39 - 15.20 -8.99 -6.48 -3.39 187.58 -26.46 -26.46 

8.27 5.97 3.10 14.04 8.27 5.96 3.09 103.24 23.14 23.14 

-1.46 -1.12 -0.57 -2.08 -1.47 -1.12 -0.57 58.83 -1.11 -1.11 

-0.99 -0.71 -0.27 -0.86 -0.99 -0.72 -0.27 -3.86 -1.58 -1.58 

1.49 1.08 0.49 1.15 1.49 1.08 0.49 -4.31 1.87 1.87 

-1.14 -0.75 -0.28 -1.16 -1.14 -0.75 -0.28 -11.92 -3.32 -3.32 

1.05 0.69 0.26 1.07 1.05 0.69 0.26 6.56 2.90 2.90 

-6.09 -5.08 -3.50 -8.18 - 6.09 -5.08 -3.50 -31.23 - 10.53 - 10.53 

1.89 1.49 0.90 2.52 1.89 1.49 0.90 11.49 3.19 3.19 

-1.83 -1.42 -0.84 -2.08 -1.83 -1.42 -0.84 -9.11 -2.95 -2.95 

0.06 0.06 0.06 0.44 0.06 0.06 0.06 2.38 0.24 0.24 
Table A-5. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

E int 11.65 7.77 2.52 17.06 11.64 7.77 2.52 156.85 27.28 27.29 

,y $$+mb) -7.14 -6.01 -4.22 - 10.07 -7.14 -6.01 - 4.22 -38.61 - 13.03 - 13.03 

E (+mb) 10.59 6.84 1.80 15.17 10.58 6.83 1.80 149.48 24.78 24.78 bit 
. 

Table A-6. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 5 5 5 5 5 5 5 5 5 5 

PI 0 0 0 45 45 45 45 45 45 45 

Y1 0 0 60 0 0 0 0 60 60 60 

Pz 0 45 45 0 45 45 45 0 45 45 

a, 0 0 0 0 0 45 90 0 0 45 

EE 5.14 1.27 1.35 0.77 0.50 0.38 0.20 2.79 0.64 0.60 

&lo) -3.90 -1.01 - 1.05 -1.50 0.25 0.04 -0.45 -3.59 -0.15 -0.33 

PO1 

E (lo) 9.87 2.56 2.69 2.55 0.31 0.42 0.79 7.49 1 .oo 1.16 

exch 

E (20) md,resp -2.23 -0.62 -0.67 -0.61 -0.10 -0.13 -0.22 -2.36 -0.31 -0.35 

Y E t20) 1.92 0.49 0.53 0.48 0.05 0.07 0.14 1.90 0.20 0.23 

exch-ind,mp 

6 -0.53 -0.14 -0.15 -0.15 -0.02 - 0.03 -0.06 - 0.65 - 0.09 -0.11 

& (1) (3) -0.12 - 0.04 - 0.05 0.07 -0.08 -0.05 0.01 0.04 -0.06 -0.04 

pobesp 

&;:ch c2) 1.16 0.34 0.35 0.34 0.05 0.06 0.11 0.76 0.11 0.13 

‘E (22) -0.38 -0.09 -0.09 - 0.07 0.00 -0.01 -0.02 -0.25 -0.02 -0.03 

ind 

tE (22) 

exch -ind 

0.33 0.07 0.07 0.06 0.00 0.00 0.01 0.20 0.01 0.02 

E (20) disp 

E’T” 

dlsp 

E (22) 

disp 

-3.75 -1.78 -1.82 -1.69 -0.66 -0.72 -0.92 - 2.66 -0.93 -0.99 

0.66 0.26 0.26 0.30 0.11 0.12 0.14 0.44 0.12 0.13 

-0.80 -0.37 -0.38 -0.40 -0.15 -0.16 -0.21 -0.59 - 0.20 -0.21 

&$)sp (2) -0.14 -0.12 -0.11 -0.10 -0.04 - 0.04 -0.06 -0.15 -0.08 -0.08 
Table A-6. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

E :ip (2) -3.89 -1.90 - 1.93 - 1.78 -0.69 -0.77 -0.98 -2.81 -1.01 - 1.07 

E t20) 0.52 0.17 0.17 0.16 exch -disp 0.02 0.03 0.06 0.40 0.06 0.07 

E COlT -2.39 -1.45 -1.47 - 1.23 int -0.70 -0.73 -0.81 - 1.67 -0.90 -0.92 

E int 2.75 -0.18 -0.12 -0.46 -0.20 -0.35 -0.61 1.12 -0.26 -0.31 

,d$$+mb) -4.55 - 2.09 -2.13 - 1.96 -0.74 -0.82 - 1.04 -3.11 -1.06 -1.13 

E (+mW 1.95 int -0.49 -0.43 -0.73 -0.29 -0.44 -0.73 0.68 -0.39 -0.46 
Table A-7. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 

Pl 

Yl 

P2 

a, 

EE 

E (lo) 

PO1 

E (lo) 

exch 

E c20) 

ind,resp 

E t20) 

exch ind,resp 

_ 

6 

~(pYl,lesp (3)

&$, c2) 

‘E (22) 

ind 

‘E (22) 

exch -ind 

E (20) 

disp 

Et21) 

disp 

E (22) 

disp 

Ey$p (2) 

5 5 5 5 5 5 5 5 5 5 

45 90 90 90 90 90 90 90 90 135 

60 0 0 0 0 60 60 60 60 0 

45 0 45 45 45 0 45 45 45 0 

90 0 0 45 90 0 0 45 90 0 

0.57 -0.03 0.65 0.44 -0.04 -0.09 0.68 0.48 -0.03 1.64 

-0.82 -0.09 0.64 0.43 -0.04 -0.17 0.68 0.47 -0.04 0.64 

1.69 0.10 0.04 0.04 0.03 0.13 0.04 0.04 0.04 1.23 

-0.49 -0.06 -0.04 -0.04 -0.03 -0.07 -0.04 -0.04 -0.03 -0.44 

0.35 0.02 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.30 

-0.15 -0.01 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 -0.09 

0.02 0.00 -0.14 -0.10 0.00 0.01 -0.15 -0.10 0.00 -0.25 

0.19 0.01 0.00 0.00 0.00 0.02 0.00 0.00 0.01 0.17 

-0.05 0.01 0.00 0.00 0.00 0.01 0.01 0.00 0.00 - 0.03 

0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 

-1.18 -0.50 -0.32 -0.31 -0.31 -0.54 -0.33 -0.32 -0.33 -1.16 

0.15 0.14 0.08 0.08 0.08 0.14 0.08 0:OS 0.08 0.33 

-0.25 -0.14 -0.08 -0.08 -0.08 -0.15 -0.08 -0.08 -0.08 -0.34 

-0.10 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 -0.02 
Table A-7. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

-1.28 1 -0.50 1 -0.32 1 -0.31 1 -0.31 1 -0.55 1 -0.33 1 -0.32 1 -0.33 1 -1.18 

E (20) 

exch-disp 

Eint cot-r 

E int 

,yf$+mb’ 

E (+mb) 

int 

0.10 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.11 

-0.98 -0.47 -0.44 -0.39 -0.29 -0.51 -0.46 -0.41 -0.32 -1.16 

-0.41 -0.50 0.21 0.05 -0.33 -0.60 0.22 0.06 -0.35 0.48 

-1.35 -0.55 -0.35 -0.34 -0.33 -0.60 -0.36 -0.35 -0.36 - 1.34 

-0.59 -0.55 ,0.18 0.02 -0.36 -0.66 0.19 0.03 -0.38 0.29 

I I 
. 

. 

Table A-8. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 

Pl 

Yl 

P2 

a, 

EL? 

E(‘o) 

PO1 

E(‘O) 

exch 

E (20) 

ind,resp 

E t20) 

exch-ind.resp 

6 

&jf&esp (3) 

$;& c2) 

‘E ?;’ 

tE (22) 

exch -ind 

E c20) 

disp 

E’T1’ 

dlsp 

E (22) 

disp 

$isp (2) 

5 5 5 5 5 5 5 5 5 5 

135 135 135 135 135 135 135 180 180 180 

0 0 0 60 60 60 60 0 0 60 

45 45 45 0 45 45 45 0 45 45 

0 45 90 0 0 45 90 0 0 0 

1.37 1.03 0.33 1.63 1.37 1.03 0.33 7.51 1.58 1.58 

0.92 0.67 0.10 0.64 0.92 0.67 0.10 -0.47 -0.04 -0.04 

0.63 0.52 0.33 1.23 0.63 0.52 0.33 8.86 1.96 1.96 

-0.27 -0.23 -0.15 -0.44 -0.27 -0.23 -0.15 -2.73 -0.66 -0.66 

0.13 0.11 0.07 0.30 0.13 0.11 0.07 2.33 0.43 0.43 

-0.04 -0.03 -0.02 -0.09 -0.04 -0.03 -0.02 -0.49 -0.11 -0.11 

-0.21 -0.16 -0.07 -0.25 -0.21 -0.16 -0.07 -0.74 -0.21 -0.21 

0.11 0.09 0.05 0.17 0.11 0.09 0.05 1.15 0.33 0.33 

-0.02 -0.02 0.00 -0.03 -0.02 -0.02 0.00 -0.57 -0.13 -0.13 

0.01 0.01 0.00 0.02 0.01 0.01 0.00 0.49 0.09 0.09 

-0.82 - 0.74 -0.60 -1.16 -0.82 -0.74 -0.60 -3.12 -1.38 -1.38 

0.24 0.21 0.15 0.33 0.24 0.21 0.15 0.93 0.36 0.36 

-0.28 -0.24 -0.17 -0.34 -0.28 -0.24 -0.17 -1.08 -0.45 -0.45 

-0.04 -0.03 -0.01 -0.02 -0.04 -0.03 -0.01 -0.15 -0.08 -0.08 
Table A-8. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 
. 

Table A-9. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 6 6 6 6 6 6 6 6 6 6 

PI 0 0 0 45 45 45 45 45 45 45 

YI 0 0 60 0 0 0 0 60 60 60 

P2 0 45 45 0 45 45 45 0 45 45 

cl, 0 0 0 0 0 45 90 0 0 45 

EE -0.54 -0.15 -0.15 -0.43 0.14 0.05 -0.13 -0.54 0.07 0.00 

p) -0.67 -0.17 -0.17 -0.45 0.14 0.06 -0.12 -0.65 0.06 0.00 

PO1 

E (lo) 0.20 0.06 0.06 0.06 0.01 0.01 0.02 0.18 0.03 0.04 

exch 

E !20) -0.08 -0.04 -0.04 -0.04 -0.02 -0.02 -0.02 -0.08 -0.03 - 0.03 

md, resp 

pa 0.02 0.01 0.01 0.01 0.00 0.00 0.00 0.03 0.00 0.00 

exch-ind,resp 

6 -0.01 0.00 0.00 -0.01 0.00 0.00 0.00 -0.01 -0.01 -0.01 

EpolJesp(3) (1) 0.12 0.03 0.03 0.08 -0.03 -0.01 0.02 0.10 -0.02 -0.01 

$ich (2) 0.05 0.01 0.01 0.02 0.00 0.00 0.00 0.04 0.01 0.01 

‘E !22) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 

md 

‘E (22) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 

exch -ind 

E 0-4 -0.58 -0.34 -0.34 -0.33 -0.17 -0.18 -0.21 -0.43 -0.21 -0.22 

disp 

E’T” 0.11 0.06 0.06 0.07 0.03 0.04 0.04 0.08 0.03 0.04 

dlsp 

E (22) -0.15 -0.08 -0.08 -0.09 -0.04 -0.04 -0.05 -0.12 -0.05 -0.05 

disp 

$sp (2) -0.04 -0.02 -0.02 -0.02 -0.01 -0.01 -0.01 -0.04 - 0.02 -0.02 
Table A-9. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 
65 
Table A-10. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

EEfj(+mb) -0.26 -0.14 -0.10 -0.10 -0.10 -0.15 -0.10 -0.10 -0,lO -0.26 

E (+mb) -0.39 -0.18 0.16 0.08 -0.12 -0.22 0.16 0.08 -0.12 0.14 int 
Table A-11. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 

Pl 

Yl 

P2 

cl, 

GE 

E (lo) 

PO1 

E (lo) 

exch 

E c20) 

ind, resp 

E t20) 

exch-ind,resp 

6 

E$. resp (3) 

&;)ch c2) 

tE (22) 

ind 

tE (22) 

exch -ind 

E t20) 

disp 

E t21) 

disp 

E (22) 

disp 

&:;sp (2) 

6 6 6 6 6 6 6 6 6 6 

135 135 135 135 135 135 135 180 180 180 

0 0 0 60 60 60 60 0 0 60 

45 45 45 0 45 45 45 0 45 45 

0 45 90 0 0 45 90 0 0 0 

0.48 0.36 0.09 0.50 0.48 0.36 0.09 1.07 0.23 0.23 

0.51 0.38 0.11 0.51 0.51 0.39 0.11 0.99 0.24 0.24 

0.02 0.01 0.01 0.03 0.02 0.01 0.01 0.20 0.05 0.05 

-0.04 -0.04 -0.03 -0.05 - 0.04 - 0.04 -0.03 -0.15 -0.07 -0.07 

0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.03 0.01 0.01 

0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 

-0.08 -0.07 - 0.03 -0.10 -0.08 -0.07 -0.03 -0.17 - 0.05 -0.05 

0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.06 0.02 0.02 

0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 

-0.18 -0.17 -0.15 -0.24 -0.18 -0.17 -0.15 -0.48 -0.27 -0.27 

0.06 0.05 0.04 0.08 0.06 0.05 0.04 0.16 0.08 0.08 

-0.07 -0.06 -0.05 -0.08 -0.07 -0.06 -0.05 -0.20 -0.10 -0.10 

-0.01 -0.01 0.00 -0.01 -0.01 -0.01 0.00 -0.04 - 0.02 -0.02 
Table A-11. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

E@) 

E (20) exch-disp 

E. corr mt 

E int 

Ef$+mb) 

E (+mb) illt 

-0.19 -0.18 -0.15 -0.25 -0.19 -0.18 -0.15 -0.51 -0.28 -0.28 

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 

-0.27 -0.24 -0.17 -0.34 -0.27 -0.24 -0.17 -0.61 -0.31 -0.31 

0.21 0.12 -0.08 0.16 ,0.21 0.12 -0.08 0.45 -0.08 -0.08 

-0.20 -0.19 -0.16 -0.26 -0.20 -0.19 -0.16 -0.52 -0.29 -0.29 

0.20 0.11 -0.09 0.14 0.20 0.11 -0.09 0.40 -0.11 -0.11 

. . 
. . 

Table A-12. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) 

R 3.33” 3.33 3.33 3.33 3.33 3.50 3.50 3.50 3.50 3.50 

Pl 135 90 45 45 180 135 90 45 45 180 

Yl 60.15b 60.15 60.15 0.15” 0.15 60.15 60.15 60.15 0.15 0.15 

P2 116.67 116.67 116.67 116.67 116.67 116.67 116.67 116.67 116.67 116.67 

a-2 359.98 359.98 359.98 359.98 359.98 359.98 359.98 359.98 359.98 359.98 

EE 4.04 5.40 163.58 101.09 82.56 1.39 2.15 97.75 58.89 0.23 

E (lo) 

PO1 

E (lo) 

exch 

-8.47 -6.71 -93.18 - 60.46 -70.35 -5.85 -4.36 -56.06 - 34.04 -2.44 

14.22 14.19 300.97 172.72 168.33 8.33 7.73 178.44 99.29 3.13 

E t20) -7.71 -4.76 - 194.21 - 80.67 - 100.25 -4.38 -2.47 - 102.66 -41.41 -1.05 

ind,resp 

E t20) 6.52 3.81 107.01 58.81 73.29 3.63 1.88 69.11 33.77 0.75 

exch-ind,mp 

6 -0.54 -1.13 42.99 10.70 11.56 -0.34 -0.62 8.92 1.28 -0.17 

Ey;,,resp(3) o-44 0.22 -0.90 -1.25 - 2.09 0.40 0.25 -0.94 -1.03 0.26 

d&h c2) 0.68 1.00 - 4.09 0.42 1.10 0.46 0.65 -0.54 1.67 0.35 

f E (22) 

ind 

-0.06 -0.40 -7.84 -5.38 -7.41 -0.02 -0.20 -5.10 -3.27 -0.07 

‘E (22) 

exch -ind 

0.05 0.32 4.32 3.92 5.41 0.02 0.16 3.43 2.67 0.05 

E (20) 

disp 

-5.55 - 4.90 -31.98 -22.33 - 22.56 - 4.02 -3.47 -21.74 - 15.22 -2.59 

E t21) 

disp 

1.48 0.97 7.38 4.77 7.09 1.04 0.67 4.54 2.95 0.58 

. . -_- ^^ _ -_ Unless otherwise noted, the full value of the coordinates are given in ‘l‘able Z tor the ti 1 geometry. 

b Full coordinate value is 60.147002. 

’ Full coordinate value is 0.147002. 
Table A-12. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l.) (continued) 

a Unless otherwise noted, the full value of the coordinates are given in Table 2 for the Gl geometry. 

b Full coordinate value is 60.147002. 

’ Full coordinate value is 0.147002. 

. 
ds!e 

SS’Z- S9’0- W’O - LS’I - 92’2 - OI‘Z- IS’O- S9’0- IZ’P- SO’1 - (zz) g 

We 

09’2 P9’0 LE.0 6P’ I 12-z 22’2 IV0 i79.0 TL’P PO’ I (Iz)g 

ds!e 

PtT’6- SS’Z- 99’T- 8L’8- CL’21 - 9CZI - SI’Z- SS’Z- PL’SI - IO’P- (oz) g 

pu!- q3xa 

LZ’Z 00’0 10’0 ZE’I P6’ I L6’T SO’0 00’0 SO’P 20’0 (zz) z 

19x- 00-0 20’0 - 6i7*1- 82’2 - 8P’Z - LO’0 - 00’0 ZO’S- 20’0 - , (3~ 

q3xa 

SI’Z SZ’O LI’O 69’ I SVZ ICI iTiT’ SZ’O LT.2 9t7.0 (2) co3 

dsa’lod 

ZO’I- PC’0 PZ’O C9’0- LP’T. - ZL’O- 92’0 St70 P9’T - m-0 (0 (II3 

OS’O- LI’O- LO’0 - II’I- 88’0- 81X-- LZ’O - LI’O- 29’2 PE’O- 9 

dw‘pn!-qaxa 

92’8 T SS’I 82’0 99x I S6’TZ L6’O‘iT 99’0 PSI 02’ EP L9.C (oz) g 

dsa ‘pm 

IO’IZ- L6’1- LP’O - 9CSI - LL’SZ- SO’6E - 66-O- 96’1- SS’ES - IP’P- mj B 

qsxa 

6Z’SV P8’E 92’ I 9ixP 26’99 Pp.08 LT’C 18’S VS.66 658 (01) B 

vJ 

82’67 - 29x- 6S’T - ~S’PI - ZO’IZ- 9fYsz - SS’Z- P9’E - 89’lP- ‘iI8.S - (or) B 

W! 

9L’ZZ 9E’O- 6S’O - 20’92 IZ’IP Z8’PP 20’0 i3’0 - SI’OS 8P’ I AH 3 

86’6% 86’6% 86’6SS 86’6SC 86’6% 86’6% 86’61;s 86’6s 86’6s 86’6% % 

L9’9 T I L9’9 I I L9’9 I I L9’91 I L9’9 I I L9’9 I I L9’9 I I L9’9 I I L9’9 I I L9’9 I I “d 

SI’O SI’O ST’0 SI’O ST’0 ST’09 ST-09 ST-09 SI’O ST’0 ‘A 

081 SE1 06 SP 0 SV 06 SET 081 SE1 ‘d 

SL’E _ SL’E _ SL’E _ SL’fT _ SL’C _ SL’E _ SL’fz SL’tY OS’C OS’S 2l 

(YIopu.IoJuI ap?u!p300~ JOJ 21-V alqua 

u! sa)ou)ood aas i1-v aIqu& JO uo!$dt.z3 aq~ aas %gun pm uo!$dyxaa .IO& panuguo3 salqrr& b;rquatua~ddng l sl-v aIqlr& 

. 

. 
Table A-13. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l; See Footnotes in 

Table A-12 for Coordinate Information.) (continued) 
, 

Table A-14. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l; See Footnotes in 

Table A-12 for Coordinate Information.) 

R 

Pl 

Yl 

P2 

Q-2 

EE 

E(‘O) 

PO1 

E (lo) 

exch 

E !20, 

md, tap 

E t20) 

exch -ind.resp 

6 

& (1) (3) 

pol,resp 

‘$;ch t2) 

‘E ?;’ 

‘E (22) 

exch -ind 

E (TO’ 

dlsp 

p) 

disp 

E (22) 

disp 

4.00 4.00 4.00 4.25 4.25 4.25 4.25 4.25 4.25 4.25 

135 90 45 135 90 45 0 45 90 135 

60.15 60.15 60.15 60.15 60.15 60.15 0.15 0.15 0.15 0.15 

116.67 116.67 116.67 116.67 116.67 116.67 116.67 116.67 116.67 116.67 

359.98 359.98 359.98 359.98 359.98 359.98 359.98 359.98 359.98 359.98 

-1.05 -0.69 19.82 -1.17 -0.84 8.47 8.21 4.47 - 0.78 -1.09 

-2.44 -1.65 -11.03 -1.74 -1.17 - 4.69 -3.39 -2.61 -0.88 -1.26 

1.73 1.28 35.01 0.78 0.51 14.86 12.64 7.71 0.20 0.29 

-0.90 -0.43 - 14.51 -0.43 -0.21 -5.37 -3.67 -2.10 -0.12 -0.20 

0.64 0.23 12.37 0.26 0.08 4.64 3.25 1.89 0.04 0.10 

-0.08 0.11 -2.02 -0.04 -0.05 -0.97 -0.62 -0.41 -0.01 -0.02 

0.29 0.24 -0.44 0.24 0.20 -0.23 -0.48 -0.14 0.18 0.25 

0.13 0.16 1.31 0.07 0.07 0.87 1.02 0.64 0.03 0.02 

0.01 - 0.02 -1.12 0.01 -0.01 -0.48 -0.43 -0.26 0.00 0.02 

-0.01 0.01 0.95 -0.01 0.00 0.41 0.38 0.23 0.00 -0.01 

-1.64 -1.37 -7.07 -1.08 -0.89 -4.11 -4.52 -3.06 -0.73 -0.74 

0.41 0.27 1.09 0.27 0.18 0.56 0.64 0.43 0.17 0.19 

-0.42 -0.34 -1.24 -0.28 -0.23 -0.75 -0.85 -0.59 - 0.20 -0.20 
74 
. 

(wogauI.xoJuI a)au!pJoo~ .IOJ 21-V alqE& 

. 

. 
Table A-15. Supplementary Tables Continued (For Description and Units, See the Caption of Table A-l; See Footnotes in 

Table A-12 for Coordinate Information.) (continued) 

4& (2) -0.12 -0.01 -0.03 -0.16 -0.17 -0.12 -0.01 0.00 -0.10 0.00 -0.02 -0.12 

E:;,(2) -3.48 -0.73 - 0.63 -2.60 -2.93 - 1.99 -0.52 -0.73 -2.16 -0.50 -0.43 -1.61 

E (20) 0.60 0.03 0.02 0.34 0.32 0.20 0.01 0.03 0.28 0.01 0.01 0.15 

exch-disp 

J%lt corr -2.30 -0.46 -0.41 -1.91 -2.36 -1.52 -0.34 -0.46 -1.52 -0.30 -0.27 -1.26 

E int 1.34 -1.55 - 1.20 1.55 1.22 0.17 -1.03 -1.53 -0.41 - 1.25 -0.96 0.07 

,d$(+mb) - 4.02 -0.84 -0.66 -2.85 -3.39 -2.17 -0.55 -0.84 -2.43 -0.57 -0.45 -1.72 

E (+mb) 0.68 -1.67 -1.26 1.14 0.59 -0.13 -1.07 -1.64 -0.78 - 1.32 -0.99 -0.15 int 
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, 

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

Investigation of the CH,CN-CO2 Potential Energy Surface (PES) 

Using Symmetry-Adapted Perturbation Theory (SAPT) 

3ayes L. Williams, Betsy M. Rice, and Cary F. Chabalowski 

ITS. Army Research Laboratory 

4’ITN: AMSRL-WM-BD 

REPORT NUMBER 

Il. SUPPLEMENTARY NOTES 

12a. DISTRIBUTION/AVAILABILlTY STATEMENT 

Eipproved for public release; distribution is unlimited. 

12b. DISTRIBUTION CODE 

13. ABSTRACT(Maxlmum 200 words) 

Symmetry-adapted perturbation theory (SAPT) has been used to investigate the intermolecular potential energy surface 

(PES) of CH,CN-CO,. A SAPT computation was performed for approximately 200 geometrical configurations using both 

a coarse grid in the five intermolecular coordinates as well as selected representative cuts. Four near-local minima are 

located on the PES. The deepest of these is -2.90 kcal/mol. 

14. SUBJECT TERMS 

ntermolecular interactions, symmetry adapted perturbation theory, quantum chemistry 

15. NUMBER OF PAGES 

86 

16. PRICE CODE 

7. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSlFlCATlON 20. LIMITATION OF ABSTRACT 

OF REPORT OF THIS PAGE OF ABSTRACT 

UNCLASSIFIED UNCLASSJFIED UNCLASSJFIED UL ,CLl -JC”,-, n. eon ccnn C+lnAlrr( L-em 9cm mm, %Ra\ 

79 

“Lc,,I”UI” I “llll b”” \. a”.. - “.d, 

Prescribed by ANSI Std. 239-l 8 298-l 02 
INTENTIONALLY LEFT BLANK. 
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