*Ab initio*investigation of benzene clusters: Molecular tailoring approach

^{1}, Anuja P. Rahalkar

^{2}, Shridhar R. Gadre

^{2,3,a)}and G. Narahari Sastry

^{1,a)}

### Abstract

An exhaustive study on the clusters of benzene , , at level of theory is reported. The relative strengths of and interactions in these aggregates are examined, which eventually govern the pattern of cluster formation. A linear scaling method, *viz.*, molecular tailoring approach (MTA), is efficiently employed for studying the energetics and growth patterns of benzene clusters consisting up to eight benzene (Bz) units. Accuracy of MTA-based calculations is appraised by performing the corresponding standard calculations wherever possible, i.e., up to tetramers. For benzene tetramers, the error introduced in energy is of the order of 0.1 mH . Although for higher clusters the error may build up, further corrections based on many-body interaction energy analysis substantially reduce the error in the MTA-estimate. This is demonstrated for a prototypical case of benzene hexamer. A systematic way of building up a cluster of n monomers (-mer) which employs molecular electrostatic potential of an -mer is illustrated. The trends obtained using MTA method are essentially identical to those of the standard methods in terms of structure and energy. In summary, this study clearly brings out the possibility of effecting such large calculations, which are not possible conventionally, by the use of MTA without a significant loss of accuracy.

Financial support from DAE-BRNS, Mumbai and CAS program by University Grant Commission (UGC), New Delhi is gratefully acknowledged. S.R.G., G.N.S., and A.S.M. are thankful to the Department of Science and Technology (DST), New Delhi for award of J. C. Bose Fellowship, Swarnajayanti Fellowship, and Women Scientist Scheme, respectively. A.P.R. thanks the Council of Scientific and Industrial Research (CSIR), New Delhi for financial support.

I. INTRODUCTION

II. METHODOLOGY

III. COMPUTATIONAL DETAILS

A. Geometry optimization

B. Benchmarking of MTA

C. Cooperativity

D. Addition of missing two- and three-body correction terms for improvement of MTA-energy estimates

E. MESP-guided method for building clusters

IV. RESULTS AND DISCUSSION

A. Aggregation patterns

B. Validation of MTA: Test case of tetramers

C. How does a pair of interactions influence each other?

D. Addition of missing two- and three-body correction terms for improvement of MTA-energy estimates

E. MESP-guided method for building clusters

V. CONCLUSIONS

### Key Topics

- Polymers
- 15.0
- Atomic and molecular clusters
- 11.0
- Electrostatics
- 10.0
- Ab initio calculations
- 7.0
- Cluster analysis
- 7.0

## Figures

Illustration of fragmentation pattern employed in MTA, taking hexamer (hex-01) as a prototypical case.

Illustration of fragmentation pattern employed in MTA, taking hexamer (hex-01) as a prototypical case.

optimized geometries of three predominant structures of benzene dimers. Important and interactions in these clusters are depicted along with distances (in angstrom) between H-atom and ring center for interaction and between two ring centers for interaction. These dimers are used as building blocks for higher clusters with three or more benzene units. Total energy of the structures (in hartree) along with complexation energies (CE in kcal/mol) for each structure is mentioned.

optimized geometries of three predominant structures of benzene dimers. Important and interactions in these clusters are depicted along with distances (in angstrom) between H-atom and ring center for interaction and between two ring centers for interaction. These dimers are used as building blocks for higher clusters with three or more benzene units. Total energy of the structures (in hartree) along with complexation energies (CE in kcal/mol) for each structure is mentioned.

(a) Numbering key for fragments used to study the effect of BSSE by MTA. Optimized geometry of tet-09 at level of theory chosen to study the effect. (b) MTA-optimized geometry of a hexamer (hex-10) chosen to study the effect of missing two- and three-body correction terms for improvement of MTA-energy estimates. The numbering key for fragments used is also indicated.

(a) Numbering key for fragments used to study the effect of BSSE by MTA. Optimized geometry of tet-09 at level of theory chosen to study the effect. (b) MTA-optimized geometry of a hexamer (hex-10) chosen to study the effect of missing two- and three-body correction terms for improvement of MTA-energy estimates. The numbering key for fragments used is also indicated.

optimized geometries of selected structures of , to 8. Important and interactions in these clusters are depicted along with distances (in angstrom) between H-atom and ring center for interaction and between two ring centers for interaction at (bold) and (italics) level. Total energy (in hartrees) of each cluster at is also indicated in italics. In case of heptamers and octamers distances in bold are those obtained at MP2/STO-3G level. tri-05 is optimized at level of theory.

optimized geometries of selected structures of , to 8. Important and interactions in these clusters are depicted along with distances (in angstrom) between H-atom and ring center for interaction and between two ring centers for interaction at (bold) and (italics) level. Total energy (in hartrees) of each cluster at is also indicated in italics. In case of heptamers and octamers distances in bold are those obtained at MP2/STO-3G level. tri-05 is optimized at level of theory.

(i) MESP isosurface at −0.015 a.u. for pen-18 at level plotted using METASTUDIO (Ref. 43). The white dot depicting the deepest minimum is the most suitable site for the next incoming benzene monomer. (ii) Different ways of adding a benzene (red line) to 5 benzenes (black lines) of pen-18 (A) perfect T-shaped interaction, [(B) and (C)] parallel shifted interactions, and (D) the most stable trimer formation as highlighted by a circle.

(i) MESP isosurface at −0.015 a.u. for pen-18 at level plotted using METASTUDIO (Ref. 43). The white dot depicting the deepest minimum is the most suitable site for the next incoming benzene monomer. (ii) Different ways of adding a benzene (red line) to 5 benzenes (black lines) of pen-18 (A) perfect T-shaped interaction, [(B) and (C)] parallel shifted interactions, and (D) the most stable trimer formation as highlighted by a circle.

(i) MESP isosurface at −0.015 a.u. for hex-10 evaluated at level, plotted using METASTUDIO (Ref. 43). The deepest minimum, , and other local minima depicted by white dots indicate the most suitable sites for addition of the next benzene moiety. (ii) Different possible ways of adding new benzene (shown by red line) to hex-18 (black lines): (A) a perfect T-shaped interaction, [(B) and (C)] parallel shifted interactions, and [(D) and (E)] most stable trimer formation as highlighted by circles.

(i) MESP isosurface at −0.015 a.u. for hex-10 evaluated at level, plotted using METASTUDIO (Ref. 43). The deepest minimum, , and other local minima depicted by white dots indicate the most suitable sites for addition of the next benzene moiety. (ii) Different possible ways of adding new benzene (shown by red line) to hex-18 (black lines): (A) a perfect T-shaped interaction, [(B) and (C)] parallel shifted interactions, and [(D) and (E)] most stable trimer formation as highlighted by circles.

## Tables

Actual total energies ( in a.u.) with corresponding complexation energies (CE in kcal/mol) at , MP2/STO-3G levels of theory, and MTA-based estimates of energy ( in a.u.) with corresponding complexation energies ( in kcal/mol) at level of theory for selected important benzene clusters . Optimization of dimers and trimers are done only at level of theory. See Figs. 2 and 4 for optimized geometries and text for details.

Actual total energies ( in a.u.) with corresponding complexation energies (CE in kcal/mol) at , MP2/STO-3G levels of theory, and MTA-based estimates of energy ( in a.u.) with corresponding complexation energies ( in kcal/mol) at level of theory for selected important benzene clusters . Optimization of dimers and trimers are done only at level of theory. See Figs. 2 and 4 for optimized geometries and text for details.

Actual total energies, MTA-based single point energies, and MTA-based optimized energies (, , and in a.u.) with corresponding complexation energies (CE, and in kcal/mol) at the level of theory for benzene tetramers shown below.

Actual total energies, MTA-based single point energies, and MTA-based optimized energies (, , and in a.u.) with corresponding complexation energies (CE, and in kcal/mol) at the level of theory for benzene tetramers shown below.

MTA-optimized energies, actual single point energy from calculation on MTA-optimized geometries (, in a.u.), and their corresponding complexation energies (, in kcal/mol) at for benzene tetramers . BSSE-corrected complexation energy is indicated as .

MTA-optimized energies, actual single point energy from calculation on MTA-optimized geometries (, in a.u.), and their corresponding complexation energies (, in kcal/mol) at for benzene tetramers . BSSE-corrected complexation energy is indicated as .

Comparison of CE and complexation energy per interaction for optimized clusters at and level (MTA-optimized) to assess cooperativity. denotes the number of interactions present in the type of cluster. PD indicates parallel displaced clusters. See Fig. 2 and 4 for optimized structures and text for details.

Comparison of CE and complexation energy per interaction for optimized clusters at and level (MTA-optimized) to assess cooperativity. denotes the number of interactions present in the type of cluster. PD indicates parallel displaced clusters. See Fig. 2 and 4 for optimized structures and text for details.

Missing two- and three-body correction to the MTA-based energy estimate for hex-10 [cf. Figs. 3(b) and 4 for structure]. and denote MTA-energy before and after missing two- and three-body contributions are added. All the energies are in a.u. See text for details.

Missing two- and three-body correction to the MTA-based energy estimate for hex-10 [cf. Figs. 3(b) and 4 for structure]. and denote MTA-energy before and after missing two- and three-body contributions are added. All the energies are in a.u. See text for details.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content