1. Derivation of a Kirchhoff-Like Law for
Capacitance Combination in Molecules
Nalini Singh
TJHSST '13
MITRE Corporation Summer Technical Aide

2. Background Information
 Kirchhoff’s laws can be used to determine the total capacitance
of a macroscopic circuit
Capacitors in Series Capacitors in Parallel
C1 C1
C2
C2
C3
C3
1 1 1 1
= + + CT = C1 + C2 + C3
CT C1 C2 C3

3. Background Information
 We modeled molecules, i.e. molecular capacitors, as a combination of smaller
molecular capacitors and atomic capacitors
Capacitors in Series Capacitors in Parallel
Atoms in Molecules
C1 C1
C1
C4
C6
C2 C C8
2 C2
C3 C5
C7
C3
C3
1 1 1 1 CT = ?
= + + CT = C1 + C2 + C3
CT C1 C2 C3

4. Results
 Neither a parallel or series capacitance
model adequately explains trends in
molecular capacitances

5. Results
 Neither a parallel or series capacitance
model adequately explains trends in
molecular capacitances
 A new law was derived based on a
parallel capacitance model with
modifications to account for “surface
area” contraction:

6. What’s Next
 Next steps:
- Generalize capacitance combination law for other classes of
molecules
- Analyze implications for other combination laws (i.e. conductance
combination laws)
 Application:
- Modeling of electronic properties of miniaturized/molecular-scale
circuits

7. What’s Next
 Next steps:
- Generalize capacitance combination law for other classes of
molecules
- Analyze implications for other combination laws (i.e. conductance
combination laws)
 Application:
- Modeling of electronic properties of miniaturized/molecular-scale
circuits