Exercise 6: Cyanoacetylene

Lattice Energy Convergence

Initial Analysis

1. Open the CAACTY CIF
2. Generate Hirshfeld surface with HF/3-21G electrostatic potential

Surface Properties

3. Analyze electrostatic features:
   • Rescale surface to ±0.025 au range
   • Note strong dipolar nature:
     • HF/3-21G dipole moment: 3.90 D
     • Experimental value: 3.72 D
   • Observe structured surface features

Deformation Density

4. Generate Deformation Density isosurface:
   • Use existing wavefunction
   • Superimpose transparent Hirshfeld surface
   • Compare:
     • Electron density accumulation (blue)
     • Electronegative surface features (red)

Structure Analysis

5. Examine molecular arrangement:
   • Use Generate All External Fragments
   • Create surfaces with Clone Surface
   • Observe structure features:
     • Head-to-tail molecular rows in layers
     • Alternating layer orientations (antiparallel dipoles)

Historical Context

The original structure determination noted:

• "Linear chains of cyanoacetylene, nearly close-packed"
• "All molecules in a chain oriented alike"
• "Each chain surrounded by two parallel and four antiparallel nearest neighbor chains"
• "No obvious explanation for relative positions of molecules in adjacent chains"

The Hirshfeld surfaces with mapped electrostatic potential help explain these observations

Energy Analysis

6. Calculate extensive interaction energies:
   • Return to single molecule (Reset Crystal)
   • Generate 20 Å radius cluster
   • Complete all fragments
   • Calculate energies for 230 unique molecular pairs

Data Analysis

Export the energy data to a spreadsheet for detailed analysis:

1. Click Information
2. Copy energy table
3. Paste into spreadsheet

Energy Analysis in Spreadsheet

7. Process the energy data:

   • Multiply 'R' and '$E_\text{tot}$' columns
   • Sort by molecule-molecule distance 'R'
   • Observe energy component behavior:
     • '$E_\text{rep}$' and '$E_\text{pol}$': rapid decay
     • '$E_\text{dis}$': intermediate range
     • '$E_\text{ele}$': very long range (significant beyond 20 Å)

8. Calculate lattice energy convergence:

   • Create partial sum column '$E_\text{lat}$'
   • Excel formula example: =0.5*SUM($K$2:K2)
   • Note convergence around 8 Å
   • Plot '$E_\text{lat}$' vs 'R':

Results

Final lattice energy estimate: -42.3 kJ/mol

Compare with experimental sublimation enthalpy (42.3 kJ/mol)

note

The agreement is fortuitous as these quantities differ by ~2RT (~5 kJ/mol) at room temperature: $\Delta H_\text{sub} = -E_\text{lat} - 2RT$