Small Be Clusters

• Original aim was to examine Be3 and Be4 with CCSD, and compare with multireference methods.
• Be has very large near-degeneracy correlation effects - suggest that single-reference methods will be useless for small systems containing Be.
• Multireference treatments quickly get expensive, however,
• Be3 and Be4 are both totally symmetric singlets, the former equilateral triangular and the latter tetrahedral.

Be3 Bond Lengths and Binding Energies

Observations

• Be3 is not bound at either the SCF or CASSCF levels.
• Single-reference treatments are not in very good agreement with MRCI. So it appears essential to describe the nondynamical correlation, just to get the dynamical correlation contribution to binding correct.
• Very substantial basis set effect.
• A method like CCSD that is exact for the separated atom limit performs worse that CISD + Q, because there is less cancellation of error.

Small Be Clusters

Be4 Binding Energies

Observations

• Be4 is bound at the SCF and CASSCF levels.
• Again, there is a very large dynamical correlation contribution to the binding.
• Estimate binding energies as 24+- kcal/mol for Be3 and 83+-3kcal/mol for Be4.

CCSD(T) Results

Be3 and Be4

Small Be Clusters: CCSD(T) Calculations

• Generate a full quartic force field for each cluster, and obtain fundamental frequencies.

Be3 and Be4 Vibrations(a)

• Basis set effects are large, but remaining effects should be small - fundamentals accurate to within 20 cm -1, and probably to within 10.

Observations

• IR intensity of the Be3 e' mode is very small. The t2 mode in Be4 might be observable.
• Harmonic frequencies would be useless.
• Also treated Mg and Ca trimers and tetramers - same excellent agreement between MRCI and CCSD(T).

Structure of C3+

• Is the ground state of C3+ linear or cyclic?
• Linear form is 2E+, cyclic form has C2v symmetry (2B2 state): Jahn-Teller distorted equilateral triangle.
• Experiments were initially analyzed as indicating a cyclic ground state, but it was pointed out that this was not unambiguous.
• Grev et al. used DZP basis and CI method: cyclic by 7 kcal/mol (+-4!).
• Raghavachari, and Martin et al., TZ2Pf QCISD (T), cyclic by only 2 or 3 kcal/mol.
• Very multiconfigurational.
• Grev et al. discovered an error in their calculations: estimate 4+-4.

C3+ DZP Basis Results

Cyclic/ Linear Separation (kcal/mol)

Observations

• Very substantial nondynamical correlation effects. But dynamical correlation contribution (relative to MCSCF) is very small.
• Best multireference values do not support Grev et al. directly computed single-reference numbers.

C3+ Extended Basis Results

[5s 3p 2d 1f] Cyclic/Linear Separation (kcal/mol)

• Comparing with the DZP results, we would expect the best MRCI result in this basis to be about 4.2 kcal/mol.
• Incompleteness of the one-particle basis set should be responsible for most of the remaining deficiencies in this calculation.

Structure of C3+

• Scuseria: CCSD(T) calculations in a [5s 4p 3d 2f 1g] basis set show that basis set extension could give another 2.5 kcal/mol.
• Hard to see any effect that could push the separation below 4.2 kcal/mol.
• Estimate 5.2 +1.5, -1.0 kcal/mol, taking account of basis set and N-particle space effects on our best computed number.

C20

• What is the most stable form?
• Experiments: only the ring structure is seen.
• Is the ring structure the most stable? Or is it simply too costly (energetically) to form the fullerene from the ring?
• Large system, relatively speaking: hard to do much better than DZP basis.

C20 results

C20 relative energies (eV)