- 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.

Method | Basis | re (ao) | De(kcal/mol) |
---|---|---|---|

SCF | [4s 2p 1d] | (4.472)a | -3.2 |

CISD+Q | [4s 2p 1d] | (4.472) | 8.9 |

CCSD | [4s 2p 1d] | 4.472 | 4.2 |

CPF | [4s 2p 1d] | 4.488 | 8.6 |

MCSCF | [4s 2p 1d] | (4.372) | -2.3 |

MCRI | [4s 2p 1d] | 4.373 | 14.2 |

SCF | [5s 3p 12d 1f] | (4.240) | -1.4 |

CCSD | [5s 3p 12d 1f] | 4.240 | 11.3 |

CPF | [5s 3p 12d 1f] | 4.202 | 14.9 |

MCSCF | [5s 3p 12d 1f] | (4.199) | .2 |

MCRI | [5s 3p 12d 1f] | 4.199 | 22.4 |

- 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.

Method | Basis | De(kcal/mol) |
---|---|---|

SCF | [4s 2p 1d] | 32.9 |

CCSD | [4s 2p 1d] | 42.9 |

MCSCF | [4s 2p 1d] | 34.9 |

MCRI | [4s 2p 1d] | 56.1 |

SCF | [5s 3p 2d 1f] | 40.0 |

CCSD | [5s 3p 2d 1f] | 63.5 |

CASSCF | [5s 3p 2d 1f] | 45.0 |

MCRI | [5s 3p 2d 1f] | 77.3 |

- 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.

Method | Basis | re (ao) | De(lcal/mol |
---|---|---|---|

CCSD | [5s 3p 2d 1f] | 4.239 | 11.3 |

CCSD(T) | [5s 3p 2d 1f] | 4.2317 | 20.4 |

CMCRI | [5s 3p 2d 1f] | 4.2300 | 22.5 |

CCSD | [4s 2p 1d] | 4.041 | 44.2 |

CCSD(T) | [4s 2p 1d] | 4.060 | 58.5 |

MCRI | [4s 2p 1d] | 4.054 | 59.2 |

CCSD | [5s 3p 2d 1f] | 43.900 | 63.5 |

CCSD(T) | [5s 3p 2d 1f] | 3.921 | 79.5 |

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

Method | Basis | a' mode | e'mode |
---|---|---|---|

CCSD | [5s 3p 2d 1f] | 433 | 407 |

MCRI | [5s 3p 2d 1f] | 490 | 427 |

CCSD(T) | [5s 3p 2d 1f] | 480 | 417 |

CCSD(T)b | [5s 3p 2d 1f] | 459 | 400 |

Method | Basis | a' mode | e'mode | t2 mode |
---|---|---|---|---|

CCSD | [4s 2p 1d] | 597 | 445 | 534 |

MCRI | [4s 2p 1d] | 602 | 451 | 529 |

CCSD(T) | [4s 2p 1d] | 602 | 436 | 527 |

CCSD | [5s 3p 2d 1f] | 667 | 480 | 581 |

CCSD(T) | [5s 3p 2d 1f] | 662 | 469 | 571 |

CCSD(T)b | [5s 3p 2d 1f] | 639 | 455 | 682 |

(b)Fundamental frequency.

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

- 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).

- 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.

Method | Separation |
---|---|

MCSCF | 1.46 |

MCRI | 1.68 |

CISD | 15.69 |

QCISD | 9.38 |

QCISD(T) | .87 |

MP4(SDTQ) | -24.63 |

- 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.

Method | Separation |
---|---|

MCSCF | 3.18 |

MCRI | 5.18 |

QCISD | 12.62 |

QCISD(T) | 3.42 |

- 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.

- 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.

- 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.

Method | fullerene | flake | ring |
---|---|---|---|

SCF | 0. | -2.0 | -2.2 |

LDA | 0. | 1.1 | 3.3 |

MP2 | 0. | 1.1 | 2.8 |

CCSD | 0. | -0.6 | 0.9 |

CCSD(T) | 0. | -0.0 | 1.7 |

Best estimate | 0. | 0.7 | 3.0 |

Method | fullerene | flake | ring |
---|---|---|---|

SCF | 0. | -2.5 | -3.4 |

LDA | 0. | 1.0 | 3.8 |

DFT | 0. | -2.3 | -3.4 |

MP2 | 0. | 0.8 | 3.9 |

CCSD | 0. | -1.2 | -0.9 |

CCSD(T) | 0. | -0.6 | -2.2 |

Best estimate | 0. | 0.5 | 4.1 |