Except from and , all the molecules presented here belong to the standard G1 reference set; all their properties are well known and well reproduced by standard quantum chemistry methods, therefore they constitute a good case for testing new approaches and new wave functions.

-7.47806 (59) | -7.432727 (59) | -7.47721(11) | 98.12(24) | -7.47791(12) | 99.67(27) | |

-14.9954 (16) | -14.87152 (16) | -14.99002(12) | 95.7(1) | -14.99472(17) | 99.45(14) | |

-14.66736 (59) | -14.573023 (59) | -14.66328(19) | 95.67(20) | -14.66705(12) | 99.67(13) | |

-29.33854(5) (16) | -29.13242 (16) | -29.3179(5) | 89.99(24) | -29.33341(25) | 97.51(12) | |

-75.0673 (59) | -74.809398 (59) | -75.0237(5) | 83.09(19) | -75.0522(3) | 94.14(11) | |

-76.438(3) (60) | -76.068(1) (60) | -76.3803(4) | 84.40(10) | -76.4175(4) | 94.46(10) | |

-150.3268 (16) | -149.6659 (16) | -150.1992(5) | 80.69(7) | -150.272(2) | 91.7(3) | |

-37.8450 (59) | -37.688619 (59) | -37.81303(17) | 79.55(11) | -37.8350(6) | 93.6(4) | |

-75.923(5) (16) | -75.40620 (16) | -75.8293(5) | 81.87(10) | -75.8810(5) | 91.87(10) | |

-40.515 (61) | -40.219 (61) | -40.4627(3) | 82.33(10) | -40.5041(8) | 96.3(3) | |

-232.247(4) (62) | -230.82(2) (63) | -231.8084(15) | 69.25(10) | -232.156(3) | 93.60(21) |

The dimer is one of the easiest molecules to be studied after the , which is exact for any Diffusion Monte Carlo (FN DMC) calculation with a trial wave function that preserves the node-less structure. is less trivial due to the presence of core electrons that are only partially involved in the chemical bond and to the near degeneracy for the valence electrons. Therefore many authors have done benchmark calculation on this molecule to check the accuracy of the method or to determine the variance of the inter-nuclear force calculated within a QMC framework. In this thesis we start from to move toward a structural analysis of more complex compounds, thus showing that our QMC approach is able to handle relevant chemical problems.

With our approach more than of the correlation energy is recovered by a DMC simulation (Table 3.1), and the atomization energy is exact within few thousands of eV ( ) (Table 3.3). Similar accuracy have been previously reached within a DMC approach(16), only by using a multi-reference CI like wave function, that before our work, was the usual way to improve the electronic nodal structure. As stressed before, the JAGP wave function includes many resonating configurations through the geminal expansion, beyond the HF ground state. The bond length has been calculated at the variational level through the fully optimized JAGP wave function: the resulting equilibrium geometry turns out to be highly accurate (Table 3.2), with a discrepancy of only from the exact result.

5.051 | 5.0516(2) | |||

2.282 | 2.3425(18) | |||

2.348 | 2.366(2) | |||

1.809 | 1.8071(23) | 104.52 | 104.74(17) | |

2.041 | 2.049(1) | 109.47 | 109.55(6) | |

2.640 | 2.662(4) | 2.028 | 1.992(2) |

The good bond length, we obtained, is partially due to the energy optimization that is often more effective than the variance minimization, as shown by different authors (40,41,42), and partially due to the quality of the trial-function.

Indeed within our scheme we obtain good results without exploiting the computationally much more demanding DMC, thus highlighting the importance of the SR minimization described in Subsection 2.2.

-1.069 | -0.967(3) | 90.4(3) | -1.058(5) | 99.0(5) | |

-5.230 | -4.13(4) | 78.9(8) | -4.56(5) | 87.1(9) | |

-10.087 | -9.704(24) | 96.2(1.0) | -9.940(19) | 98.5(9) | |

-6.340 | -5.530(13) | 87.22(20) | -5.74(3) | 90.6(5) | |

-18.232 | -17.678(9) | 96.96(5) | -18.21(4) | 99.86(22) | |

-59.25 | -52.53(4) | 88.67(7) | -58.41(8) | 98.60(13) |

Let us now consider larger molecules.
Both
and
are poorly described by a single Slater
determinant, since the presence of the non-dynamic correlation is
strong.
Instead with a single geminal JAGP wave function, including implicitly
many Slater-determinants(15),
it is possible to obtain a quite good
description of their molecular properties.
In both
the cases, the variational energies recover more than
of the correlation
energy, the DMC ones yield more than
, as shown in Tab. 3.1.
These results are of the same level of accuracy as
those obtained by Filippi *et al*(16) with a multi-reference
wave function by using the same Slater basis for the antisymmetric part
and a different Jastrow factor.
From the Table 3.3 of the atomization
energies, it is apparent that DMC considerably improves the binding
energy with respect to the VMC values,
although for these two molecules it is quite far from the chemical
accuracy (
0.1 eV): for
the error is 0.60(3) eV, for
is 0.67(5) eV. Indeed, it is well known that the electronic
structure of the atoms is described better than the corresponding molecules if
the basis set remains the same, and the nodal error is not compensated
by the energy difference between the separated atoms and the molecule.
In a benchmark DMC calculation with pseudo-potentials (64),
Grossman found an error
of 0.27 eV in the atomization energy for
, by using a single determinant
wave function. Probably, pseudo-potentials allow the error
between the pseudo-atoms and the pseudo-molecule to compensate better,
thus yielding more accurate energy differences.
As a final remark on the
and
molecules,
our bond lengths are in
between the LDA and GGA precision, and
still worse than the best CCSD calculations,
but our results may be considerably improved by a larger atomic basis
set.

Methane and water are very well described by the JAGP wave function. Also for these molecules we recover more than of correlation energy at the VMC level, while DMC yields more than , with the same level of accuracy reached in previous Monte Carlo studies (65,61,67,66). Here the binding energy is almost exact, since in this case the nodal energy error arises essentially from only one atom (carbon or oxygen) and therefore it is exactly compensated when the atomization energy is calculated. Also the bond lengths are highly accurate, with an error lower then 0.005 .

For
we applied
a large Gaussian and exponential basis set for the determinant and the Jastrow factor and we recovered, at the experimental equilibrium geometry, the
of the
total correlation energy in the VMC, while DMC gives
of correlation, i.e. a total energy of -29.33341(25) H.
Although this value is
better than the one obtained by Filippi *et al* (16) (-29.3301(2)
H) with a smaller basis (
atomic orbitals not included), it is not enough
to bind the molecule, because the binding energy remains still positive
(0.0069(37) H). Instead, once the molecular geometry has been relaxed,
the SR optimization finds a bond distance of
at the VMC level;
therefore the employed basis allows the molecule to have a Van der Waals like
minimum, quite far from the experimental value.
In order to have a reasonable description of the bond length and the atomization
energy, one needs to include at least a
basis in the antisymmetric
part, as pointed out in Ref. (68). Indeed an atomization
energy compatible with the experimental result (0.11(1) eV) has been obtained
within the extended geminal model (69) by using a much larger basis
set (9s,7p,4d,2f,1g) (70).
This suggests that a complete basis set calculation with JAGP
may describe also this molecule.
However our SR method can not cope with a very large basis in a
feasible computational time. Therefore we believe that at present
the accuracy needed to describe correctly
is
out of the possibilities of the approach.

Kekule + 2body | -30.57(5) | 51.60(8) | - | - |

resonating Kekule + 2body | -32.78(5) | 55.33(8) | - | - |

resonating Dewar Kekule + 2body | -34.75(5) | 58.66(8) | -56.84(11) | 95.95(18) |

Kekule + 3body | -49.20(4) | 83.05(7) | -55.54(10) | 93.75(17) |

resonating Kekule + 3body | -51.33(4) | 86.65(7) | -57.25(9) | 96.64(15) |

resonating Dewar Kekule + 3body | -52.53(4) | 88.67(7) | -58.41(8) | 98.60(13) |

full resonating + 3body | -52.65(4) | 88.869(7) | -58.30(8) | 98.40(13) |