Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces

Abstract

The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

“…On such high performance computing machines a wave function approach based on QMC is currently becoming practical and competitive with DFT, allowing to treat geometry optimization of molecules up to 100 atoms 36 , vibrational properties 37,38 and molecular dynamics simulations 39,40 .…”

Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule

“…In order to control the propagation of the errors on the predicted quantities, it is important to adopt a method that takes explicitly into consideration the presence of the stochastic error. In a recent work, 51 some of us have shown how this can be achieved, by performing several single point calculations of the energies and the forces in a grid centered around a good guess of the minimum of the PES. The values of the energies or the forces are then used to perform a multidimensional fit of the PES, to obtain a better estimate of the minimum and of the vibrational properties.…”

“…3,50 Recently, by using a procedure based on the multidimensional fitting of the potential energy surface (PES) of a molecule in proximity of its configurational minimum, it has also been shown that it is possible to calculate the harmonic vibrational frequencies and the anharmonic corrections by QMC, despite the presence of stochastic errors. 51…”

Worthwhile Relevance of Infrared Spectroscopy in Characterization of Samples and Concept of Infrared Spectroscopy-Based Synchrotron Radiation

“…Linear molecules, like simple diatomic molecules (e.g., CO 2 ; O�C�O), have solely one bond and solely one vibrational bond calculated from 3N-5 degrees of vibrational modes. On the other side, nonlinear molecules, such as water, have 3N-6 degrees of vibrational modes [44,46]. Here, water has 3 atoms; that is, 3 × 3 − 6 � 3 degrees of freedom.…”