MD+QM for solutions and surfaces

1. Development of a QM + MD + QM method for liquid solutions

We want to know how the properties of a solvent molecule change in solution. Therefore we calculate the effects of thermal motion and intermolecular interactions in the solution on, for example, the molecular vibrations. We use the following scheme.

  1. Perform an MC or MD simulation and select configurations (snapshots) from the trajectory.

  2. Perform QM embedded-cluster calculations (incl. electron correlation treatment) of the OH potential energy curves for selected water (HDO) molecules in the selected snapshots.

  3. Fit the harmonic and anharmonic force constants to each OH potential energy curve from 2.

  4. Solve the Schrödinger equation for the 1-dimensional anharmonic oscillator problem for each potential energy curve, calculate the fundamental (anharmonic) frequency, IR-intensity-weigh each frequency using the calculated dipole-moment derivative, collect the frequencies in a histogram.

All aspects of this scheme were implemented in the work descrbed in the paper "The O-H Vibrational Spectrum of Liquid Water from Combined ab initio and Monte Carlo Calculations" by K. Hermansson, S. Knuts and J. Lindgren, J. Chem. Phys. 95, 7486-7496 (1991). However, today we have also applied it to ionic solutions and we are able to use larger QM clusters in step 2, better force-fields in step 1, more accurate methods in step 4.

The picture below shows how we recently calculated the OH vibrational frequency shift for the hydration shell around Al3+(aq). The experimental frequency shift (with respect to the average OH frequency of a gas-phase water molecule) is very large, -850 cm-1. Our calculations give -750 cm-1, i.e. we retrieve almost 90% of the experimentally measured downshift. The method shown in the figure can in fact be called "QM + MD + QM + QM" since the force-field used was also based on QM calculations, and the anharmonic frequencies are calculated from quantum mechanics. We have applied the same method to Li+(aq); these results are published in:

Using MD Snapshots in ab initio and DFT Calculations: OH Vibrations in the First Hydration Shell around Li+(aq) L. Pejov, D. Spångberg and K. Hermansson, J. Phys. Chem. A 109, 5144-5152 (2005). We have also calculated the frequencies more accurately and for more ions in the paper "Al3+, Ca2+, Mg2+, and Li+ in aqueous solution: Calculated first shell anharmonic vibrations at 300K" L. Pejov, D. Spångberg and K. Hermansson J. Chem. Phys. 133 174513 (2010).

2. Development of an MD + QM method for metal oxide surfaces

The method of combining classical MD simulations and embedded-cluster QM calculations which we have proposed for studying processes on ionic surfaces consists of four steps.

  1. A MD simulation is performed for the surface system.

  2. An analysis of the instantaneous structural, dynamic, and electrostatic surface properties from the MD simulation forms the basis for the selection of sites for further investigation.

  3. The infinite, periodic surface surrounding each selected site region (to be described by QM calculations) is replaced with a PC-embedding.

  4. The desired process (e.g., adsorption) is studied using QM calculations for the embedded cluster.

The method is discussed in more detail in: "A combined molecular dynamics + quantum mechanics method for investigation of dynamical effects on local surface structures" B. Herschend, M. Baudin and K. Hermansson J. Chem. Phys. 120, 4939-4948 (2004).