Ilkka Kylänpää

Beyond the Born-Oppenheimer approximation with quantum Monte Carlo methods

In this work we develop tools that enable the study of nonadiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave-function ansatz for electron-ion systems that can involve a combination of both clamped ions and quantum nuclei. We explicitly calculate the ground-state energies of

Finite temperature quantum statistics of H3+ molecular ion

{\mathrm{H}}_{2}

QMCPACK: An open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids

, LiH,

How large are nonadiabatic effects in atomic and diatomic systems

{\mathrm{H}}_{2}\mathrm{O}

Few-body reference data for multicomponent formalisms: Light-nuclei molecules

, and

First-principles simulation of molecular dissociation–recombination equilibrium

{\mathrm{FHF}}^{\ensuremath{-}}

Finite-size effects and interactions in artificial graphene formed by repulsive scatterers.

using fixed-node quantum Monte Carlo with wave-function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement.

Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke’s atom

Full quantum statistical NVT simulation of the five-particle system H(3) (+) has been carried out using the path integral Monte Carlo method. Structure and energetics are evaluated as a function of temperature up to the thermal dissociation limit. The weakly density dependent dissociation temperature is found to be around 4000 K. Contributions from the quantum dynamics and thermal motion are sorted out by comparing differences between simulations with quantum and classical nuclei. The essential role of the quantum description of the protons is established.

Hydrogen molecule ion: Path-integral Monte Carlo approach

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the programs capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo

With recent developments in simulating nonadiabatic systems to high accuracy, it has become possible to determine how much energy is attributed to nuclear quantum effects beyond zero-point energy. In this work, we calculate the non-relativistic ground-state energies of atomic and molecular systems without the Born-Oppenheimer approximation. For this purpose, we utilize the fixed-node diffusion Monte Carlo method, in which the nodes depend on both the electronic and ionic positions. We report ground-state energies for all systems studied, ionization energies for the first-row atoms and atomization energies for the first-row hydrides. We find the ionization energies of the atoms to be nearly independent of the Born-Oppenheimer approximation, within the accuracy of our results. The atomization energies of molecular systems, however, show small effects of the nonadiabatic coupling between electrons and nuclei.