#### Abstract

Chemistry is a quantitative science in which rate processes play a major role.

Not only they determine the time-scale for molecular transformations, they

also determine the preferential outcome of complex reaction networks, such

as those occurring in biological environments, at the solid-gas interface of

a catalytic system, in the earth atmosphere and in the interstellar medium.

Despite this, the quantitative study of the rate of chemical reactions is

largely a young field of research. This is due to both inherent difficulties

in obtaining accurate potential energy functions for dynamical simulations

and in following the dynamical processes themselves. In this work we summarize

the efforts we have made in recent years in this exciting field. We start

showing how accurate quantum-chemistry methods can be used to map the

interaction potentials governing the dynamics in small, yet complex systems

where the common Born-Oppenheimer approximation ceases to be valid. Then,

we show how classical molecular dynamics may be applied in predicting the

behaviour of atoms/molecules impinging on a surface, an issue of paramount

importance in catalysis. Quantum molecular dynamics is mandatory when

inherently quantum systems are involved, and we show how present-day

techniques allow to solve exactly the time-dependent Schrödinger equation

in simple molecular systems. We finally show our very recent results in

describing interaction and energy dissipation of simple quantum systems

coupled to a heat reservoir. These represent the first real-time quantum

dynamical simulations in very large systems.

Not only they determine the time-scale for molecular transformations, they

also determine the preferential outcome of complex reaction networks, such

as those occurring in biological environments, at the solid-gas interface of

a catalytic system, in the earth atmosphere and in the interstellar medium.

Despite this, the quantitative study of the rate of chemical reactions is

largely a young field of research. This is due to both inherent difficulties

in obtaining accurate potential energy functions for dynamical simulations

and in following the dynamical processes themselves. In this work we summarize

the efforts we have made in recent years in this exciting field. We start

showing how accurate quantum-chemistry methods can be used to map the

interaction potentials governing the dynamics in small, yet complex systems

where the common Born-Oppenheimer approximation ceases to be valid. Then,

we show how classical molecular dynamics may be applied in predicting the

behaviour of atoms/molecules impinging on a surface, an issue of paramount

importance in catalysis. Quantum molecular dynamics is mandatory when

inherently quantum systems are involved, and we show how present-day

techniques allow to solve exactly the time-dependent Schrödinger equation

in simple molecular systems. We finally show our very recent results in

describing interaction and energy dissipation of simple quantum systems

coupled to a heat reservoir. These represent the first real-time quantum

dynamical simulations in very large systems.

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