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The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Molecular Orbital Theory I

Molecular Orbital Theory I

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Molecular Orbital Theory II

Molecular Orbital Theory II

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Electronic Structure of Atoms

Electronic Structure of Atoms

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...

Atomic Nuclei: Nuclear Relaxation Processes

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.

The Bohr Model

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...

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High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water

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Nuclear-Electronic Orbital Quantum Mechanical/Molecular Mechanical Real-Time Dynamics.

Mathew Chow¹, Tao E Li¹, Sharon Hammes-Schiffer¹

¹Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.

The Journal of Physical Chemistry Letters

|October 19, 2023

Summary

This study introduces a novel quantum dynamics simulation method combining real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) with QM/MM. This approach accurately models complex molecular systems, revealing significant nuclear quantum effects in condensed-phase chemical reactions.

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Area of Science:

Computational Chemistry
Quantum Dynamics
Molecular Simulation

Background:

Accurate simulation of nuclear-electronic quantum dynamics is crucial for understanding biological and chemical processes.
Existing methods often struggle with large-scale systems and complex environments.

Purpose of the Study:

To develop and apply a computational framework for simulating quantum dynamics in condensed-phase molecular systems.
To accurately describe coupled nuclear-electronic dynamics in heterogeneous environments.

Main Methods:

Integration of real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) with a hybrid quantum mechanical/molecular mechanical (QM/MM) strategy.
Real-time propagation of electron and quantum proton densities.
Classical propagation of other nuclei on the vibronic surface.

Main Results:

The RT-NEO-TDDFT/QM/MM approach successfully simulated complex systems like phenol in lysozyme and intramolecular proton transfer reactions.
Demonstrated the capability to capture significant nuclear quantum effects in condensed-phase simulations.

Conclusions:

The developed framework enables accurate simulations of coupled nuclear-electronic quantum dynamics in realistic environments.
This method provides a powerful tool for studying chemical and biological processes involving proton transfer.