Questions tagged [quantum-chemistry]

Quantum chemistry is a subfield of quantum mechanics. Like its parent field, quantum chemistry focuses on understanding physical phenomena occuring at the atomic scale. Quantum chemistry however is more focused on providing useful descriptions of electronic structure to aid in understanding chemical problems (e.g. reactions, spectra, dynamics, ...).

Quantum chemistry is a subfield of . Like its parent field, quantum chemistry focuses on physical phenomena that occur at an atomic scale, usually specifically aiming at chemical reactions.

It is closely related to for which it provides the working equations and is therefore of more general nature.

The roots of quantum theories go back to the early 20th century. Their postulation was a result of observed atomic-level phenomena that could not be suitably described by classical mechanics. The Pioneers of this field include Heisenberg and Schrödinger, that are nowadays very well known not only to chemists.

Today, quantum theory has many applications in computing and a diversity of other areas of science. Modern applications include accurate description of chemical as well as the development of . It has therefore also contributed to our understanding of atoms, molecules, and reactions.

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What do the quantum numbers actually signify?

I know how to calculate them and such stuff, but I wanted to know what they actually signify. I have a vague idea that they have something to do with an electron's position in an atom but what do all of them mean? Any help would be greatly…
Jyotinder Singh
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Why are full and half filled orbitals the most stable?

Why are degenerate orbitals (restricted to a single spin) less stable when neither fully filled nor completely empty? Why, in most molecules, are half-filled and fully-filled shells more stable than partially filled shells? I understand that…
Niels Kornerup
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Should chemistry students worry about quarks and such?

Even chemistry textbooks less than five years old start by describing atomic structure based only on protons, neutrons and electrons. Is an understanding of chemistry fundamentals likely to become out of date when the textbooks start to include…
Brian Renshaw
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What is the difference between ψ, |ψ|², radial probability, and radial distribution of electrons?

I am very confused regarding these four terms- ψ,|ψ|², radial probability and radial distribution I know that ψ is called the wave function but is it the same as radial probability? I also know that |ψ|² is called the probability density of finding…
Aura Sartori
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Functional variation in derivation of the Hartree-Fock equations

In Szabo and Ostlund's Modern Quantum Chemistry, the procedure of single determinant energy minimization is presented. Omitting the whole procedure, I have a question about functional variation during the derivation of the Hartree-Fock…
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Mathematically, how does the exchange integral for a closed-shell system reduce to zero?

I am looking at the Hartree-Fock method of approximation for a closed-shell two-electron system. I have the basis functions $$ \chi_1(\vec{x}_1) = \psi_1(\vec{r}_1) \alpha(s_1) \\ \chi_2(\vec{x}_2) = \psi_1(\vec{r}_2) \beta(s_2) $$ where…
Yoda
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Significance of 4π in the uncertainty principle

What is the significance of the quantity 4π in the Heisenberg uncertainty principle? $Δp \times Δx = \frac{h}{4π}$ The focus of the question is to learn why the ratio of a circle's circumference to its diameter, universally known as $π$, is used in…
TheStarVoyager
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Why do we use J(J+1) instead of J² in the rigid body rotor energy equation?

I looked for the reason, but it seems to be taken for granted that it must be $J(J+1)$ instead of $J$. I'm making use of the analogy of the particle in a box energy where $$E=\frac{n^2h^2}{8mL^2}$$
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Can quantum entanglement affect the chemistry of molecules?

I recently heard a talk from a physicist about experiments on simple two-atom molecules in vacuum that showed that certain behaviour of the molecules was explained by quantum entanglement. Now this experiment was about creating holes in the inner…
Mad Scientist
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Uncertainty Principle in the Ground State of a Rigid Rotor

This is a fairly basic question which has bothered me for some time and I haven't been able to satisfactorily resolve. In the ground state of the rigid rotor the energy is zero. That is, there is no zero point energy for this system. This means we…
jheindel
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What's the difference between radial probability and probability density?

I understand that radial probability is the probability of finding an electron at some distance from nucleus in a shell. But what does that exactly mean? What does it tell us about the atom and electrons?
user33683
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Trying to understand the necessity of orbital approximation or the independent electron model

I'm reading the approximations used for solving the Schroedinger's equation for molecules; the first is the the Born-Oppenheimer approximation: Freeze the molecule with a fixed internuclear separation $R;$ then carry out calculations to obtain…
user5764
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Computing the commutator of the Fock and density matrices in AO basis (Hartree-Fock theory)

I am making a simple restricted HF code using the Python interface of Psi4. I am now evaluating convergence by tracking the change in the sum of orbital energies, but I want to do this in a better way. It is common to use the fact that at…
Yoda
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Prove that idempotency is a necessary and sufficient condition for a densiy matrix to be N-representable

As I understand, a necessary and sufficient condition for a density matrix $P$ to be represented by a wavefunction $|\Psi\rangle$ is that it is idempotent, i.e. $P^2=P$. It is easy to see that if $P=|\Psi\rangle\langle \Psi|$ then $P$ is…
BGreen
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Why is the square of the wavefunction a probability density?

Can anyone explain it in simple words? I tried to read about the Born rule on Wikipedia but it seems it is just describing the rule. Is there any proof that is suitable for person with no solid math background?
Osman Mamun
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