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, ...).

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QMOT | Orbital mixing in methyl

The following picture is from E. V. Anslyn Physical Organic Chemistry and shows constructing of MO of methyl using QMOT. MOs $\textbf{E'}$ and $\textbf{D'}$ are formed by mixing $\textbf{D}$ and $\...
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Experimental Validation of Schrodinger's Electron Cloud theory

I am currently doing a report for school on the electron cloud atomic structure theory. One of the major points on my report is the experiments performed by the scientists (Schrodinger and Heisenberg) ...
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Physical Meaning of the Difference between MO and VB Wave Function of H2?

What would be the physical meaning of the difference between the MO wave function and VB wave function of $\ce{H2}$?
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What happens when we heat an atom?

Question is simple.. If we take an atom of any element and then supply heat energy to it then what will happen? What I thought is that in the beginning, energy (quanta; due to excitement of electron ...
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How to find the number of valence electrons?

I need to understand the following: Considering an element Sulfur - S which has 16 electrons. How do we calculate the number of valence electrons of S? Please correct me if I am wrong:2+2+6+2+4=16. ...
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How to calculate probability of finding an electron at a point?

In school i learned how to calculate probability of finding electrons in some volume but how can we calculate the probability of finding a electron at a particular point. Point here ...
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H2 Triplet State

How does $\ce{H2}$ triplet state exist if there are electrons in both bonding and antibonding ($1\sigma$ and $1\sigma^*$) orbitals? Or am I being taught the hypothetical triplet states of the ...
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Electron vs electron density

I recently read somewhere that electrons do not exist. it's just the electron density. Is it true that there are no electrons (particles) but only in the form of electron density? And does this ...
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Why do 1s and 2s orbitals intersect? [closed]

So I was going through the Schrödinger wave equation to determine the shapes of orbitals. We know that an orbital is nothing more than a region where probability of finding an electron is maximum. ...
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Molecular orbitals in an ionic diatomic compound

The wavefunction of a heteronuclear diatomic molecule, after the orbital approximation and the Born-Oppenheimer approximation, is $$\psi = c_A \chi_A \pm c_B \chi_B $$ where $\chi$ are the starting AO ...
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Is the pz orbital wave function three- or four-dimensional?

The wave function of the $2\mathrm{p}_z$ orbital is $$Ψ = \frac{1}{4\sqrt{2π}}\left(\frac Z a\right)^{5/2} r \mathrm e^{-Zr/a}\cos θ.$$ I'm confused if this function will be a three-dimensional ...
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Spin Operator algebra

I am trying to teach myself some QM. In Christopher J. Cramers textbook Essentials of Computational Chemistry: theory and models, in Appendix C, he goes over Spin algebra. I am unable to calculate ...
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Hamiltonian 2nd positional derivative analogous to acceleration?

In Quantum Mechanics, we learn that the Hamiltonian operator for an electron confined to a 1-D space is: We learn in QM that many operators have analogous interpretations familiar to us from ...
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Degenerate orbitals in the Hydrogen atom

I came across the following link: Which orbitals of the hydrogen atom are degenerate for $n=3$ And all the answers said that for the hydrogen atom, the energy of an orbital depends only on n. Is ...
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when do we indicate the "+ or -" sign in uncertainty [closed]

how can we know when to indicate "+ or -" sign in uncertainty calculations because I noticed some problems has been solved by this sign and some has not.
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What does Pauli’s exclusion principle mean in atomic or fundamental way? [closed]

It means is that no electron can have same n , l and $m_l$ but can have two different spin quantum number. I want to know why is this rule valid?Means there must be some other things happening also ...
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How can an electron being a wave have such property as spin?

Here's what I know about electrons. Electrons have wave-like properties and the number of wavelengths in the $n^\text{th}$ shell is equal to $n(\lambda).$ Also, I read in my book that they have ...
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Quantitative MO theory- how is the overlap integral and the weighting coefficients of the molecular orbital actually evaluated?

Title. In my inorganic chemistry course, we learn about SALCs and qualitative MO treatment, with only a fleeting reference to the S integral and actual molecular wave functions (only hydrogen, $\ce{H2}...
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Relationship between the first and the second quantum number

Does the secondary quantum number tell how many subshells a specific principal quantum number shell has? E.g., if the principal quantum number is $n$, there are ($n-1$) subshells.
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why we can use the equipartition theorem for translational motion of molecules at room temperature and above because quantization is unimportant

From the book Chemical Principles The Quest for Insight, 5th Edition by Peter Atkins, Loretta Jones The equipartition theorem is a result from classical mechanics; so we can use it for translational ...
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Classically permitted position values in a quantum harmonic oscillator [closed]

In a quantum harmonic oscillator that is in the state with quantum number $n$, what range of the position $x$ is allowed classically? Does it have something to do with Bohr's correspondence principle?...
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What is the form of the Hamiltonian for solids?

For atoms, and even molecules, I can understand how the Hamiltonian would be constructed, but what of solids (as in, for electronic structure calculations)? Thank you for any help.
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Confusion in half filled or full filled electronic configuration

At the end of electronic configuration, we were taught that, electron orbitals are most stable when they are either fully filled or half filled. E.g., the final valence configuration of chromium is $\...
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antisymmetric wavefunction [closed]

Why can't we choose any other antisymmetric function instead of a Slater determinant for a multi-electron system? Why do we choose our wavefunction for a multi-electron atom as a product of single-...
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Is this what an orbital means?

In this picture, there is a $1s$ and a $2s$ orbital. Are the orbitals only the dark gray circles ? Or are the light gray circles (which are surrounding the dark gray ones on both sides) also included ...
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Angular Momentum Of S-subshell of an atom?

The angular momentum of every S-subshell of an atom is 0 by Azimuthal Quantum No. Relation. But if angular momentum of S-subshell is zero. Then by, Angular Momentum =Mass×Velocity×Radius; Radius of S-...
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Which is the bigger ion, F- or O-?

Well, according to the proton-electron ratio $\ce{O-}$ should be bigger than $\ce{F-}$ What about the charge/electron density in $\ce{F}$? Will it not affect the size of the atom of $\ce{F-}$?
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How do we write spin multiplicity for Mn(2+), Mn(7+)?

Mn has atomic number = 25 Since it is an exception to electronic configuration , unlike having = $\mathrm{3d^7}$ , it has electronic configuration = $\mathrm{3d^5,4s^2}$. Formula for spin multiplicity ...
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Why is the radial distribution at the nucleus 0 but not the radial wave function?

The modulus squared of the radial wave function gives the probability of finding an electron in an infinitesimal volume dv. On the other hand, the radial distribution gives the probability of finding ...
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Binding energy vs. ionization energy [closed]

I am studying binding energy in the context of photoelectric spectroscopy, and I came across a graph of relative numbers of electrons vs binding energy (in units of megajoules per mole). The element ...
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Expression of the potential in the hydrogen atom while solving radial part of the wave function

I was reading about the derivation of wavefunction of Hydrogen atom from Atkins book. After the separation of variables and writing the wave function, $\psi_{(r,\theta,\phi)}=R_{(r)}Y_{(\theta,\phi)}$...
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Do quantum particles have mass? [closed]

Quantum particles are never objects but are always waves. But do they have mass or can they carry mass?
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Why is atomic orbital one electron wave function? Why distance from centre is proportional to angular wave function?

Consider the following statements: An atomic orbital is one electron wave function $\psi(r,\theta,\varphi)$ obtained from the solution to the Schrödinger equation. There two electrons in an atomic ...
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What's the definition for mole before Avogadro's constant?

I have been searching for about 3 days how Avogadro's constant is found, and as all of us know the value is determined by division of charge of one mole of electrons (Faraday's constant) by the charge ...
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On the meaning of distinguishability, and wavefunctions for 3 electron atoms

In a 2-electron atom at lowest energy, the $(1s)^2$ is occupied and the electronic wave-function must satisfy anti-symmetry requirements in the particle coordinates, as the spatial wave function is ...
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Quantization and Bohr's model

According to quantization it's said that emitted or absorbed energy is quantized. Then, when it's said in bohr's model an electron changes its orbit (Let's say it goes to a higher energy shell from $...
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Where is the probability of finding an electron in 1s orbital maximum? [duplicate]

So the way I understand the question is that it asks us at what r (distance from nucleus) and at what angles is the probability going to be maximum. The way I see probability of finding at a point in ...
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Thermal and photochemical excitation of electron in photochemistry

One of the basic rules of photochemistry is that the electronic configuration of a conjugated polyene does not change when excited thermally, but changes when photochemically excited, i.e. an electron ...
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What is the wavelength of an electron?

The kinetic energy of an electron is $1.67 \times 10^{-17}\mathrm{J}$. Calculate the wavelength ($\lambda$) of the electron. I know the formula $\lambda= \frac{h}{mv}$; where h is Planck's constant. ...
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Evidence that electrons don't exist between orbitals? [closed]

I don't understand the logical jump that was made early on in the atomic age, to conclude that electrons jump in and out of existence when moving between orbitals? Similarly, why do electrons need to ...
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Apparent inversion of oxidation state of sulfate ion using minimal basis set

It is well known that the sulfate ion has essentially no 3d-2p bonding; hence I used the minimal basis set(STO-3G) for the NBO calculation I did via Gaussian, just to check it. However, I got a ...
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Role of 'p' Orbitals in Graphite Carbons

In the graphite arrangement of carbons, if we model them according to hybridization theory, the carbons in graphite are sp2 hybridized. This would mean that one s and two p orbitals hybridize, making ...
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The quantum mechanics behind periodicity of elements

Especially in high school/first-year undergraduate chemistry courses, we learn with great dedication the periodicities along groups and periods. There are various useful and interesting trends. I ...
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nodes and probability density

The square of the wavefunction gives probability density of finding an electron somewhere in the orbital. The text I'm referring to says that the value of probability density is always higher than ...
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Proof for second-order perturbation term of energy

In perturbation theory, if \begin{align}{\hat {H}} &= {\hat {H}^{(0)}} + λ{\hat {H}^{(1)}} \tag{1}\\ {ψ} &= {ψ^{(0)}} + λ{ψ^{(1)}} +λ^2{ψ^{(2)}} + ... \tag{2}\\ {E} &= {E^{(0)}} + λ{E^{...
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How to calculate Hirshfeld charges from Gaussian?

I am new to Gaussian and want to calculate Hirshfeld charges from Gaussian 09 or 16. I found this input file for Methanol: ...
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Quantum mechanics electron probability [closed]

Schrödinger's equation yields us the solutions of 90% probability of presence of electrons in orbitals. Hence, the electrons in theory should be able to exist elsewhere in space as well. In that case, ...
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Wave function of a perturbed system

In perturbation theory, wave function of a perturbed system can be expressed in a power series of some $\lambda$ as $\psi^{(0)} + \lambda\psi^{(1)}+\lambda^2\psi^{(2)}......$. Then we express ...
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Expectation value of an observable in quantum system

In quantum systems, sometimes if the wave function is not an eigen value of an operator then it is expanded in terms of bases states, then we apply the operator over the bases states and we get ...
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Normal modes of vibration [closed]

Why Normal modes of vibration are important when compared to translational and rotation modes. And why the frequencies for rotational and translational modes are close to zero?
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