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

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Explaining the Relative Energies of Various Vibrational Modes

Specifically, I'm wondering why it is that the asymmetric stretch in most (although there are exceptions to this I believe) molecules is higher in energy than the symmetric stretch. Similarly, I ...
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Newtonian physics scale [on hold]

So as I am starting to understand there is a scale at which Newtonian physics ceases and the quantum world takes hold. My question is what is the smallest molecular structure that still exhibits ...
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How to explain the discrepancy between the calculated absorption wavelength within the particle in the box theory and the observed wavelength?

The experimental observed wavelength for this molecule is 425 nm. We are supposed to estimate this wavelength theoretically using this equation (energy change in a 1D box), where $N$ is the number of ...
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How to identify the number of pi electrons in a conjugated system to calculate the HOMO-LUMO gap with the particle in the box approach?

It's my understanding that for a particle in a 1-D box, the change in energy from the HOMO to LUMO can be approximated with the following equation: $$\Delta E=\frac{h^2 ( N + 1 )}{8 m_\mathrm{e} ...
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Is there any software package for quantum chemistry that includes CAMB3LYP?

I want to do calculations on systems with photoinduced electron transfer, and I've read that the Coloumb Attenuating Method is a modification of the functionals that makes calculations including ...
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Use of statistics in this field

I am currently pursuing a statistics course and I an interested in knowing how can statistics help this field in future. (I am interested because I love chemistry very much) Specifically, are there ...
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What is the difference between Fukui FMO approach and Woodward-Hoffman rules?

If I understand correctly Frontier MO-theory is based on the perturbation theory of reactivity and the Woodward-Hoffman rules consider conservation of orbital symmetry. Does FMO use symmetry ...
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How the Azimuthal quantum number describes 3d shape of the orbital?

I read yesterday that Azimuthal Quantum number describes the shape of orbital....
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Jahn-Teller Distortions in Square Planar Complexes?

A Jahn-Teller distortion is predicted whenever a non-linear symmetric molecule has degenerate orbitals and has unequal electron occupation in those degenerate orbitals. Of course this most often is ...
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Constructing a Walsh diagram of AH2

According to Wikipedia, for the $\ce{AH2}$ Walsh diagram: and the Walsh diagram in Shriver and Atkins Inorganic Chemistry, the $a_1$ orbital sinks in energy going from 90 to 180°. Furthermore, the ...
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How to determine the best computational method for energy calculation of a molecule?

In computational or quantum chemistry text books comparing between various methods for energy calculation of a molecule (e.g geometry optimization) such as Semi-empirical, Ab-initio or DFT and also ...
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Sulfur atomic absorption

Would the atomic absorption from FAA for Sulfur be from 3s2 -> 3p4 or 3p4 -> 4s0? I think according to the electronic partition function, there would be zero electrons in the 4s0 state at the ...
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22 views

What is the velocity of an ejected electron in lithium when subjected to UV radiation?

If UV radiation strikes an atom of lithium with one electron in its lowest allowed energy state with enough energy to eject the electron from orbit, what is the electron's velocity upon ejection? The ...
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How does CASSCF yield a more-negative total energy from less-negative orbital energies?

When comparing single-configurational Hartree-Fock computations with corresponding CASSCF results, it appears that the CASSCF calculation is somehow able to generate more-negative total energies from ...
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Does light absorption result in a momentarily weaker bond?

I may have just misunderstood the topic, but light absorption by a molecule is a result of a promotion of an electron into an empty antibonding orbital; hence, does that mean that the strength of the ...
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61 views

Pauli's Exclusion Principle

While reading Pauli's Exclusion principal from here, they said that The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum ...
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Do orbital models derive from the solution of the stationary Schrödinger equation?

I know that hydrogen-like atomic orbitals can be seen as a solution of the stationary Schrödinger equation - but what about atoms with more electrons? As I am a pupil and quite uneducated about this ...
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Do really the electrons could only orbit in specific orbits with a fixed radius?

According to Bohr's model of atom The electrons could only orbit the nucleus in specific orbits or shells with a fixed radius. Only shells with a radius given by the equation below would be ...
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Reference value for two-electron repulsion integral over GTO's

I am currently trying to implement a Full CI program from scratch. The energies I get are a bit too high, so I'm looking for the mistake. One possibility is my implementation of the two-electron ...
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Initial guess for Unrestricted Hartree-Fock calculation

I am implementing an Unrestricted Hartree-Fock calculation, following Ref. [1]. It works fine for a odd number of electrons ($N_\alpha\neq N_\beta$) since, despite the same initial guess for $\alpha$ ...
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If chemical bonding is quantum mechanic, is saying they bend and vibrate like springs wrong?

I don't know much about quantum mechanics, but I do know that it's quite far removed from the easily observable and that anything "quantum" involves things that are discreet. So, how close is the ...
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Non-mathematical explanation for why the 3d orbital generally has higher energy than the 3p orbital [duplicate]

Why does the angular momentum of orbitals(l) affect the orbital's energy? Please provide a qualitative answer.
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197 views

Gaussian09 vs home made Hartree-Fock implementation

I implemented a restricted Hartree-Fock (RHF) calculation in the STO-3G basis set, as described in Szabo and Ostlund's book [1]. I managed to reproduce the energies of all their calculations ...
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How to find probability in different basis representations?

The matrix representation of the Hamiltonian is given in the position basis: $\{|+a\rangle,|-a\rangle\}$. $$H = \begin{pmatrix} E_{0} & E_{-A} \\ E_{-A} & E_{0} \end{pmatrix}$$ The initial ...
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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 ...
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How to convert from spin orbitals to spatial orbitals in the Hartree-Fock approximation?

I need to calculate some of the more complicated self-energy terms from chapter 7 of Szabo and Ostlund's "Modern Quantum Chemistry", and I'm having trouble converting summations from spin orbitals to ...
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A question about exercise 2.1 in Szabo and Ostlund's modern quantum chemistry, namely inner product between different spin orbitals

I feel quite confused about this question. Consider the spin-orbital integral $$\langle \psi_I^{\alpha} \alpha (\omega) | \psi_J^{\beta } \alpha (\omega) \rangle = \langle \psi_I^{\alpha} | ...
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Is there relation between “Plane wave basis” “Correlation-Consistent” basis and “Fourier basis”

This question is related to the following link I found while browsing the internet: http://www.gutenberg.us/articles/Basis_set_(chemistry) The question: Is there a relation between "Plane wave basis" ...
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Help solve this specific linear schrodinger equation, please

$$\left[-\frac{1}{2}\nabla^2 - \frac{2}{r} + C\right]\phi(r) = E\phi(r)$$ where $C$ is a known function. I am just looking for some help on the strategy to solve explicitly for $\phi(r)$. One thing ...
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Existence of orbitals

Do orbitals exist even when they are not occupied? For example: $\ce{Cr^{+3}}$ has the configuration $\ce{[Ar]}\mathrm{3d^3}$ with the other two $\mathrm{3d}$ orbitals empty. We know the other two ...
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Boys function for Gaussian integrals in ab-initio calculations

A few days ago I mentioned a problem with an Hartree-Fock program I am writing (HF using cartesian Gaussian STO-3G basis set). I can reproduce overlap and kinetic integrals of some references for ...
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192 views

Why does the mixing of sigma 2s and 2p orbitals lower the energy of the sigma 2s orbital and raise the energy of the sigma 2p orbital?

My general chemistry textbook (General Chemistry Principles and Modern Applications, Tenth Edition) says that for bonding in diatomic molecules with Z ≤ 7, orbital mixing occurs between the ...
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How does one calculate chemical shift in a gauge independent manner?

The literature on ab initio calculations of chemical shift in NMR experiments usually provide Lamb's and Ramsey's formulae as the solution. Yet the expressions explicitly depend on vector potential ...
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Computing two-electron integrals with an STO-3G basis set

I am trying to implement a restricted Hartree-Fock calculation using an STO-3G basis set, for fun. I managed to perform this calculation where only $\mathrm{1s}$ orbitals are present ($\ce{H2}$ and ...
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Schrödinger's equation [duplicate]

Schrodinger's equation has been successfully solved in one-electronic systems, such as the ionic molecular hydrogen $\ce{H2+}$. What is the exact reason that this equation can not be applied for ...
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Why are wavefunctions with same principal quantum number and different azimuthal quantum number orthogonal

The value turns out to be zero . This is understandable since they are completely independent of each other and also perpendicular in real space. But also turns out to be zero . How do I justify the ...
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Quantum Numbers

Why are the Lanthaide (atomic #'s 57-71) elements in period 6, but in terms of electron configuration, are assigned the principal quantum number of 4? Why are certain subshells assigned quantum ...
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Physical implications of the simple harmonic oscillator quantum mechanical solutions

Take a look at the wavefunctions for the different energy levels of a simple harmonic oscillator (a crude approximation for a diatomic). The wavefunctions seem to make sense: they tend to zero as x ...
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Periodic table- quantum numbers

I have come across many questions like: "if electron had 3 spins (-1/2,0,+12) then what change will be there in the periodic table?", also sometimes " if the capacity of each orbital becomes 5 then in ...
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Why does the two-electron exchange integral in Hartree-Fock theory have positive values?

In Section 2.3.6 of Szabo&Ostlund's Modern Quantum Chemistry, the exchange integral has the form of $$\int d\mathbf{r}_1 d\mathbf{r}_2 \psi_a^*(\mathbf{r}_1) \psi_b(\mathbf{r}_1)\frac{1}{r_{12}} ...
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How do I calculate principal quantum numbers of the Lyman series

How do I calculate principal quantum numbers of the Lyman series? I've been given that the lowest line is 121.6nm and the 5th line is 93.8nm The formula of the wavenumber is v=-R(1/n2^2 - 1/n1^2) ...
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Orthogonal Wavefunctions

My current understanding of orthogonal wavefunctions is: two wavefunctions that are perpendicular to each other and must satisfy the following equation: $$\int\psi_1\, \psi_2\, \mathrm{d}\tau =0$$ ...
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Demonstrating orthonormality for wave functions for ground state and excited state of He

I am trying to solve a homework question. The electron configuration of the ground state He atom is 1s$^2$, and the excited state configuration under study is 1s$^1$2s$^1$. I am to show that these ...
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Implications of orthonormal wavefunctions

For orthonormal functions $\psi$ and $\phi$, by definition; $$\langle \psi|\phi\rangle=0$$ However, when a wavefunction, $f$, is expressed as a linear combination of these orthonormal wavefunctions: ...
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What decides exothermic and endothermic? [closed]

A bond breakage is said to absorb energy and a bond formation is said to release energy .. Why. A bond formation leads to stability so loss of energy .. But what exactly happens to the electrons and ...
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Which type of orbital, 4s or 3d, is closer to the nucleus of an atom? [duplicate]

In my textbook it is explained that 4s electrons show greater penetration than that of 3d electrons, and, thus, the energy of the 4s orbital is lower than that of the orbitals in a 3d energy sublevel. ...
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How many valence electrons does an atom of Cu have? [duplicate]

$\ce{Cu}$ electron configuration: $\mathrm{4s^1 3d^{10}}$. Ok so the answer is $11$, shouldn't it be $1$ since the $\mathrm{d}$ shell is already filled up?
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Mathematically, how does the exchange integral for a closed-shell system reduce to 0 (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) ...
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Formation of Bonding and Anti-bonding Molecular Orbitals

If two orbitals combine in-phase, a bonding molecular orbital is formed. When they combine out-of-phase, an anti-bonding molecular orbital is formed. For a single molecule, how are both orbitals ...
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Why cannot the Schrödinger equation be solved exactly for systems in which more than two particles interact? [duplicate]

My question is simply this: "Why cannot the Schrödinger equation be solved exactly for systems in which more than two particles interact?" Is it so because it is impossible to solve mathematically? ...