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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Normal (Regular) or Inverted Terms?

I have a question on the order of the spin-orbit molecular states. I understand how to find the terms that split from a parent molecular state in a diatomic molecule. But my question is on how to find ...
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Could observer effect cause electrons in one orbital to be found in another?

The observer effect states that when unobserved, absolutely small particles like electrons can simultaneously be in two different states at the same time. (Tro, N. J. (2015). Principles of Chemistry: ...
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Cross-conjugation and aromaticity in pyrene

I have read about non-huckel double bonds and clar's rule, but what made me confuse is that huckel's perception gives me the feeling that central bonds in polycyclic aromatic hydrocarbons (ex: pyrene) ...
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What is the basic difference between accidental degeneracy and normal degeneracy?

As definition suggests accidental degeneracy is defined by the degeneracy generated by two symmetry protected states. But how is it different from a non accidental degeneracy.
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120 views

Azimuthal Quantum Number and Magnetic Quantum Number

I know that azimuthal quantum numbers and magnetic quantum numbers are used to find the no. of and the orientation of subshells respectively, but why do they have to be called so? I reckon that ...
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21 views

Approximate Hamiltonian in variational method (Example of Helium atom)

As one know, the exact Helium Hamiltonian \begin{equation} \hat H = \left( -\frac{\hbar}{2m_e}\Delta_1 - \frac{Ze^2}{r_1} \right) + \left( -\frac{\hbar}{2m_e}\Delta_2 ...
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25 views

What is the link between the classical and quantum definition of the symmetry number?

From what I understand, the symmetry number for a molecule can be defined in 2 ways: 1. The quantum mechanical symmetry number corrects for overcounting the number of possible rotational states of a ...
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32 views

Deriving the absorption coefficient from state transitions

This source states that the absorption coefficient $\gamma$ is proportional to the difference in particle number density $\Delta n$ per unit volume between the initial and the final rotational state ...
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36 views

Uncertainity principle of a particle on a ring in $m=0$ state

When a particle is on a ring, we know that the commutator $[L_z,x]=i\hbar y$ and $[L_z,y]=-i\hbar x$. So we can't measure $L_z$ and $x$ & $L_z$ and $y$ simultaneously with infinite accuracy. When $...
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71 views

What are the rules for constructing Kohn-Sham orbitals?

I just recently began to study quantum chemistry and need some clarification for the construction of Kohn-Sham orbitals. Consider a system of several atoms. Let there be $N$ electrons in this system. ...
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72 views

Two electron integrals between 1s STO [closed]

I am trying to understand SCF cycle by trying to code up solved example from Quantum Chemistry by Levine (page 443, 5th edition). The problem is shown below: One electron integrals are straight ...
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31 views

Obtaining energy and wave function for excited states

Suppose I have done a HF calculation and obtain the energy and wave function of ground state. If I want to produce the spectrum of the specie (say Hydrogen molecule), should I use CI (configuration ...
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56 views

Finding vibrational frequencies and heat capacity from bond enthalpies?

So I have heat of formation data for H2, HD, and D2, and I'm being asked to find the difference in vibrational frequency and zero point energies between H-H and H-D. I know that i need to use the ...
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44 views

Probability density of a particle in a 2D box with given coordinates

Wavefunction of particle in a $2$D box with sides $L$ in the $x$ and $y$-axis: $$φ = \sqrt{\frac {4}{L^2}} \sin\frac{n_1πx}{L}\sin\frac{n_2πy}{L}$$ For the different states ($n_1=1$, $n_2=2$), (...
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Wave function characteristics

In a book, I read that the wave function of a system should not become infinite in a finite region and also should vanish at infinity. For the first part I think that if wave function is infinite in ...
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37 views

Trouble understanding equation from density functional theory

In the review by Oliviera et. al., I do not understand how the authors get equation 14: \begin{equation} E[\rho]=\sum_i^Mn_i\langle\Psi_i|-\frac{1}{2}\nabla^2+v_{ext}(\vec{r})+\frac{1}{2}\int\frac{\...
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91 views

How to graph spherical harmonics in the Mac “Grapher” application?

I was wondering if it was possible to graph the spherical harmonics in the Mac grapher app. In their manual, there is a section that talks about graphing the spherical harmonics (page 54): This is my ...
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29 views

The meaning of magnetic quantum numbers' values

The $\mathrm{m_l}$ values in quantum mechanics, $1, 0, -1$ for p orbitals for example, do they refer to specific orbitals? Like, does $\mathrm{m_l} = 1$ refer specifically to $\mathrm{p_x, m_l} = 0$ ...
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144 views

Is this approximate equivalence table between Pople's basis sets and Jensen's DFT attuned polarization consistent basis sets (pcseg-n) correct?

I have some calculations results I runned previously using Pople's basis sets, mostly 6-311+G(d), under Gaussian09. These days I read some texts on Frank Jensen's family of polarization consistent, ...
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140 views

Spin-Adapted Configuration and Slaters determinants for Open- and Closed-shell systems

Some time ago, I asked a question about spin-adapted Configuration State Functions. I read that, when we ignore the electronic repulsion in a atom or a molecule, we can write the ground state using a ...
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29 views

A general definition of bond order in molecular orbital theory?

I stumbled upon this problem upon learning organic chemistry after learning the foundations of MO theory in physical chemistry. It seems that VBT and MOT can coexist with each other in many scenarios. ...
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70 views

Reaction energies of solids from quantum chemistry?

I was reading a paper by Catlow et al. [1], and they mentioned the dissolution of copper into copper ions, which is given by this equation: $$\ce{Cu2O(s) + 2 h+ <=> Cu+(aq) + 1/2 O2(g)} \tag{...
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What is the difference between dynamical and non-dynamical correlation and which one is accounted for in Hartree-Fock theory? [duplicate]

It is my understanding that dynamical is related to the movement of individual electrons. I don't fully understand what this means though. Non-dynamical correlation is still very unclear from my ...
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32 views

What is the justification for using the Marcus rate equation to model charge transport in organic semiconductors?

I am trying to understand the history of how Marcus theory moved from describing electron exchange reactions in aqueous ionic solutions to also being applied to describe transport in organic ...
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54 views

Theoretically predict the density of water

Is it possible to predict the density of water having just its molecular structure (basically obtain 1 g/cm3 at 3.96 °C)? Are you aware of research/textbook that dive into this topic? Is it able to ...
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25 views

Order of coordinates in a wavefunction - why do they matter?

For the past few weeks, I have been studying Quantum Chemistry and lately in these lectures something has bugged me: If I do a sum: $1 \times 2 \times 3 \times {...} $ This is the same as simply ...
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41 views

How do these restrictions on the wavefunction logically arise?

My lecturer notes that the following restrictions on the wavefunction (in addition to it being a solution to the Schrodinger equation) are logical: i) Continuous (mathematical definition of a ...
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79 views

Electron Spin, and the Stern-Gerlach Experiment

I think I understand the basics of the electron spin. However, I'm trying to figure out how to tell if, when shooting a beam of atoms (the Stern-Gerlach experiment), how to tell if an element will ...
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35 views

How can I obtain the wave function of the dihydrogen system, by hand using Self Consistent Field DFT calculations? [duplicate]

After doing some energy calculations for the $\ce{H2}$ system in Gaussian, using ωB97X-D/STO-3G level of theory, and generating a .wfn file, I wanted to understand better how the computer does ...
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141 views

What is meaning of LAV2P basis set?

I am working on energy optimization of molecular structure using DFT with Schrödinger software and I found that job is running on LAV2P basis set. I want to know what is the meaning of this basis set ...
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45 views

Ionization energy and charge localization: π-bonds/systems and ionization energy

Page 35 of my textbook, Mass Spectrometry by Jürgen H. Gross, says the following in a section on ionization energy (IE) and charge localization: Molecules with π-bonds have lower IEs than those ...
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144 views

Does the radius of the atom change when an electron is excited?

The radius of the atom increases when the electron in a hydrogen atom undergoes a transition from the 1s-orbital to a 2p-orbital. How is this possible? Why does exciting an electron to a higher ...
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55 views

Getting radial Kohn-Sham orbital from the output of an electronic structure code using gaussian basis sets

As we know that in solving the Schrodinger equation (Kohn-Sham equation), we expand the wavefunction in terms of some basis sets and them optimize the energy (the expectation value of Hamiltonian) by ...
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108 views

What is the significance of antinode at r=0 in the plot of radial wave functions of s-orbitals?

Why should there be an antinode at r=0? I can comprehend the presence of node at r=0 for p,d,f orbitals; but I don't understand that of s-orbital. Is there any intuitive approach?
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47 views

Is it possible to calculate electrostatic interactions using QM methods?

I'm trying to calculate an accurate electrostatic repulsion (and possibly attraction) energy term for various small molecules, using Quantum Mechanics (QM) methods. These may include molecules such as ...
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1answer
35 views

Potential energy curve for dissociation of cation of carbon dioxide

Can anyone suggest me some literature where I can find the potential energy curve or the electronic states for singly ionized $\ce{CO2}$ ($\ce{CO2+}$) dissociating into singly charged oxygen ($\ce{O+}$...
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47 views

Photoelectric effect — Expected observations for waves

I understand why treating light as particle-like photon packets leads to the observed results. I seek to understand why one would expect different results if light were treated as a wave (and thus ...
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1answer
73 views

Can the oxidation of hydrogen peroxide be reversed? [closed]

Hydrogen peroxide is said to be unstable, for it undergoes auto-oxidation on standing/heating: $$\ce{2H_2O_2 -> 2H_2O + O_2}$$ where $\Delta S=\pu{70.5 J {mol}^{-1}K^{-1}}$ and $\Delta H^{\Theta} ...
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64 views

Significance of this unusual matrix element

Recently, I was solving some questions on Rigid Rotor. I found this question very amusing. Evaluate the integral i) <$Y_{l,m+2}$ | $L_{x}^{2}$ | $Y_{l,m}$ > I evaluated it, found that the value ...
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192 views

Why do we neglect the zero point energy in statistical mechanics?

Quantisation associated with translational modes can be modelled like a particle in a box (PiB). $$E_n = \frac{n^2h^2}{8mL^2} \qquad n \in \mathbb{Z} \, | \, n \ge 1$$ By the equation above, the ...
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22 views

Scan type of DFT calculations adding Freq=Raman keyword [duplicate]

I´m doing a scan calculation by adding Freq=Raman keyword. My objective is to obtain the Raman spectrum of each conformation in my compound. However, when i write the Freq=Raman Keyword, only the ...
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256 views

Is OH + CO → CO2 + H an elementary reaction?

Is $$\rm OH + CO \longrightarrow CO_2 + H$$ an elementary reaction? How could I tell? I could break the reaction into $$\rm OH\ (+ M) \longrightarrow O + H\ (+ M)$$ $$\rm CO + O \longrightarrow ...
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830 views

Why does q/m ratio(specific charge) depend on nature of gas in anode ray experiment?

I can't understand why $q/m$ ratio changes in anode ray experiment (discharge tube experiment) (which was carried out by Goldstein) with change in nature of gas? Since $q=1.6\times10^{-19}\ \mathrm C$...
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59 views

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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20 views

Filling up of electrons [duplicate]

Is it necessary that filling up orbitals start from spin-up orientation only? And also, is it mandatory to fill the electrons with one kind of spin or they can be filled with spin up and spin down(as ...
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48 views

Using knowledge of radial distribution functions, how is it possible to explain the different electron configurations of V3+ and Calcium [duplicate]

I recognize that the 3d orbital decreases in energy to lower than the 4s once it becomes occupied (even if I don't completely understand why?!). However, how is the difference in electron ...
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1answer
1k views

If the electron of a hydrogen atom transitions from energy level n=5 to n=3, which level corresponds to n1 and which level corresponds to n2 [duplicate]

which level corresponds to n1 and which level corresponds to n2 in the Rydberg equation?
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$\psi$ Represents amplitude of electron wave and $\psi^2$ represents electron density in a given space. How?

The $\psi$ represents amplitude of electron wave. So it's dimension should be $\left[L\right] $. But $\psi^2$ represents density of electrons in a given space. So it's dimension should be $\left[ML^{-...
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1answer
3k views

Why the second ionization energy of helium is greater than the first? [closed]

maybe because the first electron has a lower energy. Why does this happen?
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1answer
67 views

Can carbon have electrons in a 5d orbital? [closed]

(a) Sketch the radial probability distribution for a 5d orbital in a carbon atom. You should label the axes, but do not need to include numbers. Use arrows to indicate the radial nodes. (b) Label the ...