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

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Detail from Integral Evaluation in Szabo (Appendix)

This is a step from Appendix A in Szabo and Ostlund's Quantum Chemistry. In short, the question is how to get from A.20 to A.21. We can factor out some constants in the expressions to get: A.20: $$ \...
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Type of excitation in a molecule

I am working on an assignment where I shall determine the type of excitation in a molecule and from 'where' to 'where' the electron goes, using HOMO and LUMO pictures, in detail in poly(p-phenylene) ...
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Dependence of energy on a molecule's dihedral angle

I've studied the dependence of biphenyl's Energy on its dihedral angle. I know how to describe the dependence quantitatively, but still, I don't know how to explain that the potential barrier of ...
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Can the Principal Quantum number be considered an energy barrier? [closed]

As in, can it essentially be thought of as a spherical boundary for all orbitals therein, which basically just gives us an arbitrary unit of energy for comparison between its respective orbitals? ...
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Oscillator strength of a transition

I am trying to compute the oscillator strength in a molecule. Therefore I've got its Energy level values plus both wave functions $\Psi_i$ and $\Psi_j$ for the transition I want to calculate the ...
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42 views

Why do only 2s and 2pz orbitals interact in the molecular orbitals of elements with Z<8?

I have read in my chemistry textbook that the energy of a $\sigma_{\mathrm{2p}_z}$ orbital is higher than that of $\pi_{\mathrm{2p}_x}$ and $\pi_{\mathrm{2p}_y}$ for the molecular orbital ...
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51 views

Hückel method for biphenyl

I am trying to calculate the energy levels of biphenyl (see picture below) using Hückel method. Since this is my first time using Hückel I am a little confused. Biphenyl has 12 carbon atoms, ...
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What is the difference between non-adiabatic coupling and diabatic coupling?

The diabatic couplings are the off-diagonal terms of wave functions written in a diabatic basis. There is a need to use the diabatic basis when there is a breakdown of the Born-Oppenheimer ...
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25 views

Excitation energy of a symmetric molecule [closed]

Let's suppose I have a symmetric molecule e.g. biphenyl (The dihedral angle etc. shall be negligible.) When I want to calculate its excitation energies analytically the easiest way would be something ...
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17 views

Distinguish between two possible configurations for angular momentum in carbon atom

Consider the possible values of $S$ and $L$ for carbon configuration $1s^2 2s^2 2p^2$ and the corresponding rapresentations with arrows indicating the spins (consider only $S=0,L=0$ and $S=0,L=2$, as ...
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1answer
53 views

Is there a finite number to the possible state of electron in an atom?

Okay, I know you may say, there are infinite numbers of possible state of an electron between its ground state and ionic state, since energy levels get continuous as electron gets farther away from ...
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Identifying principal quantum numbers in natural population analysis

Following a Hartree-Fock calculation, I would like my program to perform some kind of Natural Bond Orbital (NBO) analysis. Preceding this I would like to output a list of atomic orbitals, along with ...
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1answer
111 views

How do restricted open shell calculations mathematically proceed in the context of the self consistent field iterations?

I'm specifically concerned with HF theory. I understand restricted closed shell calculations use the Roothaan equations. If I understand correctly these equations assume each filled molecule orbital ...
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56 views

Understanding two-electron integrals in Gaussian 09

I was comparing the two-electron integrals (electron repulsion integrals, ERI) printed by various well-established packages (Gaussian, GAMESS, Molpro etc.) and observed that Gaussian is the oddball in ...
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29 views

How are imaginary frequencies and force constant calculated by DFT?

Computational calculations allow us to simulate the frequencies of molecules. They can even tell us if the optimized structure is a minimum, a saddle point or a maximum according to the number of ...
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Osmium is the densest element due to relativistic effects. Why not another metal affected by relativistic effects (Such as gold)? [duplicate]

All in the title. Thought of with the question after viewing links like: Why is gold golden? Why does mercury have low melting and boiling points?
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20 views

Bond formation of C2 [duplicate]

According to the molecular electronic configuration of C-C the remaining molecular orbitals are π2px^2 and π2py^2, does this mean that the first two bonds in C2 are π bonds how is this possible or do ...
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45 views

The nature of Chemical Bonds [closed]

It was nearly a year ago when I appeared for my first interview through the KVPY (a research oriented scholarship exam) when one of the questions the panel asked me was : What is a chemical bond? ...
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Quantum Number Clarification [duplicate]

So an increase in 'n'(the Principal Quantum Number) implies an increase in distance from the nucleus, right. And it also means higher energy. But according to the Classical Electromagnetism, farther ...
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29 views

Franck-Condon factors in photoelectron spectroscopy

Franck-Condon factors have been used to predict / assign the vibrational structure of photo-electron spectra. $FCF=|\langle\psi''_{vib}|\psi'_{vib}\rangle|^2 = |\langle\psi''_{vib,1}\psi''_{vib,2},\...
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How to know about radical character of a diradical molecule?

I understand that the radical character is quantified by the occupation number of the lowest unoccupied natural orbital obtained from UHF calculations or from CASSCF calculations. My issue is that I ...
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54 views

Why is spin-contamination undesirable?

Why is spin-contamination, introduced by e.g. Unrestricted Hartree Fock, undesirable, and to which problems further on can it lead? The only problem I currently see myself is that spin-contamined ...
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Does a constrained wave function method exist similar to constrained density functional theory?

I am trying to find out if a constrained wave function method exists for running quantum chemistry calculations. I know that constrained DFT exists and can be used to constrain the charge density to ...
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1answer
104 views

Do molecules change shape when they become vibrationally excited?

In quantum mechanics we learn the the classical picture of a vibrational excitation is wrong. The atoms will 'vibrate' only while the molecule is in a coherent superposition of two vibrational states, ...
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29 views

Which natural orbitals are better for CASSCF calculations for organic diradicals?

I am trying to perform CASSCF calculations for a series of diradicals. As input orbitals I have used two types of natural orbitals. One is unrestricted natural orbitals and the other MP2-based natural ...
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183 views

Why is density fitting not used to reduce four-center integrals further down to two-center integrals?

In density fitting, why don't researchers turn all the 4-center integrals into 2-center ones instead of stopping at composing them from 3-center integrals?
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How to calculate a molecule's oscillator strength?

I was wondering how to calculate a molecule's (e.g. biphenyl) oscillator strength using a very simplified model. If I want to calculate a molecule's excited states a good start is something like a ...
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37 views

Creating an IR Spectrum using Gaussian ADMP Calculation

I have a Gaussian 16 trajectory for a small cluster of water molecules carried out with ADMP technique. I was wondering if anyone knows how to compute the IR spectrum from the information in the ...
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1answer
90 views

Where can I get potential energy surface for simple molecules?

I'm looking for potential energy functions for simple molecules, such as water or hydrogen sulfide. I only need the region around the equilibrium geometry, preferably as a Taylor series expanded in ...
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67 views

Calculating excitation energies of a molecule

I am trying to calculate the excitation energies for the first three transitions of a molecule which is made up by a chain of k phenyl rings, where k shall be between 1 and 8. The angle between each ...
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1answer
93 views

Orthogonality of wavefunctions for different normal modes

Vibrational wavefunctions corresponding to different vibrational levels of the same normal mode are orthogonal because they are eigenfunctions of the harmonic oscillator Hamiltonian, which is ...
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79 views

The difference between CASSCF and MCSCF methods

I'm not sure the exact difference between the MCSCF and CASSCF methods. I know that the CASSCF method proceeds by optimizing both the CSFs and MOs (I mean the coefficients), but I don't know if this ...
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91 views

Vibrational Self-Consistent Field

There are a few things about VSCF that I don't understand: Which coordinates do you work in? If you work in normal mode coordinates, how do you evaluate the effect of the average of one normal mode ...
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1answer
94 views

Why is Coupled Cluster not variational?

It has been noted in several sources (e.g. ref. 1) that one of the disadvantages of the Coupled Cluster method for the description of electron correlation is that, since $e^T$ in $E_{CC} = \langle0|e^{...
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Evaluating Franck-Condon factors

Franck-Condon overlap integrals are given by $\langle\psi^e_{v_e}|\psi^g_{v_g}\rangle$, where $\psi^e_{v_e}$ and $\psi^g_{v_g}$ are the vibrational functions for the $v^{th}$ vibrational states of the ...
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1answer
77 views

Something about the Roothaan equation

Why we cannot solve Roothaan equation $\mathbf{F} \mathbf{C} = \mathbf{S} \mathbf{C} \mathbf{\epsilon}$ by just move S matrix to the left, as $\mathbf{S}^{-1} \mathbf{F} \mathbf{C} = \mathbf{C} \...
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Tunneling in chemical reactions

We know that quantum tunneling is the reason behind several natural phenomenon like alpha decay and thermonuclear fusion inside the stars. How can it influence chemical reactions by tunnelling a ...
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1answer
69 views

Notation for excited states

I am reading some papers about quantum chemistry and in one I found a notation for excited states of a molecule that I don't understand at all. In the picture below you can see the potential curves ...
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What does “intensity of light” mean? [closed]

In this lecture from MIT, the professor defines the intensity of a wave as the square of the amplitude of the wave. But, at the same time, the professor defines the intensity of light as the number of ...
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1answer
66 views

Maximum required order for the Boys function

I am planning to pretabulate a lookup table in order to evaluate the Boys function. We can expand the Boys function as: $$F_n (x_t + \Delta x) = \sum _{k=0}^\infty \frac{F_{n+k}(x_t)(-\Delta x)^{k}}{...
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1answer
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Why some reaction have no transition state?

All stationary point are local minimum, if any parameters changed the energy should be increase. There is no way for a stationary point that energy go straight down to reach another. I was told that ...
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1answer
69 views

Is there a more direct way to show this identity for the projection operator?

The following question I jotted down from an online quantum chemistry pdf. Show that $$i\hbar \frac{\partial P_j}{\partial t}= [H,P_j]$$ in which $P_j$ is the projection operator and $H$ is ...
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1answer
57 views

Why do we multiply two wavefunctions in valence bond theory instead of adding them?

The combined wavefunction of a hydrogen molecule in valence bond theory is the product of two wavefunctions, while in molecular orbital theory it is the sum of two wavefunctions.
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Bond order analysis in molpro

I'm trying to compute bond orders in a molecule, let's consider S2 as an example. I'm not entirely sure what's the right way to do that, but I assume NBO (Natural Bond Orbital) should give me what I ...
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1answer
218 views

The differences between integrals evaluations of contracted an uncontracted basis functions

I wanna to evaluate molecular integrals (overlap, kinetic and etc) using Gaussian basis functions. To do so, there are two approaches: contracted and uncontracted basis functions in which the former ...
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1answer
64 views

What is the theoretical quantum ground state energy of helium hydride positive ion?

What is the theoretical quantum ground state energy of helium hydride positive ion? I am speaking of the usual assumptions such as the approximate modeling of the two nuclei here - one being a ...
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1answer
36 views

How does the screening effect work for orbital in the same shell?

Energy of an orbital in a single electron system depends solely on n, while energy of orbital in multi electron system depends on n and l, why is that? I understand that the screening effect is at ...
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1answer
105 views

Spin in meta-GGAs

In density functional theory (DFT) we know that the local density approximation (LDA) leads to an exchange-correlation energy kernel of the form: $$E_\mathrm{xc}^\mathrm{LDA} =\int e_\mathrm{xc}\left(...
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1answer
82 views

How does chemistry explain consciousness? [closed]

Chemistry is defined as the branch of science that deals with the identification of the substances of which matter is composed; the investigation of their properties and the ways in which they ...
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1answer
35 views

how to manufacture PTC ink

I am trying to create a PTC ink similar to Henkel ECI8120 , I researched PTC rubber and found that it was Polydimethylsiloxane (PDMS) loaded carbon nanoparticles, I was wondering if anyone here has ...