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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Applying the constant number of electrons in DFT density optimisation

(Previous related question: Finding mathematically the ground state density in DFT) I am studying the density optimisation procedure (in particular for Orbital-Free DFT) this thesis. The derivative ...
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Cauchy-Schwarz integral screening different inequalites

Eq. (9.12.23) in [1] states that: $$\sum_{abcd}c_{ab}c_{cd}g_{abcd}>0\tag{MEST 9.12.23}\label{91223}$$ with $c_{ab}=c_ac_b$ for $c_a$ being some distribution coefficients and $g_{abcd}$ being the ...
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Correlation between dipole moment and stability

I have calculated optimized geometries and energies in water of two diastereomers of one compound. One turned out to be 1.9 kcal/mol more stable than the other (level of theory PBEo-G3bj/6-311g++(d,p)/...
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Finding mathematically the ground state density in DFT

To find the ground state density in DFT, you set the following Lagrangian: $$L = E[\rho(\vec r)] - \mu\left(\int \rho(\vec r) \mathrm{d}\vec r - N\right)$$ While minimising with respect to the ...
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Probability density “AT” the nucleus?

Just had a conceptual question from radial wave functions. I wanted to know if probability density AT the nucleus is maximum, or zero. From the attached images, it is clear that the function is at ...
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What will happen if electron as a wave undergo destructive interference while travelling in its Orbit?

Today I came across a justification of Bohr's angular momentum quantization using the De- Broglie's hypothesis. The justification said that since the electrons are having wave nature also then while ...
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What gives rise to the color of sapphires?

Here is what I know: Sapphires are composed primarily of $\ce{Al2O3}$ (in pure form colorless) as well as Fe and Ti (trace impurities responsible for the color). I know that the proportion and ...
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83 views

How to calculate molecular emission spectra?

Is there free software which can calculate the fluorescence emission spectra of organic molecules? Let's say for example: rubrene There is a bunch of quantum free quantum chemistry software: https://...
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Radial Probability Distribution Curve versus ψ² versus r curve for 1s orbitals

My question is basic, but I have already referred to a couple of books. This is an excerpt from Linus Pauling's book: the most probable distance of the electron from the nucleus, which is the ...
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Additional example determining Marcus parameters searched

Background / theory: The electron transfer in organic materials was formalized by the Marcus theory, introducing $|H_{ab}|$ to describe the how molecules (or more generally: sites) are coupled with ...
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Why does the SCF not converge in a structure optimization with GAMESS of the thiourea molecule at the PM6 level of theory?

I'm using GAMESS to run a geometry optimization on a thiourea molecule, using PM6. However, the output file keeps displaying the error message, "NO FORCE FIELD, SCF DOES NOT CONVERGE." Is there an ...
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Wave-particle duality [closed]

Can I get an answer stating some analogies on how electrons behave like a wave, and what does it even mean for an electron to behave like a wave? Also, if going around the nucleus, is electron a real ...
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The influence of diffuse functions on electron density calculations

I am not a quantum chemist, but I am (starting to be) a user of electronic structure software. In the picture (screenshot) is the electron density of the same molecule. On the left I calculated the ...
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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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How to account for solvation of a molecule explicitly in quantum calculation?

I'm looking for a way to account for hydrogen bonds formed with my molecule in aqueous solution explicitly in DFT calculation. I'll do it in order to compare stability of two structures in water. As ...
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Developing Computational Chemistry Software

I want to learn to develop novel methods in computational chemistry (e.g. Grimme's empirical dispersion, DFTB, new DFT functionals, etc.) What is the ideal way to learn this by oneself? I have read ...
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Electronic States of the (unstable) tetrahedral CrCl4

I was probing for first order Jahn-Teller instability in the coordination complex CrCl4 (2 electrons in E set). Taking the direct product yields the states A1 + A2 + E, so I took the symmetric and ...
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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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What does Brightness/ intensity of spectral lines depend on?

My book states that it depends upon "The number of photons of same frequency or wavelength ABSORBED or EMITTED" From what I understood, if many hydrogen atoms within the discharge tube EMIT the same ...
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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=|\...
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Why are there only 6 series (Lymen, Balmer, Paschen, Bracket, Pfund and H.Davy) in the hydrogen atomic spectrum? Why can't there be more? [closed]

The Balmer series, for example, is formed when the electron jumps from $n_2 = 3, 4, 5, \ldots, ∞$ to $n_1 = 2.$ The Humphry Davy series (The last series is formed when electron jumps from $n_2 = 7, 8,...
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Is there a reliable chemical theory that predicts pKa based on structure?

Obviously, there are general stability arguments that can be made to estimate relative pKas, such as evaluating the stability of the conjugate base of an acid, or thinking about how polarized the bond ...
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What drives vibrational cooling in an excited stated?

As we excite a molecule from its ground state, $S_{0,v=0}$, to some excited state in a higher vibrational state, i.e. $S_{1,v'=3}$, what drives vibrational cooling within that excited state manifold (...
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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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Why is there a z² label for d orbitals, but no x² and y² labels with corresponding shapes?

I know that the $\mathrm{d}_{z^2}$ orbitals are named as a result from the conversion of the angular component of the hydrogen-like wave function in terms of Cartesian coordinates, but how come we ...
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Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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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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How to calculate S² value of a broken-symmetry wave function?

$S$ represents spin, signifies the number of unpaired electrons in the system. For example, if the number of unpaired electrons is $1$, then $S=1/2$. $S^2$ is calculated as $S(S+1)$. From what I have ...
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Why do solutions of electron in a box (and in a ring) predict coefficients for LCAO (linear combination of atomic orbitals) in 1D systems?

The solutions to the 1D particle in a box quantum mechanic system are standing waves (zero at both ends of the box) with 0,1,2... nodes for increasing energy (zero for the ground state). If I look ...
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Ab Initio and Molecular Orbitals [closed]

What is the difference between ab initio calculations and molecular orbital theory?
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What does the number of orbitals in a subshell represent? [closed]

s subshell has 1 orbital and p subshell has 3 orbitals. Does that mean that there is a high probability that the electron is in the p subshell? As orbital are the space where there is a high ...
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Explaining hypervalency in the framework of molecular orbital theory

In preparing for teaching duties in an introductory course in inorganic chemistry, I seem to have made a digression into how we understand the hypervalent molecules. Just to re-iterate what this ...
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All possible determinants forms a complete basis [closed]

How do we mathematically prove that the set of all possible excited determinants forms a complete basis for expanding the wavefunction (as in full configuration interaction)?
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Guide to DFT functionals [duplicate]

Having recently begun studying Quantum and computational chemistry in depth... I am looking for a manual, text, or guide of any form that could explain the basic formulations and potential of the ...
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1answer
96 views

Quantum numbers required to specify the position of an electron

In a test today, there was this question: How many quantum numbers are required to specify the position of an electron? $$(A)\ 1 \quad (B)\ 2 \quad (C)\ 3 \quad (D)\ 4$$ The answer key says ...
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Multiplicity letter codes for large amount of states

Well, let's say we have a large amount of states computed (e.g. over 50), all with the same multiplicity. So, our ground state can be $X^2\Sigma^+_g$ and we can continue with $B^2, C^2$ etc. as ...
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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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Why is the dz2 orbital so different from the rest?

What makes dz2 orbital so special? Although degenerate with other d orbitals, It has no nodal planes, instead it has 2 nodal "cones". Instead of having 4 lobes, it has 2 lobes and 1 ring. Also, ...
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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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What will be the form of coulomb and exchange operators for electron m in an n-electron molecule?

I know that the Fock operator for electron $m$ in $n$-electron molecule would be: $$\hat{f}\!(m)u_i(m) = \varepsilon_iu_i(m)$$ $$\hat{f}\!(m) \equiv -\frac 1 2 ∇_m^2 - \sum_α\frac{Z_α}{r_{ma}} + \...
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How To Calculate “İntermolecular Energy” as QM and MM? [closed]

In this article: http://ambermd.org/antechamber/gaff.pdf, in Table-7, authors have calculated "intermolecular energy" of a molecule set. I wonder how can I calculate this energy by using gaussian09 ...
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189 views

How do you calculate the correct charge on F after F2 dissociates?

When you ionize $\ce{F2}$ to $\ce{F2^5+}$, it quickly dissociates. Experiments show that the products of dissociation are $\ce{F^2+}$ and $\ce{F^3+}$. I have tried to model the dissociation of $\ce{...
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Reaction of HF in water [closed]

I was wondering, if we put $\ce{HF}$ into a glass of water the acid will be dissolved according to this reaction: $$\ce{HF->F- + H+}$$ Now there is a proton travelling across the water. All $\ce{...
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Why is a LCAO necessary within Hartree Fock?

As I understand it, the electronic Schrödinger equation cannot be solved for polyelectronic systems. To circumvent this problem in the Hartree-Fock method, it is assumed that the polyelectronic ...
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Can pi backdonation occur on non-metal centers?

The common example of back-donation is the interaction of a CO molecule with a metal center (d-orbitals) on a surface. Can a similar mechanism occur between CO and a non-metal center, like oxygen on ...
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Chemical reaction energy barrier width [closed]

Well chemistry before the discovery of quantum world was saying:"In order for a chemical reaction to happen , reactants must have enough energy to be converted into products."I was wondering now that ...
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Variational method: Hydrogen atom ground state in STO-3G basis expansion

I computed numerically the ground state energy of hydrogen by variational procedure, firstly expanding the wave function over the s-wave basis set STO-3G $$\psi(r)=\sum_{i=0}^3 C_{i} e^{-\alpha_ir^2}$$...
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How to Scan Aromatic Dihedrals To Obtain Force Field Parameters

I am trying to generate new force field parameters based on quantum mechanical calculation. I used amber manual "parameter development" title for this and I calculated bond-angle-non bond parameters ...
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3answers
54 views

Particle-wave duality for atoms [closed]

Hmm Hello . I was wondering if we could apply the particle-wave duality of a subatomic particle for an entire atom.I know that atom is better described as space but could we apply the de Broglie ...
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416 views

When does Hartree-Fock fundamentally fail?

The Hartree-Fock approximation (HFA) works by assuming each electron sees the effective electric field from all the other electrons as some self-consistent field. The HFA is known to give pretty ...