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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Has QTPIE ever been applied to 1D metals such as polyacetylene?

QTPIE is a fluctuating charge model that substantially improves modeling of polarization and charge transfer. I was curious whether it has ever been applied to 1D metals such as polyacetylene to ...
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Hybrid orbitals, photoionization and time dependence

Wikipedia, in the article on Orbital Hybridisation, states the following: One misconception concerning orbital hybridisation is that it incorrectly predicts the ultraviolet photoelectron spectra of ...
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Uncertainty Principle in the Ground State of a Rigid Rotor

This is a fairly basic question which has bothered me for some time and I haven't been able to satisfactorily resolve. In the ground state of the rigid rotor the energy is zero. That is, there is no ...
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What is the point of introducing virtual orbitals in Hartree-Fock calculations?

Let us for simplicity discuss RHF formalism. For $2n$-electron system we have $n$ Hartree-Fock equations written for $n$ spatial orbitals $\{ \phi_{k} \}_{k=1}^{n}$ $$ \newcommand{\mat}[1]{\boldsymbol{...
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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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Transition state optimisation on the surface of periclase

I want to model a reaction catalysed by periclase ($\ce{MgO}$) using DFT. I have a good guess on the transition state (TS) of the reaction that goes in gas phase/solvent (produced using MOPAC). The ...
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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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What is the biggest known difference between rₑ and r₀?

What is the biggest known difference between $r_e$ and $r_0$? Where $r_0$ is the average bond length of the lowest vibrational state, and $r_e$ is the location where the potential is lowest. For a ...
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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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What is d-orbital collapse?

When I was perusing the works of Schwarz on atomic structure, I came across the unfamiliar term of d-orbital collapse. He describes it as a variation in energetic sequence from group 1 to 3 elements ...
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Can you explain DFT and TDDFT functioning (math aside)? [closed]

I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT, and Time Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in ...
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multielectron spin-orbit coupling and energy level

For multi-electron atoms for which the Hamiltonian (including the spin-orbit coupling) reads $$H=\sum_i T_i-Z\sum_i V_i+\sum_i V_i^{\text{s.o.}}+\sum_{i>j}V_{ij}$$ The $T_i$ are the kinetic ...
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How is Negative Temperature Hotter than Infinite Temperature?

Recently I have read articles stating that negative Kelvin has been achieved. I was a bit speculative at first as I though how can you get cold than 0 Kelvin, but after doing some research it makes ...
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How is the bond length calculated from the total electronic energy?

In the quantum chemistry course that I currently attend, it was said several times that one of the key quantities derived from molecules by means of computation is the total electronic energy $E_\text{...
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Why is the alpha particle called a particle when it is made of four particles?

We know the alpha particle is the nucleus of helium. It contains four subatomic particles - two protons and two neutrons. The protons and neutrons are further made of particles called up and down ...
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Temperature of an atom

I read somewhere that the temperature of an atom is not defined. The definition of temperature is only for larger systems. Why is this so?
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The time scale of calculations in computational chemistry

Is it possible to determine or get a range of the time required for a specific calculation with knowledge of the type (MM or QM), class (semi-empirical, ab initio or DFT), the degree of theory (MP, CI,...
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Why is there a need of polar coordinates to solve the Schrödinger wave equation for the hydrogen atom?

Why is there a need of polar coordinate to solve the Schrödinger wave equation for the hydrogen atom? I went through some standard text books but I am feeling rather confused about the explanation.
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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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Trying to understand the statement: 'Resonance is not a flickering between the contributing states. '

So, the famous resonance definition: it is the weighted average of different Lewis structures.... Well, this is purely wrong. Resonance is nothing but quantum 'superposition of the wavefunctions ...
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Pauli exclusion principle

Pauli exclusion principle states that 'No two electron can exist in same state' or 'No two electron can have same set of quantum numbers'. But in reality there is no state of electron. The state is ...
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658 views

Column order, signs of MO coefficients, and density matrix construction in Hartree-Fock

I'm attempting to make a Hartree-Fock solver, using Python, following Daniel Crawford's guide. I have been successful with the first four steps. However, I am having some trouble with this part in ...
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Has it been observed that the dihydrogen molecule dissociates into ions?

As we know from the improved methods valence bond theory (VB), as well as molecular orbital theory (MO-LCAO), the wave function of the $\ce{H2}$ molecule consist of two terms, which belong to covalent ...
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How does one compute the number of unique 2-electron integrals for a given basis set?

I have run into trouble with an exercise in Szabo and Ostlund's Modern Quantum Chemistry. Exercise 3.14: Assume the basis functions are real and use the symmetry of the two-electron integrals [$(\...
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Significance of phase of atomic orbitals

I am learning about orbitals and bonding and antibonding MOs. So far, I know that when you combine s orbitals, you form both bonding and antibonding MOs- bonding when the wavefunctions are added in ...
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Ab initio effective potentials

I have been reading a journal article on ab-initio pseudo-potentials, and I need some help understanding it. The article is C. F. Melius and W. A. Goddard, III. Phys. Rev. A 1974, 10, 1528. A summary ...
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Alternative Program for Orbital Population Analysis

Gaussian has Orbital-by-Orbital Population Analysis. From the manual: ...
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Trying to understand the necessity of orbital approximation or the independent electron model

I'm reading the approximations used for solving the Schroedinger's equation for molecules; the first is the the Born-Oppenheimer approximation: Freeze the molecule with a fixed internuclear ...
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Why do electrons need to be paired?

I’d read that it takes energy to place electrons in pairs, just less than it would take to place two electrons in different subshells. I get that. What I don’t get is, then, why would electrons want ...
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Rayleigh–Jeans Law

In McQuarrie's Quantum Chemistry, the Rayleigh–Jeans law is given as: $$\operatorname{d}\!\rho(\nu,T)=\rho_v(T)\operatorname{d}\!\nu=\frac{8\pi k_bT\nu^2\operatorname{d}\!\nu}{c^3}$$ where $\rho_v(T)\...
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Excited-states properties with traditional density functional theory

Recently I was shown the book "Density Functional Theory II, Relativistic and Time Dependent Extensions" by Nalewajski in which a chapter from E. K. U. Gross et al. is printed. [1] This chapter ...
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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 $\sigma_{...
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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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Relativistic effects and lanthanide contraction

So I understand than the lanthanide contraction is due to poor shielding of the 4f electrons which decreases the radius. However, if Im not mistaken the relativistic effects lead to a contraction of ...
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how are the frequencies at a local maximum of PES like?

On the potential energy surface, if you find a local maximum and calculate its frequencies in Gaussian or something like that, will you get all negative frequencies or all positive frequencies? I know ...
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Minimal basis CI of H2 dissociation

In Modern Quantum Chemistry by Szabo and Ostlund, they give an example of a minimal basis, full CI calculation of the dissociation of $\ce{H2}$ (on p.$241$ if you have the book). In explaining why ...
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Why is no dynamical correlation recovered in the CASSCF method?

Configuration interaction is the only certain way to get a calculation to converge toward the exact solution of the many-body Schrödinger equation (within the approximations used for the framework of ...
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What is an orbital boundary surface?

Could anybody explain the following statement: "The boundary surface is a common way to represent atomic orbitals, incorporating the volume in which there is about a 90 percent probability of finding ...
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How can two orbitals constructively and destructively interfere simultaneously?

The molecular orbital theory dictates that when two atomic orbitals form molecular orbitals, then two molecular orbitals must form (i.e number of atomic orbitals = number of molecular orbitals). For ...
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Can electrons switch orbitals within a shell?

I know that electrons can move from say 2s orbital to an unoccupied 2p orbital, as in Carbon atom which can form 4 bonds this way. But I want to know is it possible for an electron say in orbital 2p ...
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How does Fermi's golden rule yield a specific rate?

According to Fermi’s golden rule, the rate of an electronic transition is proportional to the magnitude squared of $\langle i|\hat{H}|f\rangle$. Since energy is always relative to some reference ...
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Tunneling corrections in reaction rates

I've studied Transition State Theory since I asked this a while ago, but so far I have not been able to find a detailed explanation of how tunneling corrections are implemented into reaction rates ...
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What happens to the complex part of the wave function when doing LCAO?

I understand that in general the wave function can take complex numbers, however when talking about combining atomic orbitals to form molecular orbitals we talk about the phase of the orbital being ...
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Intrinsic Reaction Coordinate - What does 'Connectivity' really mean?

I am currently in the process of connecting transition state (TS) structures to other minima in order to determine a reaction pathway. Now I understand the basic concepts of this method. You start ...
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What is meant when people say a molecule has high multi-reference character?

I have read some other posts explaining what multi-reference and multi-configuration are with regards to the wave-function (such as What exactly is meant by 'multi-configurational' and 'multireference'...
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Spectroscopy of excited state lithium

I have used data from a question regarding the reciprocal wavelengths observed when lithium transitions from excited states to a common ground state. The lowest energy transition is from n=3 to n=2. ...
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Why do two atomic orbitals form two molecular orbitals? [duplicate]

According to molecular orbital theory, two atomic orbitals form two molecular orbitals analogous to waves combining constructively or destructively but how can a wave combine destructively and ...
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How does the radial distribution function of Vanadium differ from that of Calcium and how does this affect the ionic electron configurations?

When Vanadium is ionised it loses the 4s electron first, meaning that it's 3+ ion has a different electron configuration to Calcium despite it being isoelectronic. Can it be explained in terms of ...
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Connection of term symbols with specific microstates for atomic carbon

I'm currently studying atomic term symbols. I wanted to try it on a simple atomic carbon with the electron configuration $1s^22s^22p^2$. I know, that only open-shell electrons are involved in the ...
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What's a good measure of the Eigen-ness of a wavefunction?

Just wondering if someone can recommend an easy-to-compute measure for the Eigen-ness of a wave function, such as the wave functions computed using ab initio method? For a wave function solved using ...

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