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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How to calculate molecular dipole moment from a known wavefunction?

Say I have a molecular wavefunction as a set of molecular orbitals and want to calculate the molecule's dipole moment, but don't know how! I searched a lot but couldn't find any practical example. $$\...
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Why is black-body radiation curve smooth without a sharp cutoff?

Planck's law is able to predict a graph that is consistent with experimental observation: In essence, unlike Rayleigh-Jeans law that assumes equipartition theorem to hold (that each mode of motion ...
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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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Difference between Coupled Cluster and Full CI

I'm looking at some high precision quantum chemistry methods like Coupled Cluster (CC) and FULL CI (FCI). It seems both CC and FCI start from Hartree-Fock and then excite the electron to higher ...
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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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What exactly is meant by 'multi-configurational' and 'multireference'?

Some topics here have touched on this before (see 1, 2, 3), but I haven't found a clear definition yet. I would like to know what exact property of the wave function these terms refer to. It would ...
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What is the relation between surface tension and initial molecular harmonic?

Initial harmonic is measured as Hartree/Bohr^2 ( like IHarmonic=n in Gaussian Software ). As I am from physics background I am used to look at features from their dimension point of view: Actually ...
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623 views

Analytical solution of the Schrödinger Equation for AB^+ systems

According to Wikipedia, there are not many problems for which the Schrödinger equation can be solved analytically. [1] The $\ce{H2+}$ ion is probably the most complex molecule that can be treated this ...
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Observability of Orbitals and Orbital Energies

This question comes from some thoughts I had after reading this question. First of all, is an orbital an observable? I know the answer to this question is no because there is no "single-orbital ...
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Why is the electron-nucleus attraction modelled with only electrostatic interactions?

While reading about the structure of an atom, I've encountered (even in some renowned books) the statement that electrons and nuclei are attracted due to electrostatic, or Coulombic, attractions. ...
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Can two electron occupy the same spatial spot in a statistical way?

My friend claimed that if we have a two-electron atom in the ground state, and somehow we get the "real" electronic wavefunction $\psi(\mathbf{x_1},\mathbf{x_2})$ of the system, the statistical ...
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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 Pople's STO-3G basis set). I can reproduce overlap and kinetic integrals of some references for ($\ce{...
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How to compute 2-electron integral for Hartree-Fock code?

I'm working on writing my own code for $\ce{H2}$ in an STO-3G basis set using Hartree-Fock (HF), and I am currently stuck on how to construct the two-electron integral matrix. I know how to evaluate ...
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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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Hellmann-Feynman Forces with Hartree-Fock

The energy in the Hartree-Fock approximation is given as: $$E_{HF}=\left<\psi_{HF} \left| \hat{H} \right| \psi_{HF} \right>=\sum_{i,j}P_{i,j}H_{i,j}^{core}+\frac{1}{2}\sum_{i,j,k,l}P_{i,j}P_{l,...
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Why is MP2 failing to calculate proper IR frequencies for [Co(CO)4]- and [Fe(CO)4]2-?

I was doing some IR calculations on different 3d transition metal carbonyl complexes during some practical courses where we were introduced to effective core potentials. While doing this we found that ...
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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 \mathrm{d}\mathbf{r}_1\,\mathrm{d}\mathbf{r}_2\, \psi_a^*(\mathbf{r}_1) \psi_b(\...
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Are the canonical orbitals of Hartree-Fock also the natural orbitals?

My question stems from the comments on my answer to After a unitary transformation, is Koopmans' theorem still valid?. There was some confusion relating to differing terminology referring to different,...
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Why are there quantised energy levels in the vibrational energy of a molecule?

Why are the energy levels for vibrational energy in a molecule discrete as opposed to continuous? I don't understand how a vibration can't have continuous amounts of energy that depend on the ...
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555 views

Practical differences between storing 2-electron integrals and calculating them as needed?

Some texts that I read suggest calculating all of the 2-electron integrals at once (taking into account permutational symmetry) and some suggest calculating them on demand when building the Fock ...
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Interpretation of TD-DFT results

For the first time I'm doing TD-DFT calculations (wB97XD functional) in Gaussian 09 for an open-shell system and the results look like the hell of a mess for me. The molecule is rather big, so I ...
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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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Are there any full worked examples of DFT calculations?

I just started learning DFT and now I am totally confused. Assuming I want to use B3LYP: \begin{align} v_s\left(\textbf{r}\right) &= v_\text{ext}\left(\textbf{r}\right) + \int d^3r\frac{n\left( \...
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Why does the transverse magnetization in Fourier Transform NMR consist of Ix+iIy ($\hat{I}_{\!x}+\mathrm{i}\hat{I}_{\!y}$)?

More specifically, the expression for the average expectation value of the transverse magnetization has the following form: $$M^+(t)=N\gamma \hbar\,\text{Tr}(\hat{\sigma}(t)\hat{F}^+)$$ with $\hat{\...
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Band gap of fullerenes

From what I have read about fullerenes, the lower fullerenes like $\ce{C60}$ or $\ce{C70}$ have higher bandgaps around 3.5 eV or such, while the higher fullerenes have much smaller bandgaps of the ...
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Are there any datasets containing molecules with more than 38 heavy atoms?

I have been testing a machine learning approach for molecular energy prediction. The current dataset that I have is QM9, which is consist of molecules with up to 9 heavy atoms. I was wondering if ...
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Born–Oppenheimer adiabaticity

The Born–Oppenheimer aproximation is said to be adiabatic. What does "adiabatic" mean? What would be a non-adiabatic approximation to the Schrödinger equation?
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Why are full and half filled orbitals the most stable?

Why are degenerate orbitals (restricted to a single spin) less stable when neither fully filled nor completely empty? Why, in most molecules, are half-filled and fully-filled shells more stable than ...
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What constraints are imposed on a wavefunction by the symmetry of the system?

As a follow-up to my answer here, I'd like to ask what exactly does it mean for a wavefunction to "respect the symmetry" of the system. The original context is: immediately after ionisation of $\ce{...
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How are the atomic orbitals for multi electron atoms obtained?

The problem with Schrödinger's equation is that it isn't exactly solvable for multi-electron species. In the past, atomic orbitals were used to construct a solution for molecules (LCAO). My question ...
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Difference between radial, planar, angular and spherical nodes

What is the difference between them? I think radial nodes and spherical nodes are the same, and angular and planar nodes are the same. Reference Finally, how many spherical nodes are there in ...
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What to do with (large) imaginary frequencies for constrained minimum structures?

I am performing DFT calculations using ORCA 4.0.1 on an enzyme active site model. The model contains 89 atoms including the substrate (see Animation 1), five of which are fixed in space (the spherical ...
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Naming of quantum chemistry basis sets

For some DFT calculations I performed with localized (Gaussian) basis sets, I wonder how the basis sets I used are properly named. The names I could gather are: H, C and O: 6-311G(d,p) Al: 8-511G* ...
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How to Calculate Transition Dipole Moment from Two Known Wavefunctions

I am interested in calculating the transition dipole moment (TDM) from the information from two wavefunctions of different states. This is somewhat similar to calculating the molecular dipole moment ...
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After a unitary transformation, is Koopmans' theorem still valid?

Koopmans' theorem says that the energy of the HOMO of the Hartree-Fock orbitals is equal to the first ionization energy of whatever system is being studied. This is only approximate because it assumes ...
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Restricted open-shell versus unrestricted methods for open shell systems

Open-Shell systems (radicals and so on) can be modeled by single-determinant quantum chemical methods using unrestricted (u) or restricted open-shell (ro) methods (I am aware that single-determinant ...
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What do short-range and long-range corrections mean in DFT methods?

Currently I am looking for the most accurate calculation method for a simple non-conjugate molecule consist of C, N, O and H. Normally I would try each method for a similar and known molecule then ...
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Why do electrons jump back after absorbing energy and moving to a higher energy level?

Electrons in a shell absorb energy and move to higher energy levels, but they release their energy and jump back to the shell they originally were in. Why do they jump back? Why can they not keep ...
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Shape of a wavefunction

I am trying to plotting the angular parts of a wavefunction ($Y_{(m,l)}(\theta, \phi)$) with Wolfram Mathematica. this is the table of spherical harmonics. I think the shape of these function should ...
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Molecular orbital diagram and irreducible representations for dinitrogen

I'm trying to understand how to draw molecular orbital diagrams, since I'd like to use the molecular orbitals to determine the total state of the molecule (i.e. $A_1$, $B_1$ etc.), so I prefer the ...
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1answer
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Is Orca wrongly breaking bonds? Why can it only optimize the molecule with COPT activated?

I would like to ask for help in using Orca (v. 4.0.0) for conducting a simple optimization. First I have this structure (primarily optimized using MMFF94s force field on Avogadro): Thus I tried to ...
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Calculated 13C NMR Shifts of brominated Carbons

Since I calculate NMR spectra for a while by simply using one of recommendations by CHEmical SHIft REpository: mPW1PW91/6-311+G(2d,p)-SCRF//B3LYP/6-31+G(d,p) ...
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Why are the total energies of transition states so commonly corrected for zero-point vibrational energy?

So often I see total energies of transition states corrected for zero-point vibrational energy which always confuses me. Zero point energy is the lowest energy that a ground state minimum energy ...
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Should chemistry students worry about quarks and such? [closed]

Even chemistry textbooks less than five years old start by describing atomic structure based only on protons, neutrons and electrons. Is an understanding of chemistry fundamentals likely to become out ...
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Help with derivation on why antibonding orbitals are more antibonding

I have read How can antibonding orbitals be more antibonding than bonding orbitals are bonding?. But I am intersted in a specific derivation. During lecture my professor stated that the overlap $S_{ij}...
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Analysis of post-HF wavefunctions

Hartree-Fock method introduces electron (spin)orbitals and they are commonly used for qualitative rationalization of many molecular properties. However, MOs have meaning only if we ignore electron ...
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What is a “hydrogen-like” or “hydrogenic” atom?

I'm studying some chemistry on my own in anticipation for the new school year and in my book, I came across the Rydberg equation for the first time. I worked through some examples and everything was ...
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Is coupled cluster variational for two electrons?

I know that coupled cluster (CC) is not variational for the general case. However, if we only have two electrons with one nucleus, CCSD should be exact for this system like full configuration ...
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Relationship between the symmetry number of a molecule as used in rotational spectroscopy and point group

While doing a problem set I noticed that the symmetry number of a molecule turns out (usually) to be half the number of symmetry elements that the point group the molecule belongs to. When I say ...
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Is HF the only method for trying to solve the many-electron Schrödinger equation?

The Schrödinger equation can only be solved analytically for the smallest of "molecular" systems. The Hartree-Fock method is a method of obtaining approximate solutions to the many-electron ...

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