I have the following problem at hand Ψ= -sqrt(At) + icos(xt)/4 This is the wave function for a skinless, non relativistic particle moving in 1 dimension. It is observed that the particle never goes more than a distance of π units away from a fixed point. What is, then, the maximum valu...

According to Bohr's quantum theory, energy is directly proportional to the quantum number, meaning higher quantum numbers correspond to higher energy levels. Since shells contain subshells, it would seem logical for 4s to have higher energy than 3d. However, the Aufbau principle states that 3d ha...

I need to draw a molecular energy orbital diagram for $\ce{SnCl2}$. I know I need to consider the point group which is $C_{2v}$ and find the symmetries for the orbitals. I just can't figure out how to actually draw the diagram and add in electrons. The symmetry labels I figured out so far are: Sn...

I am studying the symmetry orbitals combining the 1s orbitals of Hydrogen in 2 different configurations I dont understand how to obtain the values of the reducible representation for these orbitals. The picture shows the character table with values of -2/3 and -1/3. How are these values obtained?

So, hybridisation theory says "Atomic orbitals of same elements combine to form hybrid orbitals andit is involved in bonding with other elements ". Now MOT says "atomic orbitals of different elements combine to form bonds" Both are used to understand bonding, so i wondered if both could co-exi...

I was just learning about complex ions in my chemistry course. We further learnt about the factors that lead to the crystal field energy splitting of the d orbitals. One of which is orbital overlap (Source). I further know that the shape of atomic orbitals change in an applied magnetic field due ...

I ran some vertical excitation energy calculations, and I'm a little confused about the results. Would someone be able to help me to understand? Here are my results: I'm trying to understand the significance of the numbers associated with the orbitals in the following text: Excited State 7: 149 ->...

I am a new computational chemistry student currently running calculations to generate orbitals. However, I am finding it challenging to identify the types of orbitals I have. I would appreciate any advice you have, and I welcome anyone who can help me with this. I have run a calculation for the f...

It is found that for all the elements succeeding calcium the energy of 3d is less than the energy of 4s, I have heard this effect being termed as 'd-wavefunction collapse' here but I didn't understand it being explained as "the result of the interplay of nuclear attraction, of imperfect shielding...

1)In the above attached image it is observed that the energy of any orbital decreases and the atomic number increases, what is the main reason behind this? Is it due to an increase in nuclear charge? 2)Also it is found that for all the elements succeeding Calcium the energy if 3d is less than t...

During my study of atomic orbitals I found myself asking this question alot but I never received a satisfactory response. I have observed that except for p orbitals the subscripts of orbitals represent the nodes of the orbitals. But then I ran into a problem in the form of dz^2 and fz^3 orbitals....

I keep stumbling across the idea that electrons closer to the nucleus shield the nuclear charge that valence electrons feel (zeff). I'm a bit confused though by what this "shielding" means. How can electrons closer to the nucleus diminish the attraction that valence electrons "feel"? I was told t...

"Crystal Field Splitting Energy increases significantly down a group because of size of metal d-orbitals which increases the repulsion to Ligand-electrons" - ppt for topic on d-orbitals at uni. Referring specifically to these effects: (crystal field splitting energy on the right given in units o...

When atoms forms bond with other atoms , their orbitals take such forms that the overlap is maximum . These forms are linear combinations of orbitals . While not in any bonding , the electron can be in any form but while bonding , the form is such that they are equivalent in orientation and it's ...

What is the ground state molecular term symbol for $\ce{HF}$? My attempt went like this: I drew the molecular orbital diagram and found that in the ground state, the highest energy MOs were two degenerate orbitals with 2 electrons each. Since there are no unpaired electrons, the term symbol assig...

I am a high-school student learning about hybridisation. From sp to sp3d2/d2sp3 (for coordination compounds), each type of hybridisation includes 's'-orbital. My teacher says it's because the 's'-orbital provides for the orientation or spatial arrangement of the hybridised orbitals at angles for ...

A hydrogen like atom (Atomic No.Z) is in a higher excited state of quantum number n. This excited atom can make a transition to the first excited state by successively emitting 2 photons of energies 10.200eV and 17.00eV respectively. Alternatively, the atom from the same excited state can make a ...

Suppose there is an electron with the second lowest energy eigenvalue or in second energy level of hydrogen atom . The probability density of the finding the electron will not be same at all directions but it will be more in certain directions . It will be maximum at the direction of the alignmen...

My textbook just shows the higher energy bonding and antibonding orbitals, and starts naming them from 1sigma(u), I don't think this is correct and it's really confusing me. I want to know what can I write if a question asks me to write the electronic configuration for something like O2 using ger...

Why does the linear combination of atomic orbitals (LCAO), which is determined based on the symmetry of a molecular in its ground state atomic structure, remains valid considering that the molecule is constantly vibrating? As a molecule is constantly vibrating under different modes, its atomic st...

I am trying to calculate theoretical electron momentum profiles (TMP) of individual orbitals of a molecule using Gaussian16 for theoretical calculation of electron momentum spectroscopy. I there a way to do it using Gaussian?

The octahedral point group contains the irreducible representations T2g and Eg, which correspond to the triply degenerate and doubly degenerate irreps which are symmetric with respect to a centre of inversion. These irreps give the labels to the molecular orbitals formed in octahedral coordinatio...

I'm trying to understand more about orbitals and term symbols from the book Orbitals, Terms and States by Malcolm Gerloch. In chapter 2, section 2.3, page 18, of the book the author writes as follows : a measurement of the $x$ co-ordinate of a particle manifests the particle in an eigenstate-sa...

How do valence bond theory and molecular orbital theory describe the same wavefunction despite one having localized electrons in a bond overlap and one having wave superimposition forming delocalized molecular orbitals. Some explain it using the fact VBT measures wavefunction of different resonan...

As far as I know, the configuration-interaction scheme is simple. It simply expand the many-electron eigenstate with respect to a basis, which is often a set of Slater determinants built of some orthonormal single-particle orbitals. The problem is, while in principle, one has to take a complete s...

If I understand correctly, LCAO states that the molecular orbitals in Born-Oppenheimer can be written as a linear combination of Atomic Orbitals for single nuclei. The coefficients in the sum can be calculated through a minimization algorithm, such as Hartree-Fock. In examples I see online, this ...

can anyone tell why in H atom degeneracy is same although there is a single electron already filled in 1s what is need for other subshell what is need for 2s 2p Please don't delete this question as I haven't found it anywhere

Is there any QC program which in calculation of NMR, magnetizabilities or other magnetic response properties at DFT level allows to print overlap matrix of the perturbation-dependent atomic orbitals S(B)? I found that Dalton, Psi4, and PySCF can print the first order overlap matrix dS(B) / dB, th...

In Crystal Field Theory, for a tetrahedral (metallic) complex, shouldn't the $d_{z^2}$ and the $d_{x^2 - y^2}$ have different energies, since the repulsion between one lobe and ligands happens $2$ times in the $d_{z^2}$ orbital and $4$ times in the $d_{x^2 - y^2}$ ? If we were to note down the am...

As we know that when a ligand approaches the transition metals, the d-orbital loses its degeneracy and in this case electron can jump from lower orbitals to higher orbitals adsorbing the visible light. Till this I am very clear. My question is if the energy gap is constant, when the electron retu...

From crystal field theory, the splitting of the degenerate $d$ orbitals gives the opportunity for electrons to be promoted, and therefore absorb some light. The colour of the complex is then determined by the light that is not absorbed. However, this doesn't make much sense to me. In physics, whe...

We all know that an orbital only has two electrons of opposite spin. Why can't orbital holds more than two electrons. Case 1 : It is defined that if an orbital has two electrons of opposite spin then the orbital is stable. Electrons of opposite spin Case 2 : If an orbital has three electrons of ...

When I was reading about the hydrogen spectrum , I came across the statement; Only Balmer series of hydrogen spectrum can be visible to our eyes. I really got surprised how only Balmer series can be visible to our eyes. However I can agree this because of the abundance of hydrogen in the univer...

I have been studying quantum mechanics recently and I have come across this: d orbitals oriented along the $z^2$ axis is assigned zero magnetic quantum number I am wondering why specifically the $dz^2$ orbital has zero magnetic number. I am thinking if this is just randomly chosen for reference...

What are the consequences of overlapping orbitals (with electrons with different quantum numbers other than spin) in the same atom? Why don't we draw the resulting orbital, taking into account the effect of the other, to better understand the chemical behavior?

Is there any coherent visual diagram that might explain how orbitals and subshells co exist in the same shell? I'm unable to find any online, except for those which indicate only orbitals as dense electron clouds, but not 'what' specifically a subshell is and I feel I'll only be able to understan...

In MIT $5.111$ class (lecture $6$), we are to compare the most probable radius of a $2s$ orbital and a $2p$ orbital. The graph used by the professor represents the RPD versus $r$: My question is: in the second figure, are we talking about the RPD along the z-axis (i.e. across a $2p_z$ orbital) o...

I am interested in diagonalising the fermionic Hamiltonian of small molecules, such as LiH in second quantisation. The Hamiltonian is \begin{align} H(R) = \sum_{ij} h_{ij}(R) a_i^\dagger a_j + \frac{1}{2} \sum_{ijkl} h_{ijkl}(R) a_i^\dagger a_j^\dagger a_k a_l \end{align} as usual [1]. Using the ...

While studying the graph I often find that some of the orbitals namely 3s, 2s,......3p have RDF plots on radius less than their peak. Assuming probability of finding an e- is everywhere (except nucleus) why don't small peaks come after the main peak with the curve just tending towards infinity

"However, accurate quantum-mechanical calculations (starting in the 1970s)... singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract and electron–nucleus attraction energy becomes greater in magnitude (or decreases algebraically)." http...

In square planar complexes, the d$_{x^2-y^2}$ occupies the highest energy level due to it interacting greatest with the ligands. The d$_{z^2}$ orbital is also raised slightly higher in energy than the d$_{xz}$ and d$_{yz}$ orbitals as the toroid can interact slightly with the ligands Why is the d...

A. Slater-type orbital is B. Gaussian-type orbital is C. A contracted Gaussian-type orbital is D. In quantum chemistry, the basis set usually refers to the set of (nonorthogonal) one-particle function used to build molecular orbitals

I am curious about crystal field effects on a given atom by analysing $m_l$ projected DOS, the individual d-orbitals are given with respect to the Cartesian coordinates (not the lattice constants). So if you have, say an octahedrally coordinated transition metal, we may need to rotate the cell su...

(Sorry, in advance if my question is silly or low quality but I want to ask this to someone.) When an electron enters an orbital, it should technically have an electric Field and also magnetic field(Moving charge), so shouldn't orbitals once partially or fully filled lose degeneracy? Also, why ar...

It is my understanding that $\ce{H2O}$ acts as a strong ligand for $\ce{Fe^3+}$ (along with $\ce{Cr^3+}$ and $\ce{Co^3+}$) so should the electrons not pair up in the $t_{2g}$ orbitals? Wouldn't that cause a magnetic moment of $\pu{\sqrt{3} BM}$ and not $\pu{\sqrt{35} BM}$?

What makes 1p, 1d, and 1f orbitals impossible in an atom? My teacher said that the number of angular node will become -1 By the formula n-l-1= number of nodes

I came across the term "low-lying orbital" in my readings on chemistry, but I'm unclear on its precise definition and significance. Could someone explain what qualifies an orbital as "low-lying"? My thought is that these would be non-valence electrons that are shielded by outer orbitals. How do l...

This is the information about basis functions which I am getting on doing Gaussian calculation. But according to the best of my knowledge Kr has six primitive Gaussians for 1s, 2s,2p, 3s, and 3p orbitals, and a split-valence pair of three and one primitives for valence orbitals, which are 4s, 4p,...

When I define a molecule with qiskit's PyscfDriver, it has a certain number of (spatial) orbitals. In this example, I define a NaH molecule and get an object with 10 spatial orbitals. I would like to reduce this number by reducing some orbitals from the active space. I intend to the FreezeCoreTr...

In Platinum $\text{Pt}$, why do $\text{s}$ and $\text{p}$ orbitals contract when electrons start travelling at relativistic speeds $|v|\sim c$, while $\text{d}$ and $\text{f}$ orbitals expand? The way I reasoned about this is that due to relativistic effects, relativistic mass of an electron incr...