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I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that isthat is, these values are observables, simply. Simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but for practical purposes they can't really be separated from them either.

I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that is these values are observables, simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but for practical purposes they can't really be separated from them either.

I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that is, these values are observables. Simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but for practical purposes they can't really be separated from them either.

2 added 23 characters in body
source | link

I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that is these values are observables, simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but for practical purposes they can't really be separated from them either.

I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that is these values are observables, simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but they can't really be separated from them either.

I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that is these values are observables, simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but for practical purposes they can't really be separated from them either.

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source | link

I think the answer of Stefano Borini, in its well-meaning zeal to correctly dispel some of the misconceptions surrounding the concept of electron orbitals especially in Chemistry, is itself quite reductionist and somewhat misleading.

The importance of (valence) atomic and molecular orbitals in Quantum Chemistry (bond theory, essentially) is that they show the electron probability density of the atoms/molecules in space. Take this wonderful (but also deceptive) rendition of the three $\text{2p}$ hydrogen orbitals:

2p hydrogen orbitals

(Source.)

The shiny surfaces are iso-(electron) probability surfaces: that is these values are observables, simply put: $P(R)$ values calculated from the Schrödinger equation's eigenfunctions. Parity is represented by colour.

Or take this ORCA generated molecular orbital rendition of benzene ($\mathrm{C_6H_6}$), again the surfaces are iso-(electron) probability surfaces:

Benzene electron density.

(Source: Chemistry SE).

These very Real values allow chemists to determine which chemical bonds are broken and which are formed during chemical reactions.

It's true that these calculated iso-probabilities should not be equated with the orbitals but they can't really be separated from them either.