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The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than...
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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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Response properties from frozen-density embedding approximate second-order coupled-cluster theory.

Niklas Niemeyer1, Johannes Neugebauer1

  • 1University of Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Corrensstraße 36, 48149 Münster, Germany.

The Journal of Chemical Physics
|May 2, 2025
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Summary

We developed a new computational method, coupled frozen-density embedding (FDEc), to accurately calculate molecular properties. This approach improves upon existing methods for studying complex systems like excitonically coupled dimers and solvated molecules.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Theoretical chemistry

Background:

  • Accurate calculation of molecular properties is crucial for understanding chemical phenomena.
  • Existing methods like coupled cluster with singles and approximate doubles (CC2) and frozen-density embedding (FDE) have limitations for complex systems.
  • There is a need for robust computational frameworks that can handle system-environment interactions.

Purpose of the Study:

  • To implement and validate the coupled frozen-density embedding (FDEc) formalism for calculating ground-state and excited-state properties.
  • To extend the FDEc method to linear-response properties and transition moments using the CC2 model.
  • To provide an open-source implementation of FDEc within the Serenity quantum chemistry program.

Main Methods:

  • Implementation of the FDEc formalism using projection-based embedding and non-additive kinetic-energy functionals.
  • Utilized the resolution-of-the-identity technique for computational efficiency.
  • Incorporated CC2, algebraic diagrammatic construction scheme of second order (ADC(2)), and their scaled variants.

Main Results:

  • Successfully calculated excitation energies, energy splittings, and oscillator strengths for excitonically coupled dimers.
  • Determined excited-state/difference dipole moments for a formaldehyde-water system.
  • Accurately computed optical rotatory dispersion for a microsolvated organic chromophore, resolving limitations of uncoupled methods.

Conclusions:

  • The FDEc framework accurately captures inter-subsystem couplings essential for response property calculations.
  • This implementation provides a powerful tool for studying molecular aggregates and solvated systems.
  • The results highlight the importance of including system-environment response couplings for accurate predictions.