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Newman Projections02:06

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Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
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Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.
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Related Experiment Video

Updated: Oct 19, 2025

Spatial Separation of Molecular Conformers and Clusters
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Fixed- and Partial-Node Approximations in Slater Determinant Space for Molecules.

Nick S Blunt1,2

  • 1Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, U.K.

Journal of Chemical Theory and Computation
|September 22, 2021
PubMed
Summary

Fixed-node approximations in full configuration interaction quantum Monte Carlo (FCIQMC) offer an accurate and practical method for ab initio molecular systems. Partial-node approximations are limited by large walker populations, while fixed-node FCIQMC is efficient for large active spaces.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Materials science

Background:

  • Slater determinant basis sets are crucial for electronic structure calculations.
  • Full configuration interaction quantum Monte Carlo (FCIQMC) is a powerful but computationally intensive method.
  • Nodal constraints in quantum Monte Carlo simulations can impact accuracy.

Purpose of the Study:

  • To investigate the performance of fixed- and partial-node approximations in FCIQMC.
  • To evaluate these methods for ab initio molecular systems using symmetry-projected Jastrow mean-field wave functions.
  • To assess the efficiency and accuracy for complete active space (CAS) problems.

Main Methods:

  • Utilized full configuration interaction quantum Monte Carlo (FCIQMC) for sampling.
  • Employed walker annihilation to enable partial-node simulations.
  • Applied symmetry-projected Jastrow mean-field wave functions for CAS problems.
  • Tested fixed-node and partial-node approximations on molecular systems like ferrocene and acenes.

Main Results:

  • Partial-node approximations face limitations due to large walker populations and the sign problem.
  • The fixed-node approximation provides an accurate and practical computational method.
  • Scaling analysis shows fixed-node FCIQMC is efficient for CAS problems, with specific scaling for trans-polyacetylene and acenes.
  • Validated symmetry-projected Jastrow mean-field wave functions in variational Monte Carlo for new applications.

Conclusions:

  • Fixed-node FCIQMC is a reliable and efficient approach for studying molecular systems.
  • Partial-node methods, while offering convergence, are constrained by computational demands.
  • The study demonstrates the applicability of these quantum Monte Carlo methods to large active space problems in computational chemistry.