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Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
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Electric Potential Energy in a Uniform Electric Field01:09

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When an electric field accelerates a free positive charge, it acquires kinetic energy. This process is analogous to an object being accelerated by a gravitational field as if the charge were going down an electrical hill where its electric potential energy is converted into kinetic energy, although, of course, the sources of the forces are very different. The electrostatic or Coulomb force acting on the positive test charge is conservative, which means that the work done on a test charge is...
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The electric potential energy of a test charge in a uniform eclectic field can be generalized to any electric field produced by static charge distribution. Consider a positive test charge in an electric field produced by another static positive charge. If the test charge is moved away from the static charge, then the electric field does the positive work on the test charge, and the electric potential energy of the test charge decreases as it moves away from the static charge. Here the electric...
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The Electrical Double Layer01:30

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In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...
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The principle of power preservation is applicable to both ac and dc circuits. This principle, when applied to AC power, asserts that the complex, real, and reactive powers produced by the source are equal to the total complex, real, and reactive powers absorbed by the loads. When two load impedances are connected in parallel to an ac source V, the complex power provided by the source can be calculated using the relation
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Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
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Extended Energy Divide-and-Conquer Method Based on Charge Conservation.

Guo-Liang Song1, Zhen Hua Li1, Kang-Nian Fan1

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Charge transfer errors in large quantum system calculations are reduced by a new method. The energy-based divide-and-conquer (EDC) method with charge conservation (E-EDC) improves total energy accuracy by 40-70%.

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Area of Science:

  • Quantum Mechanics
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • The divide-and-conquer (DC) scheme is a popular linear-scaling method for quantum mechanics computations of large systems.
  • DC methods often break covalent bonds, requiring capping with complementary atoms/groups, which can introduce errors.
  • Charge transfer between subsystems and capping groups is a primary source of error in computed total energies.

Purpose of the Study:

  • To address the charge conservation issue in divide-and-conquer methods.
  • To propose an extension of the many-body expansion method that incorporates charge conservation.
  • To improve the accuracy of total energy calculations in large chemical systems.

Main Methods:

  • An energy-based divide-and-conquer (EDC) method utilizing charge conservation (E-EDC) was developed.
  • The method computes total energies at various many-body correction levels using the EDC scheme.
  • Total charges are computed for subsystems without cap atoms, and total energy is extrapolated to conserve net charge.

Main Results:

  • The proposed E-EDC scheme significantly reduces total energy errors in quantum mechanics computations.
  • Tests on glycine oligomers showed a 40-70% reduction in total energy error.
  • The computational cost of the E-EDC method is comparable to the original EDC scheme.

Conclusions:

  • The E-EDC method effectively corrects for charge transfer errors in divide-and-conquer calculations.
  • This approach enhances the accuracy of total energy and other properties like atomic forces.
  • The E-EDC method offers a more reliable approach for large-scale quantum mechanical simulations.