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Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of...
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Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
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Random Sampling Method01:09

Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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Dynamic Correlation on the Adaptive Sampling Configuration Interaction (ASCI) Reference Function: ASCI-DSRG-MRPT2.

Jae Woo Park1

  • 1Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea.

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|August 23, 2023
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Summary
This summary is machine-generated.

This study introduces adaptive sampling configuration interaction self-consistent field (ASCI-SCF) with second-order perturbation theory (PT2) for accurate quantum chemistry. The new ASCI-DSRG-MRPT2 method efficiently captures dynamic electron correlations in challenging systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate quantum chemical methods require balancing static and dynamic electron correlations.
  • Strongly correlated systems necessitate large active spaces for static correlation and corrections for dynamic correlation.

Purpose of the Study:

  • To implement and evaluate second-order perturbation theory for dynamic correlations based on the adaptive sampling configuration interaction self-consistent field (ASCI-SCF) method.
  • To introduce spin-free driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2) within the ASCI framework.

Main Methods:

  • Implementation of spin-free DSRG-MRPT2.
  • Extrapolation of ASCI + PT2 energy using a relaxed Hamiltonian.
  • Application of the ASCI-DSRG-MRPT2 method to various chemical systems.

Main Results:

  • The ASCI + PT2 energy extrapolation approximates DSRG-MRPT2 based on CASSCF.
  • Accurate calculations of spin-state energy gaps in iron porphyrins, polyacenes, and periacenes.
  • Accurate calculations of reaction energies for methane oxidation by FeO+ and cethrene electrocyclic ring formation.

Conclusions:

  • The developed ASCI-DSRG-MRPT2 method provides an accurate and efficient approach for describing dynamic electron correlations.
  • This method is suitable for studying strongly correlated systems and complex chemical reactions.