Diagrammatic analysis of nonlinear response properties in time-dependent Hartree–Fock theory

1992 ◽  
Vol 70 (2) ◽  
pp. 677-685 ◽  
Author(s):  
Hideo Sekino
Keyword(s):  
Lower Order ◽  
Nonlinear Response ◽  
Time Dependent ◽  
Response Property ◽  
Coupling Term ◽  
Response Properties ◽  
First Order ◽  
Hartree Fock ◽  
Quadratic Response ◽  
Diagrammatic Analysis

Nonlinear response properties in Time-Dependent Hartree–Fock (TDHF) theory are analyzed by diagrammatic techniques and compared with the expression in propagator theory. The term that ensures that the quadratic response function is correct through first order in electron correlation emerges in the coupling term between lower order TDHF amplitudes and causes a violation of particle–hole pair conservation. It is shown diagrammatically that the dynamic hyperpolarizabilities can be expressed by lower order solutions in accordance with the 2n + 1 rule. Keywords: nonlinear response property, TDHF, diagrammatic

A First Principles Approach for Partitioning Linear Response Properties into Additive and Cooperative Contributions

2018 ◽  
Author(s):  
Daniel Lambrecht ◽  
Eric Berquist
Keyword(s):  
First Principles ◽  
Linear Response ◽  
Building Blocks ◽  
Field Method ◽  
Response Property ◽  
Response Properties ◽  
Consistent Field ◽  
Molecular Building Blocks ◽  
Self Consistent ◽  
Self Consistent Field

We present a first principles approach for decomposing molecular linear response properties into orthogonal (additive) plus non-orthogonal/cooperative contributions. This approach enables one to 1) identify the contributions of molecular building blocks like functional groups or monomer units to a given response property and 2) quantify cooperativity between these contributions. In analogy to the self consistent field method for molecular interactions, SCF(MI), we term our approach LR(MI). The theory, implementation and pilot data are described in detail in the manuscript and supporting information.

MODELLING NITROGEN PROCESSES IN SOIL: MATHEMATICAL DEVELOPMENT AND RELATIONSHIPS

1976 ◽  
Vol 56 (2) ◽  
pp. 71-78 ◽  
Author(s):  
D. R. CAMERON ◽  
C. G. KOWALENKO
Keyword(s):  
Time Dependent ◽  
Rate Coefficients ◽  
Nitrification Rate ◽  
Order Kinetic ◽  
Nitrogen Flow ◽  
First Order ◽  
Interaction Term ◽  
Flow Pathways ◽  
Adsorption Desorption ◽  
Temperature Water

A small subsystem model was developed to simulate the major nitrogen flow pathways in an unsaturated soil treated with ammonium sulphate. A nonlinear Freundlich equilibrium model and a Langmuir kinetic model were used to describe mathematically the adsorption–desorption of soluble NH4+ to the exchangeable and clay-fixed phases, respectively. Time dependent, microbial mediated first-order kinetic models were used to quantify the ammonification and nitrification processes. The subsystem model was then used as a research tool to derive ammonification and nitrification rate coefficients for a preceding incubation experiment conducted using different soil moisture contents and temperatures. The model yields reasonably good fits to the observed data. A subsequent regression analysis relating the coefficients to temperature and moisture pointed out the importance of the temperature–water content interaction term in quantifying microbial mediated processes.

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