Calculation of a bound state wavefunction using free state wavefunctions only

1975 ◽  
Vol 43 (2) ◽  
pp. 173-176 ◽  
Author(s):  
K. R. Brownstein
Keyword(s):  
Bound State ◽  
Free State ◽  
State Wavefunctions

scholarly journals Continuous absorption

1930 ◽  
Vol 229 (670-680) ◽  
pp. 163-204 ◽  
Keyword(s):  
Absorption Coefficient ◽  
Bound State ◽  
Free State ◽  
X Rays ◽  
Classical Electromagnetism ◽  
Considerable Difficulty ◽  
Positive Nucleus ◽  
Continuous Absorption ◽  
The Matrix ◽  
Good Agreement

For some years astrophysicists have been looking for an adequate theory of continuous—as opposed to line—absorption. The natural and generally accepted mechanism is the transition of an electron from a bound state to a free state, or from one free state in the neighbourhood of an ion to another free state of greater energy. The theory hitherto used is KRAMERS’ theory of the converse process of emission by a free electron passing a positive nucleus. Since emission and absorption are intimately connected by thermodynamics, the absorption coefficient can be calculated from KRAMERS’ formulae. Unfortunately, although KRAMERS’ work is in good agreement with laboratory observations of X-rays, it gives an absorption coefficient many times smaller than that found from astronomical observations. KRAMERS used classical electromagnetism, and got over the difficulty of the quantisation of negative energies by distributing the classical emission that involved captures somewhat arbitrarily among the various stationary states. It was evidently desirable to do the same work by means of quantum theory, both for the sake of greater rigour, and in the hope of finding a larger absorption. The foundations of such a theory were laid by OPPENHEIMER,|| upon the bed-rock of SCHRODINGER’s equation, in a paper to which this one is much indebted. The matrix-elements involving positive energies present considerable difficulty, and the approximations used by OPPENHEIMER in his paper of 1927 are unsuitable for stellar applications.

Semiclassical results on normalization of bound state wavefunctions

1980 ◽  
Vol 21 (7) ◽  
pp. 1688-1694 ◽  
Author(s):  
Peter Moxhay ◽  
Jonathan L. Rosner
Keyword(s):  
Bound State ◽  
State Wavefunctions

scholarly journals Application of the Movable Type Free Energy Method to the Caspase-Inhibitor BindingAffinity Study

2019 ◽  
Vol 20 (19) ◽  
pp. 4850
Author(s):  
Xue ◽  
Liu ◽  
Zheng
Keyword(s):  
Free Energy ◽  
Energy Method ◽  
Structural Changes ◽  
Binding Free Energy ◽  
Bound State ◽  
Free State ◽  
Caspase Inhibitor ◽  
Caspase Inhibition ◽  
Test Sets ◽  
Inhibitor Interaction

Many studies have provided evidence suggesting that caspases not only contribute to the neurodegeneration associated with Alzheimer’s disease (AD) but also play essential roles in promoting the underlying pathology of this disease. Studies regarding the caspase inhibition draw researchers’ attention through time due to its therapeutic value in the treatment of AD. In this work, we apply the “Movable Type” (MT) free energy method, a Monte Carlo sampling method extrapolating the binding free energy by simulating the partition functions for both free-state and bound-state protein and ligand configurations, to the caspase-inhibitor binding affinity study. Two test benchmarks are introduced to examine the robustness and sensitivity of the MT method concerning the caspase inhibition complexing. The first benchmark employs a large-scale test set including more than a hundred active inhibitors binding to caspase-3. The second benchmark includes several smaller test sets studying the relative binding free energy differences for minor structural changes at the caspase-inhibitor interaction interfaces. Calculation results show that the RMS errors for all test sets are below 1.5 kcal/mol compared to the experimental binding affinity values, demonstrating good performance in simulating the caspase-inhibitor complexing. For better understanding the protein-ligand interaction mechanism, we then take a closer look at the global minimum binding modes and free-state ligand conformations to study two pairs of caspase-inhibitor complexes with (1) different caspase targets binding to the same inhibitor, and (2) different polypeptide inhibitors targeting the same caspase target. By comparing the contact maps at the binding site of different complexes, we revealed how small structural changes affect the caspase-inhibitor interaction energies. Overall, this work provides a new free energy approach for studying the caspase inhibition, with structural insight revealed for both free-state and bound-state molecular configurations.

Molecular Crowding Stabilizes Both the Intrinsically Disordered Calcium-Free State and the Folded Calcium-Bound State of a Repeat in Toxin (RTX) Protein

2013 ◽  
Vol 135 (32) ◽  
pp. 11929-11934 ◽  
Author(s):  
Ana-Cristina Sotomayor-Pérez ◽  
Orso Subrini ◽  
Audrey Hessel ◽  
Daniel Ladant ◽  
Alexandre Chenal
Keyword(s):  
Bound State ◽  
Free State ◽  
Molecular Crowding ◽  
Intrinsically Disordered
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