Properties higher-order

Frequency-dependent higher-order properties can now by obtained as derivatives of the time-average of the quasienergy WIt- with respect... 

This raises a dilemma in treating second- and higher-order properties in coupled-cluster theory. In the EOM-CC approach, which is basically a Cl calculation for a non-Hermitian Hamiltonian H= that incorporates... 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

In short, to calculate first-order properties for a fully variational wave function, we need not evaluate the response of the wave function dX/dx. This is an extremely important result, which forms the basis for all computational techniques developed for the evaluation of molecular gradients (as well as for all higher-order properties). 

Frequency-dependent higher-order properties can now be obtained as derivatives of the real part of the time-average of the quasi-energy W j- with respect to the field strengths of the external perturbations. To derive computational efficient expressions for the derivatives of the coupled cluster quasi-energy, which obey the 2n-(-1- and 2n-(-2-rules of variational perturbation theory [44, 45, 93], the (quasi-) energy is combined with the cluster equations to a Lagrangian ... 

The approach outlined above combines the calculation of response functions (i.e. of frequency-dependent properties) with the theory of analytic derivatives developed for static higher-order properties. In the limit of a static perturbation all equations above reduce to the usual equations for (unrelaxed) coupled cluster energy derivatives. This is an invaluable advantage for the implementation of frequency-dependent properties in quantum chemistry programs. 

The situation is somewhat different for the convergence with the wavefunction model, i.e. the treatment of electron correlation. As an anisotropic and nonlinear property the first dipole hyperpolarizability is considerably more sensitive to the correlation treatment than linear dipole polarizabilities. Uncorrelated methods like HF-SCF or CCS yield for /3 results which are for small molecules at most qualitatively correct. Also CC2 is for higher-order properties not accurate enough to allow for detailed quantitative studies. Thus the CCSD model is the lowest level which provides a consistent and accurate treatment of dynamic electron correlation effects for frequency-dependent properties. With the CC3 model which also includes the effects of connected triples the electronic structure problem for j8 seems to be solved with an accuracy that surpasses that of the latest experiments (vide infra). 

But movement from order to order does not - indeed, cannot - bring new causal powers into existence. Movement to a higher-order property. 

Conclusion the causal exclusion problem aflfects only higher-t rt/cr properties, not higher-Zefc/ properties. Insofar as the proprietary properties of chemistry, biology, and other special sciences concern objects at higher levels of mereological a regation than do the objects of elementary physics, those properties are safe. As for the higher-order properties, the choice remains stark reduction or elimination. ... 

The implication is that there really is no contrast between the higher-order properties of geology and biology, on the one hand, and the higher-order properties of psychology, on the other. There is only a reluctance to accept the reducibility of the mental. This is a reluctance nursed by contemporary... 

In earlier work. I ve advocated a radical response to the exclusion argument in the case of multiply realizable properties embrace the disjunctive solution.This is the move that identifies — and thereby economically reduces - the multiply realizable, higher-order property with the disjunctive property formed by taking the alternation of all first-order (total) realizer properties. If I can persuade you that some disjunctive properties are nomic, then I ll have a solution to the incoherence problem. And if I can provide some plausible principles to distinguish objectively nomic from objectively nonnomic disjunctive properties, then I ll have a solution to the conventionality objection as well. 

This is in fact the view Jaegwon Kim has advanced in several places about instances of second-order properties and instances of their first-order realizers.As Kim has noted, such an identification requires a revision of his property-exemplification account of events assuming that mental properties are second-order properties, it requires the exclusion of mental properties as constitutive properties of events. This instance-identity thesis is supposed to support reductionism about the mental. But there is a tension between this thesis and Kim s formulation in several places of his causal inheritance principle, which says that the causal powers of an instance of a higher-order property are identical with or are a subset of [emphasis mine] the causal powers of the instance of its realizer. Clearly, if the causal powers of the realized property instance were... 

In speaking of functional properties as higher-order properties, I do not mean to be endorsing the view that these are properties defined by quantification over first-order properties. I mean simply that they are properties that are instantiated in virtue of other properties - property realizers of them — being instantiated. 

I think that the subset version of the causal inheritance principle is clearly preferable to the version that says that the causal powers of the realized property instance are identical with the causal powers of the realizer instance, so I think that the instance-identity thesis is false. We can make sense of the idea of an instance of a higher-order property having a realizer different from the realizer of the instance of its determinate or property realizer if we can make sense of the idea of the higher-order property instances having cores that are distinct from the cores of the realizers of the instances of their determinates or physical property realizers. And 1 think we can do this. 

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