Scientists crack the code for predicting how materials bend under pressure
Physicists have developed a new mathematical framework that predicts how quantum materials respond to extreme forces—a capability that could accelerate design of everything from semiconductors to energy storage devices. The breakthrough fills a 40-year gap in density functional theory, the workhorse tool that industries rely on to screen new materials before expensive lab testing.
Originaltitel: Generalized density functional theory framework for the nonlinear density response of quantum many-body systems
A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to nonlinear static density response functions in quantum many-body systems. Within this framework, explicit expressions are derived for various higher-order response functions of systems that are homogeneous on average, including the first theoretical result for the cubic response at the first harmonic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msubsup> <a:mi>χ</a:mi> <a:mn>0</a:mn> <a:mrow> <a:mo>(</a:mo> <a:mn>1</a:mn> <a:mo>,</a:mo> <a:mn>3</a:mn> <a:mo>)</a:mo> </a:mrow> </a:msubsup> <a:mrow> <a:mo>(</a:mo> <a:mi mathvariant="bold">q</a:mi> <a:mo>)</a:mo> </a:mrow> </a:mrow> </a:math> . Specifically, our framework includes hitherto neglected mode-coupling effects that are important for the nonlinear density response even in the presence of a single harmonic perturbation. We compare these predictions for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msubsup> <c:mi>χ</c:mi> <c:mn>0</c:mn> <c:mrow> <c:mo>(</c:mo> <c:mn>1</c:mn> <c:mo>,</c:mo> <c:mn>3</c:mn> <c:mo>)</c:mo> </c:mrow> </c:msubsup> <c:mrow> <c:mo>(</c:mo> <c:mi mathvariant="bold">q</c:mi> <c:mo>)</c:mo> </c:mrow> </c:mrow> </c:math> to new Kohn-Sham DFT simulations, leading to excellent agreement between theory and numerical results. Exact analytical expressions are also obtained for the long-wavelength limits of the ideal quadratic and cubic response functions. Particular emphasis is placed on the connections between the third- and fourth-order functional derivatives of the noninteracting free-energy functional <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>F</e:mi> <e:mi>s</e:mi> </e:msub> <e:mrow> <e:mo>[</e:mo> <e:mi>n</e:mi> <e:mo>]</e:mo> </e:mrow> </e:mrow> </e:math> and the ideal quadratic and cubic response functions of the uniform electron gas, respectively. These relations provide exact constraints that may prove useful for the future construction of improved approximations to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>F</f:mi> <f:mi>s</f:mi> </f:msub> <f:mrow> <f:mo>[</f:mo> <f:mi>n</f:mi> <f:mo>]</f:mo> </f:mrow> </f:mrow> </f:math> , in particular, for warm dense matter applications at finite temperatures. Here, we use this framework to assess several commonly employed approximations to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>F</g:mi> <g:mi>s</g:mi> </g:msub> <g:mrow> <g:mo>[</g:mo> <g:mi>n</g:mi> <g:mo>]</g:mo> </g:mrow> </g:mrow> </g:math> through orbital-free DFT simulations of the harmonically perturbed ideal electron gas. The results are compared with Kohn-Sham DFT calculations across temperatures ranging from the ground state to the warm dense regime. Additionally, we analyze in detail the temperature- and wave number-dependent nonmonotonic behavior of the ideal quadratic and cubic response functions.