Ladders to Heaven

Synonyms Convallaria Convallaria majalis Con-vall-lily Jacob s Ladder Ladder-to-Heaven Lilje-konvall Lily Constancy Lily convalle Male Lily May Lily Our Lady s Tears... 

The six figures shown here are selected from a 1914 Paris reissue of the Mm-tus Liber. The title page (Figure 84) shows a picture believed to depict Jacob and the Ladder to Heaven and is totally spiritual. His head rests on a rock some say represents the Philosopher s Stone. The translation is as follows ... 

Although there are exchange-correlation functionals that do not fall into this classification, they are mostly functionals correcting the above functionals for some sort of physical factor. Such physical factors for functionals are introduced in Chap. 6. In this chapter, let us focus on functionals conforming to a standard paradigm in which LDA and GGA functionals are expanded by additional terms. These standard functionals are often arranged hierarchically, as in Jacob s ladder ( the ladder to Heaven in the Old Testament, Book of Genesis, Fig. 5.2) (Perdew et al. 2006). 

Perdew has described a hierarchy of approximate treatments of the exchange-correlation term as Jacob s Ladder. The ladder is grounded in HF theory here on earth, and reaches to heaven, where the exact functional is found. Along the way are five rungs, each defining a set of assumptions made in creating an exchange-correlation expression. 

From earth to heaven a golden ladder rife ... 

The British also struck a special medal to commemorate Queen Elizabeth IPs coronation on 2 June 1953. It depicts the arrival of the throne at the British Isles. The English kept this Coronation Stone, Stone of Scone, or Stone of Destiny, in the base of the coronation chair in Westminster Abbey. The official Westminster Abbey guide labels the Coronation Stone as Jacob s pillar-stone. Jacob laid his head on this Stone when he had the famous dream of a ladder reaching to Heaven. " ... 

As we saw in Chapter 17, an initiate must pass through the luminous darkness that surrounds the Pole to achieve a reunion with his own dimension of light. Then he must look vertically upwards from the terrestrial toward the celestial pole. The stairway to heaven is a Jacob s ladder. It leads to the constellation of the Bear, Ursus Major. This same stairway to heaven existed in Dilmun for the Sumerians and Pharaohs of Egypt. 

These exchange and correlation parts are normally calculated separately by means of different approximations and then, combined into the exchange-correlation functional. Based on these approximations, John P. Perdew presented by analogy with the biblical referent of Jacob s ladder [20], his particular vision of which are the rungs to be climbed in the DFT for going from the Earth (i.e. the HF world) to Heaven (i.e. the chemical accuracy) (Fig. 2.2). 

Perdew and Schmidt (2001) compare the development of enhanced density functionals to a climb of Jacob s ladder, leading the way from the Hartree world to the heaven of chemical accuracy, illustrated in O Fig. 4-4. Each rung of the ladder adds a refinement to the approximation... 

Jacob s Ladder for Time-Dependent Density-Functional Theory Some Rungs on the Way to Photochemical Heaven... 

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