EPAWTFT/hugh_notes.txt

Bartlett and Silver, JCP (1975):
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[Supposedely the first MBPT?]
Report moderately large molecular calculations using Slater type orbitals.

Pople, Binkley, and Seeger, IJQCS (1976):
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This paper introduces MP2 as a possible route to incorporating electron correlation. Largely a 
pioneering paper that lays out the properties of MP2 etc.

Pople, Krishnan, Schlegel, and Binkley, IJQC (1978):
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Discusses different correlation techniques for quantum chemistry. This paper is particularly 
concerned with comparing the MP2 expression with the CC approach which was emerging at the
time. They show that CCD is equivalent to MP3 (?). 

Krishnan, Frisch, and Pople, JCP (1980):
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Assessed that triple excitations that appear at 4th order are important
in the quantitative treatment of chemical binding.

Laidig, Fitzgerald, and Bartett, CPL (1984):
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Investigate convergence of MBPT. They find BH is slowly convergent. HF is also slowly convergent,
accidentally so since the MBPT(4) is erroneously slow. New excitations are introduced at each even order.
Introduce Pade approximant to accelerate convergence, giving better accuracy.

Knowles, Somasundram, Handy, and Hirao, CPL (1985):
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Apply their FCI code to look at the convergence of MBPT(n).

Rate of convergence and size of terms is heavily system-dependent. Notice different convergence
behaviour for odd/even terms (oscillatory?). MP4 appears to capture the majority of the correlation
energy.

Handy, Knowles, and Somasundram, TCA (1985):
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Apply the FCI framework again to systematically investigate the convergence of the MP series. 
Attempt to identify whether the MP series is convergent or not, and compare RHF/UHF.

Observe increasingly slow RMP convergence for stretched water with erratic behaviour. For stretched
geometry with UMP, convergence appears smooth but is very slow. Suggest that this slow convergence 
probably emerges from spin contamination in the UHF solution.

[IS THERE MORE MBPT LITERATURE TO CONSIDER?]

Laidig, Saxe, and Bartlett, JCP (1986):
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Investigate binding curves for N2 and F2 using multireference CC and MBPT

Divergence in R-MBPT beyond 4 bohr. 
All finite-order U-MBPT calculations for F2 give an unphysical barrier around 2.8-2.9 bohr.
Divergence of R-MBPT observed in N2 beyond 3 bohr. Around minimum, the series is oscillatory and
very slowly convergent. In contrast, the U-MBPT is convergent and non-oscillatory, although 
low-order expansions give qualitatively wrong energetics (eg. unphysical barriers or second minima). 

Schlegel, JCP, (1986):
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Apply spin-projection to UHF and UMP to obtain improved potential enerrgy curves. Use a
post-perturbation projection to avoid mixing in higher energy states.

Perturbation corrections do not significantly reduce spin contamination. PUHF has a gradient
discontinuity at the CFP (but these are PAV). This kink is reduced by adding the perturbation
correlation. 

Gill and Radom, CP, (1986):
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Consider ``bottom-up'' approach, where look at successive contributions from HF, MP1, MP2, ...
Use a recursive approach to higher-order terms.

In \ce{He^2+}, the UHF becomes progressively more spin contaminated for large bond lengths.
RMP gives a progressively better estimate of the dissociative barrier height. In contrast, UMP
starts by increasing the barrier, before decrease after 3rd order. They conclude that poor convergence
can be attributed directly to a poor reference representation of the exact wave function.

While some properties (eg. bond length) might be well-converged, others can be far from convergence.
Worst barrier height estimate occurs at UMP4, after which there is very slow convergence.

They suspect that UMP problems can be attributed to spin-contamination. Conclude that incorrect
"qualitative" nature of RMP is not as bad as spin-contamination in UMP.

Gill, Wong, Nobes, and Radom, CPL (1988):
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Investigate performance of RMP expansions for homolytic bond breaking.

Discuss the fact that the RMP will ultimately be divergent for homolytic bond breaking at 
large extension, since the orbital energy based denominators will vanish. Propose a (2x2) matrix 
problem to estimate whether an RMP series will be convergent. They use this metric to determine if
an RMP series converges rapidly, slowly, or diverges.

Gill, Pople, Radom, and Nobes (1988):
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Investigate the effect of spin-contamination for slow UMP convergence. Spin-projection is 
difficult to do exactly, and approximate forms can lead to kinks in the potential energy surface.

Above critical point, UHF singles and doubles both mix with HF to give the exact wave function.
Contribution of singles decreases for complete dissociation.

Rate of UMP convergence slows down after critical point, with less that 3% of total correlation
captured at UMP4. Increasingly slow convergence not due to singles as the singles contribution to 
the UCI falls to zero as the rate of convergence becomes slower. It is therefore double 
contribution that is poorly captured by low-order UMP terms.

Lepetit, Pelissier, and Malrieu, JCP (1988):
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Investigate the poor convergence of unrestricted many-body perturbation theory.

UHF reference has large and spurious energy shift that dramatically slows the rate of convergence.
This comes from the localisation of the MOs in large separation and the doubly excited determinants
that result from spin exchanges in the sigma bond. This effect is seen in N2, and other systems. 
The EN partitioning avoids this, but the PT terms then become undetermined (zero on numerator and denominator).

Single excitations can interact with the doubly-excited determinants. This matrix elements goes through
a maximum at intermediate distances. This contribution enters at fourth-order.