Revision

Manuscript/stochastic_triples.bib

@@ -578,3 +578,33 @@ swh:1:dir:6d82ae7ac757c78d7720dd89dfa52d7a453d2f68;origin=https://github.com/Qua
 	publisher = {American Physical Society},
 	doi = {10.1103/RevModPhys.71.1267}
 }
+
+@article{purvis_1982,
+	author = {Purvis, George D. and Bartlett, Rodney J.},
+	title = {{A full coupled{-}cluster singles and doubles model: The inclusion of disconnected triples}},
+	journal = {J. Chem. Phys.},
+	volume = {76},
+	number = {4},
+	pages = {1910--1918},
+	year = {1982},
+	month = feb,
+	issn = {0021-9606},
+	publisher = {AIP Publishing},
+	doi = {10.1063/1.443164}
+}
+
+@article{scuseria_1988,
+	author = {Scuseria, Gustavo E. and Janssen, Curtis L. and Schaefer, Henry F.},
+	title = {{An efficient reformulation of the closed{-}shell coupled cluster single and double excitation (CCSD) equations}},
+	journal = {J. Chem. Phys.},
+	volume = {89},
+	number = {12},
+	pages = {7382--7387},
+	year = {1988},
+	month = dec,
+	issn = {0021-9606},
+	publisher = {AIP Publishing},
+	doi = {10.1063/1.455269}
+}
+
+

Manuscript/stochastic_triples.tex

@@ -129,7 +129,7 @@ The CC framework starts with a parameterized wave function, typically referred t
 \end{equation}
 where $\ket{\Phi}$ is the reference determinant, and $\hat{T}$ is the cluster operator representing single, double, triple, and higher excitations on top of the reference wave function.\cite{crawford_2000,bartlett_2007,shavitt_2009}
 
-Coupled Cluster with Singles and Doubles (CCSD) includes single and double particle-hole excitations and represents the most commonly used variant of CC theory. CCSD is exact for two-electron systems and includes all terms
+Coupled Cluster with Singles and Doubles\cite{purvis_1982,scuseria_1988} (CCSD) includes single and double particle-hole excitations and represents the most commonly used variant of CC theory. CCSD is exact for two-electron systems and includes all terms
 from third order perturbation theory and beyond.
 Coupled Cluster with Singles, Doubles, and perturbative Triples (CCSD(T)) incorporates a perturbative correction to the CCSD energy to account for some higher-order correlation effects, and has been termed in the literature as the gold standard of quantum chemistry.\cite{raghavachari_1989}
 CCSD(T) has demonstrated exceptional accuracy and reliability, making it one of the preferred choices for benchmark calculations and highly accurate predictions.
@@ -210,6 +210,7 @@ To reduce the fluctuations of the statistical estimator, we apply importance sam
 P^{abc} = \frac{1}{\mathcal{N}} \frac{1}{\max \left(\epsilon_{\min}, \epsilon_a + \epsilon_b + \epsilon_c \right)}
 \end{equation}
 where $\mathcal{N}$ normalizes the sum such that $\sum_{abc} P^{abc} = 1$, and $\epsilon_{\min}$ is an arbitrary minimal denominator to ensure that $P^{abc}$ does not diverge. In our calculations, we have set $\epsilon_{\min}$ to 0.2~a.u.
+\anthony{The algorithm is not very sensitive to the value of $\epsilon_{\min}$ as long as it is taken within reasonable bounds, in the range of the level-shift parameter in SCF calculations.}
 The perturbative contribution is then evaluated as an average over $M$ samples
 \begin{equation}
 E_{(T)} = \left\langle \frac{E^{abc}}{P^{abc}} \right \rangle_{P^{abc}} =