We introduce DMRG­[FEAST], a new method for optimizing excited-state many-body wave functions with the density matrix renormalization group (DMRG) algorithm. Our approach applies the FEAST algorithm, originally designed for large-scale diagonalization problems, to matrix product state wave functions. We show that DMRG­[FEAST] enables the stable optimization of both low- and high-energy eigenstates, therefore overcoming the limitations of state-of-the-art excited-state DMRG algorithms. We demonstrate the reliability of DMRG­[FEAST] by calculating anharmonic vibrational excitation energies of molecules with up to 30 fully coupled degrees of freedom.

An exact and finite sum representation of the Hill-Wheeler projection operator is obtained under the provision that the state on which the operator acts can be expanded as Jmax I~)= ~, e~lJ,~). J = JminThe result provides a definite advantage over numerical integration methods, especially if high spin states are considered.

In this article, we review recent first principles, anharmonic studies on the molecular vibrations of gaseous formic acid in its monomer form.

Abstract. The fact that the algebra of the operators b +a, b 2 and 2b+b+l is closed is utilized for the derivation of closed formulas for Bogoljubov transformations by means of the previously developed technique for treating the angular momentum algebra.Recently, there appeared several papers [1, 2] in which closed formulas for the Bogoljubov transformations were derived. The closed formulas find application e.g. in considering the RPA and other transformations (in which two sets of boson creation and annihilation operators are connected through linear relations) if it is required to determine matrix elements of the new (old) operators in the old (new) basis. An example of such a situation is treated in Ref. 4. We shall return to this problem and rederive these relations from the point of view of the method presented in a previous note [3] (to be referred to as I). As we shall see our derivation is at least as direct as that given in Ref. 2 enabling us to present one of the closed formulas in a more compact form. Our treatment exhibits a great resemblance to the angular momentum discussion dealt with in the previous note The operators {., a= + 1, enable us a more general, and simplified, treatment of the operator algebra. First, obviously,and we have to evaluatewhere, in the latter version, the annihilation operator stands to the right of the creation operator. We, further, needwhich proves that the algebra of operators ~-2 ~o,~2o and 2~_1~1+1 is closed. Now, we try, in analogy to Eq. (I.23), to represent the operator B in the following manner B=exp{F1 ~2} exp{F2(2~_ 1 ~lq_ 1)} exp{F 3 ~2

Abstract. A polynomial expansion of L6wdins projection operator is found to be suitable for state by state angular momentum projection using the techniques of the Lanczos algorithm. It does not seem suitable for approximations in the calculation of the projected states. For this case a variational derivation of a possible scheme is presented. !. IntroductionVariational methods constitute one of the standard approaches for an approximative solution of the many body problem in nuclear, atomic and molecular physics. These methods generally employ a trial state, which is not an eigenstate of all the operators that commute with the original Hamiltonian. Thus in open shell HF calculations the trial state is not an eigenstate of the total angular momentum operator, and the BCS ansatz violates number conservation. In order to correct for this deficiency at least partially and in order to obtain from the solution of the variational methods information to be compared more directly with experiment, projection methods have been developed. In the case of angular momentum projection, which will serve as a representative case for the following discussion, the standard methods are associated with the names Hill The advantage of the numerical manipulations used in the direct application of the Lanczos algorithm can also be employed in other methods. We demonstrate this by a brief exposition of a polynomial expansion of L/Swdin's product operator (Section II). Although this expansion might be used with advantage (compared to the direct application of the Lanczos algorithm) in the calculation of projected states of considerable complexity, it is not very suitable for approximate projection. The results obtained in this section will offer the possibility to comment critically on the results obtained by Warke. An alternative method to carry out approximate angular momentum projection is formulated in Section IlI. The method is introduced via a suitable variational principle and requires the use of a truncated Lanczos scheme for practical exploitation.