In his first contribution, Klein compared Einstein's quantum physics with his work on relativity,

Einstein's work on relativity has generated millions of words of comment and exposition on all levels of discourse. Comparatively little has been written about his probings, over a period of a quarter of a century, into the theory of radiation and its significance for our understanding of the physical world. And yet the boldness and clarity of Einstein's insight show forth as characteristically in these studies as in his more famous investigations into the nature of space and time.

Einstein’s first paper on quanta, p.60

Klein does not yet emphasize that Einstein's work on quantum physics is being ignored or dismissed by the leading physicists of the time, but he does point out how unusual Einstein's insight was into the dualism between continuous field theories and discrete particle theories.

This dualism between particle and field was probably noticed by others besides Einstein, but there is no record that anyone else suggested removing it in the drastic way that Einstein then proposed. (I am not even aware that anyone else was disturbed by the dualism at that time, and yet it was already a major theme in Einstein's own work.)

Einstein’s first paper on quanta, p.62

Klein turns next to Einstein's 1906 work on specific heats, which was accepted by several physicists as proving the importance of the quantum theory, though not for his "very revolutionary" ideas about the "light quantum." It is cited as solving the problem of anomalous specific heats.

Just as Einstein's "light quantum hypothesis" was mostly ignored until the mid-1920's, even as the 1905 paper is always cited for its explanation of the "photoelectric effect," Klein tells us that Einstein was using specific heat as an application of a much deeper insight into quantum theory. Einstein saw energy levels or "states," with transitions between them that he called "jumps," absorbing or emitting a quantum of energy hν, long before the 1913 Bohr atom.

Klein begins by quoting Einstein

we must now assume that, for ions which can vibrate at a definite frequency and which make possible the exchange of energy between radiation and matter, the manifold of possible states must be narrower than it is for the bodies in our direct experience. We must in fact assume that the mechanism of energy transfer is such that the energy can assume only the values 0, hv, 2hv, ....nhv

Einstein, specific heats, and the early quantum theory, p.175

Einstein saw that these possible "states" occupy a narrow energy range. Most of the energy levels in the classical continuum would not be accessible. Energy can not be absorbed unless the amount hν exactly matches the energy difference between the ground level and the excited level. This is a clear anticipation of the "stationary states" and quantum jumps of Niels Bohr atomic model six years later.

Einstein discovered that not all radiative transitions in matter are possible, that the possible transitions have a narrow band of energies because the available states or levels are narrow.

Some "degrees of freedom" in matter are said to be "frozen out" below some temperature. The vibrational oscillations of molecules and vibrations of ions in solid matter require a minimum of energy below which they cannot absorb heat. Once the temperature rises so that average energy E = kT (k is Boltzmann's constant) reaches the energy of the quantum state, energy can be absorbed into that degree of freedom.

Klein says Einstein's paper is inadequately described by those who refer to it as the quantum theory of solids. Einstein is concerned with apparent violations of the principle of the equipartition of energy, a foundation of classical physics.

It would be more to the point to say that the paper was written to show that there was, or would have to be, a quantum theory, and that the range of phenomena which could be clarified by such a theory included the properties of matter as well as those of radiation. Einstein was showing in a new way how deeply the foundations of classical physics had been undermined.

ibid., p.175

Klein quotes Marcel Brillouin as saying at the first Solvay Conference (in 1911)

"It seems certain that from now on we will have to introduce into our physical and chemical ideas a discontinuity, something that changes in jumps, of which we had no notion at all a few years ago"

ibid., p.178

Thus the "quantum jumps" caused by discontinuous radiative transitions between discrete energy levels in matter that we associate with the "Bohr Atom" were well known at least a year before Bohr encountered the Balmer series formula for spectral lines in hydrogen. Bohr is known to have studied the 1911 Solvay conference closely.

In his third article on Einstein in the 1960's, Klein showed that Einstein had explained wave-particle duality nearly two decades before Erwin Schrödinger's wave mechanics and Werner Heisenberg's matrix mechanics battled for the best explanation of quantum theory.

Klein lamented the great oversimplification of the history of quantum theory that came from focusing on the 1913 work of Niels Bohr.

The most common form that the oversimplification takes is an almost exclusive concentration on the problems of atomic structure and atomic spectra from Bohr’s work in 1913 to the new quantum mechanics of 1925-26...

The problems were not those of atomic structure but those of the dual nature of radiation and the properties of gases. The methods were not so much those of the “old quantum theory” as those of statistical mechanics. And the presiding genius and principal guide was not Bohr, but Einstein. It is the line of approach that led up to Schrodinger’s wave mechanics.

Einstein and the wave-particle duality, pp.3-4

When the new quantum physics was developed, Einstein greeted it sceptically even though he had done as much as anyone to bring it into being. He recognized its great successes, but he never accepted it as the new fundamental theory it claimed to be.

Einstein: A Centenary Volume, p.134

After a comprehensive summary of Einstein's work on quantum theory, Klein portrayed Einstein as out of step with almost everyone in the new field of quantum mechanics.

[He] never accepted the finality of the quantum mechanical renunciation of causality, or its claim to be the new fundamental theory. From the Solvay Conference of 1927, where the quantum mechanical synthesis had its first major discussion, to the end of his life, Einstein never stopped raising questions about this new approach to physics. At first he tried to propose conceptual experiments that would prove the logical inconsistency of quantum mechanics, but these attempts were all turned aside successfully by Bohr and his collaborators. In 1935 Einstein began to emphasize another basic limitation in quantum mechanics, as he saw it. He argued that its description of physical reality was essentially incomplete, that there were elements of physical reality that had no counterparts in the theory. Bohr’s response to this was to reject Einstein’s criterion of physical reality as ambiguous, and to claim that only through his own principle of complementarity could one arrive at an experimentally meaningful criterion of completeness.

Einstein recognized the power of quantum mechanics, calling it ‘the most successful physical theory of our time’, but he would not admit it as the basis for theoretical physics. He refused to give up the idea that there was such a thing as ‘the real state of a physical system, something that objectively exists independently of observation and measurement, and which can, in principle, be described in physical terms’. Einstein was convinced that when a theory giving a complete physical description was developed, the position of quantum mechanics in the framework of this future physics would be analogous to that of statistical mechanics in the framework of classical physics. It would be the theory to use when only incomplete information was available or when only an incomplete description was wanted.

Einstein’s colleagues could only regret that he had chosen to follow a path separate from the rest. As Born wrote: ‘Many of us regard this as a tragedy—for him, as he gropes his way in loneliness, and for us, who miss our leader and standard-bearer.’ To Einstein himself the choice was inevitable. He was prepared for the ‘accusation’ brought against him sometimes ‘in the friendliest of fashions’, but sometimes not: he was accused of ‘rigid adherence to classical theory’. But, he wrote, it was not so easy to declare guilt or innocence of this charge ‘because it is by no means immediately clear what is meant by “classical theory” ’. Newtonian mechanics was a classical theory, but it had not been an acceptable claimant as the fundamental theory underlying physics since the introduction of field theory. Field theories were never completed—neither Maxwell’s theory of electromagnetism nor his own theory of gravitation—since they were never extended to include the sources of the field in a non-singular way. Einstein did plead guilty to adherence to the programme of field theory; for it was his hope that a complete field theory would provide the basis for all of physics, giving that complete description he missed in the quantum mechanics he had helped so much to develop. He saw his whole career as striving to create a new unified foundation for physics. That was what he meant when he ended his scientific autobiography by writing that he had tried to show ‘how the efforts of a life hang together and why they have led to expectations of a definite form’.

Einstein: A Centenary Volume, pp.150-151

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Einstein and the wave-particle duality. The Natural Philosopher, 1964. Bobs-Merrill

Einstein, specific heats, and the early quantum theory. Science, 148(3667), 1965, 173-180.

The First Phase of the Bohr-Einstein Dialogue, in Historical Studies in the Physical Sciences, Vol. 2 (1970), pp. iv, 1-39

Einstein and the development of quantum physics, in Einstein: A Centenary Volume, Harvard University Press, 1979 The First Phase of the Bohr-Einstein Dialogue